Of the mensuration of running waters an excellent piece written in Italian by Don Benedetto Castelli ... ; Englished from the third and best edition ; with the addition of a second book not before extant / by Thomas Salusbury.
         Della misura dell'acque correnti. English
         Castelli, Benedetto, 1577 or 8-1643.
      
       
         
           1661
        
      
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         60312
         
           
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         Transcribed from: (Early English Books Online ; image set 60312)
         Images scanned from microfilm: (Early English books, 1641-1700 ; 651:11)
      
       
         
           
             Of the mensuration of running waters an excellent piece written in Italian by Don Benedetto Castelli ... ; Englished from the third and best edition ; with the addition of a second book not before extant / by Thomas Salusbury.
             Della misura dell'acque correnti. English
             Castelli, Benedetto, 1577 or 8-1643.
             Salusbury, Thomas. Mathematical collections.
          
           [12], 118, [5] p. : ill.
           
             Printed by William Leybourn,
             London :
             1661.
          
           
             Errata: prelim. p. [12].
             "A table ..." [i.e. index]: p. [1]-[5] at end.
             Added t.p. on p. [35]: Geometrical demonstrations of the measure of running waters.
             Also appears in the 2d tome, 2d pt. of Salusbury's Mathematical collections, ... 1661.
             Reproduction of original in Huntington Library.
          
        
      
    
     
       
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         eng
      
       
         
           Mensuration -- Early works to 1800.
           Stream measurements -- Early works to 1800.
           Reclamation of land -- Early works to 1800.
        
      
    
     
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           OF
           THE
           MENSURATION
           OF
           RUNNING
           WATERS
           .
        
         
           An
           Excellent
           Piece
           
             Written
             in
             ITALIAN
          
           BY
           DON
           BENEDETTO
           CASTELLI
           ,
           Abbot
           of
           St.
           
             BENEDETTO
             ALOYSIO
          
           ,
           and
           Professour
           of
           the
           Mathematicks
           to
           Pope
           
             URBAN
             VIII
          
           .
           in
           ROME
           .
        
         
           Englished
           from
           the
           Third
           and
           best
           Edition
           ,
           with
           the
           addition
           of
           a
           Second
           Book
           not
           before
           extant
           :
        
         
           By
           
             THOMAS
             SALUSBURY
          
           .
        
         
           LONDON
           ,
           Printed
           by
           WILLIAM
           LEYBOURN
           ,
           1661.
           
        
      
       
         
         
         
           THE
           AUTHOURS
           EPISTLE
           TO
           Pope
           VRBAN
           VIII
           .
        
         
           I
           Lay
           at
           the
           Feet
           of
           your
           Holinesse
           these
           my
           Considerations
           concerning
           the
           MENSURATION
           OF
           RUNNING
           WATERS
           :
           Wherein
           if
           I
           shall
           have
           succeeded
           ,
           being
           a
           matter
           so
           difficult
           and
           unhandled
           by
           Writers
           both
           Ancient
           Modern
           ,
           the
           discovery
           of
           any
           thing
           of
           truth
           hath
           been
           the
           Effect
           of
           Your
           Holinesses
           Command
           ;
           and
           if
           through
           inability
           I
           have
           missed
           the
           Mark
           ,
           the
           same
           
           Command
           will
           serve
           me
           for
           an
           Excuse
           with
           Men
           of
           better
           Judgment
           ,
           and
           more
           especially
           with
           Your
           Holinesse
           ,
           to
           whom
           I
           humbly
           prostrate
           my self
           ,
           and
           kisse
           Your
           Sacred
           Feet
           .
        
         
           
             From
             ROME
             .
          
           
             Your
             Holinesses
             Most
             humble
             Servant
             BENEDETTO
             .
             A
             Monk
             of
             Cassino
             .
          
        
      
       
         
         
           AN
           ACCOUNT
           OF
           THE
           Authour
           and
           Work.
           
        
         
           
             DON
             BENEDETTO
             CASTELLI
          
           ,
           the
           famous
           Authour
           of
           these
           ensuing
           Discourses
           of
           the
           
             Mensuration
             of
             Running
             Waters
          
           ,
           is
           descended
           from
           the
           Worshipful
           FAMILY
           of
           the
           CASTELLII
           ,
           and
           took
           his
           first
           breath
           near
           to
           the
           lake
           THRASIMENVS
           ,
           (
           where
           Hanibal
           gave
           a
           fatal
           overthrow
           to
           the
           Roman
           Legions
           )
           in
           that
           sweet
           and
           fertile
           part
           of
           happy
           ITALY
           ,
           called
           the
           Territory
           of
           PERUGIA
           ,
           a
           branch
           of
           the
           Dukedome
           of
           TUSCANY
           ,
           which
           at
           present
           submitteth
           to
           the
           Jurisdiction
           of
           the
           Church
           ,
           as
           being
           a
           part
           of
           
             St.
             PETER'S
             Patrimony
          
           .
           His
           Parents
           ,
           who
           were
           more
           zealous
           of
           the
           good
           of
           his
           Soul
           than
           observant
           of
           the
           Propension
           of
           his
           Genius
           ,
           dedicated
           him
           (
           according
           to
           the
           Devotion
           of
           that
           Country
           )
           to
           the
           Service
           of
           the
           Church
           ;
           and
           entered
           him
           into
           the
           Flourishing
           Order
           of
           Black-Friers
           ,
           called
           from
           the
           place
           Moncks
           of
           
             Monte
             Casino
          
           ,
           and
           from
           the
           Founder
           Benedictines
           .
           Nature
           ,
           that
           She
           might
           consummate
           the
           Profusion
           of
           her
           Favours
           upon
           him
           ,
           sent
           him
           into
           the
           World
           in
           an
           Age
           that
           was
           so
           ennobled
           and
           illuminated
           with
           Eminent
           Scholars
           in
           all
           Kinds
           of
           Literature
           ,
           that
           hardly
           any
           Century
           since
           the
           Creation
           can
           boast
           the
           like
           .
        
         
         
           §
           .
           In
           particular
           ,
           the
           
             SCIENCES
             MATHEMATICAL
          
           had
           then
           got
           that
           Fame
           and
           Esteem
           in
           the
           Learned
           World
           ,
           that
           all
           men
           of
           Spirit
           or
           Quality
           became
           either
           Students
           in
           ,
           or
           Patrons
           of
           those
           Sublime
           Knowledges
           .
           On
           this
           occasion
           the
           Curiosity
           of
           our
           AUTHOUR
           being
           awakened
           ,
           his
           Active
           Wit
           could
           not
           endure
           to
           be
           any
           longer
           confined
           to
           the
           Slavish
           Tuition
           of
           Hermetical
           Pedagogues
           ;
           but
           in
           concurrence
           with
           the
           Genius
           of
           the
           Age
           ,
           he
           also
           betook
           himself
           to
           those
           most
           Generous
           and
           Liberal
           Studies
           .
           His
           helps
           in
           this
           his
           design
           were
           so
           many
           ,
           and
           so
           extraordinary
           ,
           that
           had
           his
           Inclination
           been
           weaker
           ,
           or
           his
           Apprehension
           lesser
           ,
           he
           could
           hardly
           have
           failed
           attaining
           more
           than
           a
           Common
           Eminency
           in
           these
           Sciences
           .
           For
           besides
           the
           Deluge
           of
           Learned
           and
           Vseful
           Books
           ,
           which
           the
           Presse
           at
           that
           time
           sent
           forth
           from
           all
           parts
           of
           EUROPE
           ,
           he
           had
           the
           good
           Fortune
           to
           fall
           into
           the
           Acquaintance
           ,
           and
           under
           the
           Instruction
           of
           the
           most
           Demonstrative
           and
           most
           Familiar
           Man
           in
           the
           World
           ,
           the
           Famous
           GALILEO
           :
           whose
           successe
           being
           no
           lesse
           upon
           this
           his
           Pupil
           than
           upon
           the
           rest
           of
           those
           Illustrious
           and
           Ingenious
           Persons
           that
           resorted
           from
           all
           parts
           to
           sit
           under
           his
           Admirable
           Lectures
           ,
           he
           in
           a
           short
           time
           attained
           to
           that
           Name
           in
           the
           Mathematicks
           ,
           that
           he
           was
           invited
           to
           ROME
           ,
           Complemented
           ,
           and
           Preferred
           by
           his
           then
           Holinesse
           the
           Eighth
           URBAN
           ,
           upon
           his
           very
           first
           Accession
           to
           the
           Papacy
           ,
           which
           was
           in
           the
           Year
           1623.
           
        
         
           §
           .
           This
           Pope
           being
           moved
           with
           a
           Paternal
           Providence
           for
           the
           Concerns
           of
           his
           Subjects
           in
           that
           part
           of
           ITALY
           about
           
             BOLOGNA
             ,
             FERRARA
          
           ,
           and
           COMMACHIO
           ,
           lying
           between
           the
           Rivers
           of
           PO
           and
           RENO
           ,
           which
           is
           part
           of
           
             Lo
             Stato
             della
             Chiesa
          
           ,
           or
           the
           Church
           Patrimony
           ,
           appoints
           this
           our
           CASTELLI
           in
           the
           Year
           1625
           ,
           to
           accompany
           the
           Right
           Honourable
           
             Monsignore
             CORSINI
          
           (
           a
           most
           observant
           and
           intelligent
           person
           in
           these
           affaires
           ,
           and
           at
           that
           time
           Superintendent
           of
           the
           General
           Draines
           ,
           and
           President
           of
           ROMAGNA
           )
           in
           the
           Grand
           Visitation
           which
           he
           was
           then
           ordered
           to
           make
           concerning
           the
           disorders
           occasioned
           by
           the
           Waters
           of
           those
           parts
           .
        
         
           §
           .
           CASTELLI
           ,
           having
           now
           an
           Opportunity
           to
           employ
           ,
           yea
           more
           ,
           to
           improve
           such
           Notions
           as
           he
           had
           imbued
           from
           the
           Lectures
           of
           his
           Excellent
           MASTER
           ,
           falls
           to
           his
           work
           with
           all
           industry
           :
           and
           in
           the
           time
           that
           his
           Occasions
           detained
           him
           in
           ROMAGNA
           he
           perfected
           the
           First
           Book
           of
           this
           his
           Discourse
           concerning
           the
           
             Mensuration
             of
             Running
             Waters
          
           .
           He
           confesseth
           that
           he
           had
           some
           years
           before
           applyed
           himself
           to
           this
           part
           of
           Practical
           Geometry
           ,
           and
           from
           several
           Observations
           collected
           part
           of
           that
           Doctrine
           which
           at
           this
           time
           he
           put
           into
           Method
           ,
           and
           which
           had
           procured
           him
           the
           Repute
           of
           so
           much
           Skill
           that
           he
           began
           
           to
           be
           Courted
           by
           sundry
           Princes
           ,
           and
           great
           Prelates
           .
           In
           particular
           about
           the
           beginning
           of
           the
           Year
           1623.
           and
           before
           his
           Invitation
           to
           ROME
           he
           was
           employed
           by
           Prince
           
             Ferdinando
             I
          
           ,
           Grand
           Duke
           of
           TUSCANY
           ,
           to
           remedy
           the
           Disorders
           which
           at
           that
           time
           happened
           in
           the
           Valley
           of
           PISA
           in
           the
           Meadows
           that
           lye
           upon
           the
           Banks
           of
           Serchio
           and
           
             Fiume
             Morto
          
           :
           and
           in
           the
           presence
           of
           the
           Grand
           Duke
           ,
           Grand
           Dutchesse
           Mother
           ,
           the
           Commissioners
           of
           Sewers
           ,
           and
           sundry
           other
           Persons
           in
           a
           few
           hours
           he
           made
           so
           great
           a
           progresse
           in
           that
           affair
           ,
           as
           gave
           his
           Most
           Serene
           Highnesse
           high
           satisfaction
           ,
           and
           gained
           himself
           much
           Honour
           .
        
         
           §
           .
           No
           sooner
           had
           he
           in
           his
           fore-mentioned
           Voiage
           to
           ROMAGNA
           (
           which
           was
           but
           few
           Moneths
           after
           ,
           in
           the
           same
           Year
           )
           committed
           his
           Conceptions
           to
           paper
           ,
           but
           he
           communicated
           them
           to
           certain
           of
           his
           Friends
           .
           In
           which
           number
           we
           finde
           
             Signore
             Ciampoli
          
           Secretary
           of
           the
           Popes
           Private
           Affaires
           ;
           whom
           in
           the
           beginning
           of
           the
           First
           Book
           he
           gratefully
           acknowledgeth
           to
           have
           been
           contributary
           ,
           in
           his
           Purse
           ,
           towards
           defraying
           the
           charge
           of
           Experiments
           ,
           and
           in
           his
           Person
           ,
           towards
           the
           debating
           and
           ●●●pleating
           of
           Arguments
           upon
           this
           Subject
           .
           Some
           few
           years
           after
           the
           importunity
           of
           Friends
           ,
           and
           the
           Zeal
           he
           had
           for
           the
           Publique
           Good
           prevailed
           with
           him
           to
           present
           the
           World
           with
           his
           First
           Discourse
           ,
           accompanied
           with
           a
           Treatise
           of
           the
           Geometrical
           Demonstrations
           of
           his
           whole
           Doctrine
           .
           What
           Reception
           it
           found
           with
           the
           Judicious
           must
           needs
           be
           imagined
           by
           any
           one
           that
           hath
           observed
           how
           Novelty
           and
           Facility
           in
           conjunction
           with
           Verity
           make
           a
           Charm
           of
           irresistable
           Operation
           .
        
         
           §
           .
           New
           it
           was
           ,
           for
           that
           no
           man
           before
           him
           had
           ever
           attempted
           to
           Demonstrate
           all
           the
           three
           Dimensions
           ,
           to
           wit
           ,
           the
           Length
           ,
           Breadth
           and
           Profundity
           ,
           of
           this
           Fluid
           and
           Current
           Element
           .
           And
           he
           detecteth
           such
           grosse
           Errours
           in
           those
           few
           that
           had
           untertook
           to
           write
           upon
           the
           Subject
           (
           of
           which
           he
           instanceth
           in
           Frontinus
           and
           Fontana
           ,
           as
           those
           that
           include
           the
           rest
           )
           and
           delivereth
           such
           singular
           and
           unheard-of
           Paradoxes
           (
           for
           so
           they
           sound
           in
           Vulgar
           Eares
           )
           as
           cannot
           but
           procure
           unspeakable
           delight
           to
           his
           Reader
           .
        
         
           §
           .
           Easie
           it
           is
           likewise
           and
           True
           ;
           and
           that
           upon
           so
           Familiar
           Experiments
           and
           Manifest
           Demonstrations
           ,
           that
           I
           have
           oft
           questioned
           with
           my self
           which
           merited
           the
           greater
           wonder
           ,
           he
           ,
           for
           discovering
           ,
           or
           all
           men
           that
           handled
           the
           Argument
           before
           him
           for
           not
           discovering
           a
           Doctrine
           of
           such
           strange
           Facility
           and
           Infallibility
           .
           But
           yet
           as
           if
           our
           Authour
           designed
           to
           oblige
           the
           whole
           World
           to
           him
           by
           so
           excellent
           a
           Present
           ,
           he
           selects
           a
           Subject
           that
           he
           knew
           would
           be
           carressed
           by
           all
           persons
           of
           Nobler
           Souls
           ,
           upon
           the
           accounts
           afore-named
           ,
           and
           by
           all
           Mankind
           in
           General
           ,
           as
           gratifying
           them
           in
           their
           much
           adored
           Idol
           Utility
           .
           And
           to
           render
           
           his
           Art
           the
           more
           profitable
           ,
           he
           reduceth
           the
           lofty
           ,
           and
           easie-to-be-mistaken
           Speculations
           of
           the
           Theory
           ,
           into
           certain
           and
           facile
           Directions
           for
           Practice
           ;
           teaching
           us
           how
           to
           prevent
           and
           repaire
           the
           Breaches
           of
           Seas
           ,
           and
           Inundations
           of
           Rivers
           ;
           to
           draine
           and
           recover
           Fenns
           and
           Marches
           ;
           to
           divert
           ,
           conveigh
           and
           distribute
           Waters
           for
           the
           Flowing
           and
           Stercoration
           of
           Grounds
           ,
           strengthening
           of
           Fortifications
           ,
           serving
           of
           Aquaducts
           ,
           preserving
           of
           Health
           (
           by
           cleansing
           Streets
           ,
           and
           scowring
           Sewers
           )
           and
           maintaining
           of
           Commerse
           (
           by
           defending
           Bridges
           ,
           cleering
           Rivers
           ,
           and
           opening
           Ports
           and
           Channels
           )
           with
           innumerable
           other
           Benefits
           of
           the
           like
           nature
           .
           And
           ,
           that
           I
           may
           omit
           no
           circumstance
           that
           may
           recommend
           my
           Authour
           ,
           the
           Fortune
           of
           this
           his
           Treatise
           hath
           been
           such
           ,
           that
           as
           if
           he
           intended
           a
           
             Plus
             ultra
          
           by
           it
           ,
           or
           as
           if
           all
           men
           despaired
           to
           out-do
           it
           ,
           or
           lastly
           ,
           as
           if
           CASTELLI
           hath
           been
           so
           great
           a
           Master
           that
           none
           have
           presumed
           to
           take
           Pencil
           in
           hand
           for
           the
           finishing
           of
           what
           he
           Pourfoild
           ,
           this
           small
           Tract
           like
           the
           Arabian
           Phoenix
           (
           of
           which
           it
           is
           said
           
             Unica
             semper
             Avis
          
           )
           did
           for
           several
           years
           together
           continue
           single
           in
           the
           World
           ,
           till
           that
           to
           verifie
           it
           to
           be
           truly
           Phoenician
           ,
           it
           renewed
           its
           Age
           by
           undergoing
           a
           second
           Impression
           .
           And
           as
           if
           this
           did
           not
           make
           out
           the
           Immortal
           vertue
           of
           it
           ,
           it
           hath
           had
           Anno
           1660
           a
           third
           Circulation
           ,
           and
           risen
           in
           this
           last
           Edition
           as
           it
           were
           from
           the
           Vrne
           of
           its
           Authour
           ;
           and
           that
           so
           improved
           by
           the
           Addition
           of
           a
           second
           part
           ,
           that
           it
           promiseth
           to
           perpetuate
           his
           Merits
           to
           all
           Posterity
           .
           To
           be
           brief
           ,
           the
           meer
           Fame
           of
           this
           Work
           resounded
           the
           Honourable
           Name
           of
           CASTELLI
           into
           all
           the
           Corners
           of
           Italy
           ,
           I
           may
           say
           of
           Europe
           ;
           insomuch
           ,
           that
           ,
           in
           hopes
           to
           reap
           great
           benefit
           by
           his
           Art
           ,
           the
           respective
           Grandees
           of
           the
           adjacent
           Countries
           courted
           his
           Judgment
           and
           Advice
           about
           their
           Draining
           of
           Fenns
           ,
           Diversion
           of
           Rivers
           ,
           Evacuation
           of
           Ports
           ,
           Preventing
           of
           Inundations
           ,
           &c.
           
           So
           that
           every
           Summer
           he
           made
           one
           or
           more
           of
           these
           Journies
           or
           Visitations
           .
           Particularly
           ,
           the
           Senate
           of
           Venice
           consulted
           him
           about
           their
           Lake
           ;
           to
           whom
           he
           delivered
           his
           Opinion
           in
           May
           1641.
           and
           upon
           farther
           thoughts
           he
           presented
           them
           with
           another
           Paper
           of
           Considerations
           the
           20
           December
           following
           .
           Prince
           LEOPOLDO
           of
           TUSCANY
           likewise
           requested
           his
           Advice
           in
           the
           beginning
           of
           the
           ensuing
           year
           1642
           ,
           which
           occasioned
           his
           Letter
           to
           Father
           
             Francesco
             di
             San
             Giuseppe
          
           ,
           bearing
           date
           February
           1
           ,
           To
           which
           
             Signore
             Bartolotti
          
           opposing
           ,
           he
           writes
           a
           second
           Letter
           ,
           directed
           to
           one
           of
           the
           Commissioners
           of
           Sewers
           ,
           vindicating
           his
           former
           ,
           and
           refuting
           Bartolotti
           ,
           both
           which
           I
           here
           give
           you
           .
        
         
           §
           .
           The
           Preferments
           which
           his
           Merits
           recommended
           him
           unto
           ,
           were
           first
           to
           be
           Abbot
           of
           Cassino
           ,
           from
           which
           he
           was
           removed
           
           Anno
           1640
           ,
           or
           thereabouts
           ,
           unto
           the
           Abbey
           of
           
             Santo
             Benedetto
             Aloysio
          
           ;
           and
           much
           about
           the
           same
           time
           preferred
           to
           the
           Dignity
           of
           Chief
           Mathematician
           to
           his
           grand
           Patron
           Pope
           
             URBAN
             VIII
          
           .
           and
           Publique
           Professour
           of
           Mathematicks
           in
           the
           Vniversity
           of
           ROME
           .
        
         
           §
           .
           Here
           a
           Stop
           was
           put
           to
           the
           Carier
           of
           his
           Fortunes
           ,
           and
           being
           fuller
           of
           Honour
           than
           of
           Years
           ,
           was
           by
           Death
           ,
           the
           Importunate
           Intrerupter
           of
           Generous
           Designs
           ,
           prevented
           in
           doing
           that
           farther
           Good
           which
           the
           World
           had
           good
           reason
           to
           promise
           it self
           from
           so
           Profound
           and
           Industrious
           a
           Personage
           ,
           leaving
           many
           Friends
           and
           Disciples
           of
           all
           Degrees
           and
           Qualities
           to
           lament
           his
           losse
           ,
           and
           honour
           his
           Memory
           .
        
         
           §
           .
           His
           singular
           Virtues
           and
           Abilities
           had
           gained
           him
           the
           Friendship
           of
           very
           many
           ;
           as
           to
           instance
           in
           some
           ,
           he
           had
           contracted
           strict
           Amity
           with
           
             Monsignore
             Maffei
             Barberino
          
           a
           Florentine
           ,
           Praefect
           of
           the
           Publique
           Wayes
           ,
           and
           afterwards
           Pope
           with
           the
           Name
           of
           
             URBAN
             VIII
          
           .
           as
           was
           said
           before
           ;
           with
           the
           above-named
           
             Monsignore
             Corsini
          
           Superintendant
           of
           the
           General
           Draines
           :
           with
           
             Monsignore
             Piccolomini
          
           Arch-Bishop
           of
           Siena
           :
           with
           Cardinal
           Serra
           :
           with
           Cardinal
           Caponi
           ,
           who
           hath
           studied
           much
           and
           writ
           well
           upon
           this
           Subject
           ;
           and
           with
           Cardinal
           Gaetano
           who
           frequently
           consulted
           with
           him
           in
           his
           design
           of
           Draining
           the
           Fenns
           of
           ROMAGNA
           .
           Moreover
           Prince
           LEOPOLDO
           ,
           and
           his
           Brother
           the
           Grand
           Duke
           had
           very
           great
           kindnesse
           for
           him
           ;
           which
           speaks
           no
           small
           attractions
           in
           him
           ,
           considering
           him
           as
           a
           favourite
           of
           the
           Family
           of
           Barberini
           ,
           between
           whom
           and
           the
           House
           of
           Medeci
           there
           is
           an
           inveterate
           Fewd
           .
           Amongst
           persons
           of
           a
           lower
           Quality
           he
           acknowledgeth
           
             Signore
             Ciampoli
          
           the
           Popes
           Secretary
           ,
           
             Sig.
             Ferrante
             Cesarini
             ,
             Sig.
             Giovanni
             Basadonna
          
           Senator
           of
           Venice
           ;
           and
           I
           find
           mentioned
           
             Sig.
             Lana
             ,
             Sig.
             Albano
             ,
             Padre
             Serafino
             ,
             Pad
             .
             Francesco
             de
             San.
             Giuseppe
             ,
          
           and
           many
           others
           .
        
         
           §
           .
           The
           Works
           in
           which
           he
           will
           survive
           to
           all
           succeeding
           Ages
           are
           first
           His
           solid
           and
           sober
           Confutation
           of
           the
           Arguments
           of
           
             Signore
             Lodovico
             dell
             Columbo
          
           ,
           and
           
             Signore
             Vincentio
             di
             Gratia
          
           against
           the
           Tract
           of
           
             Galileo
             Delle
             cose
             che
             stanno
             sopra
             Aqua
             ,
          
           wherein
           he
           vindicates
           bis
           said
           Master
           with
           a
           Gratitude
           that
           Tutors
           very
           rarely
           reap
           from
           the
           pains
           they
           take
           in
           Cultivating
           their
           Pupils
           .
           This
           Apology
           was
           first
           Printed
           Anno
           1615.
           and
           was
           a
           second
           time
           published
           ,
           as
           also
           those
           of
           his
           Antagonists
           ,
           amongst
           the
           Works
           of
           GALILEO
           ,
           set
           forth
           by
           the
           Learned
           Viviani
           1656.
           
           He
           hath
           likewise
           writ
           several
           other
           curious
           Pieces
           ,
           as
           I
           am
           informed
           by
           the
           most
           Courteous
           
             Carolo
             Manolessi
          
           of
           Bologna
           ;
           amongst
           others
           an
           excellent
           Treatise
           concerning
           Colours
           ,
           which
           he
           putteth
           me
           in
           hopes
           to
           see
           printed
           
           very
           speedily
           .
           And
           last
           of
           all
           these
           Discourses
           and
           Reflections
           upon
           the
           
             Mensuration
             of
             Running
             Waters
          
           ,
           with
           the
           addition
           of
           a
           Second
           Book
           ,
           three
           Epistles
           ,
           and
           four
           Considerations
           upon
           the
           same
           Argument
           ,
           which
           conduce
           much
           to
           Illustrate
           his
           Doctrine
           and
           Facilitate
           the
           Practice
           of
           it
           ;
           and
           which
           with
           a
           Relation
           of
           
             Monsignore
             Corsini
          
           ,
           make
           the
           second
           part
           of
           my
           First
           Tome
           .
        
         
           §
           .
           
             I
             might
             here
             sally
             forth
             into
             the
             Citation
             of
             sundry
             Authours
             of
             Good
             Account
             ,
             that
             have
             transmitted
             his
             Character
             to
             Posterity
             ,
             but
             shall
             confine
             my self
             to
             onely
             two
             ;
             the
             one
             is
             of
             his
          
           Master
           ,
           
             the
             other
             of
             his
          
           Scholar
           ;
           
             than
             whom
             there
             cannot
             be
             two
             more
             competent
             Judges
             of
             his
             Accomplishments
             .
             To
             begin
             with
             his
          
           Master
           ,
           the
           Quick-sighted
           ,
           and
           truly
           Lyncean
           GALILEO
           ,
           
             who
             speaking
             of
             his
             Abilities
             in
             Astronomy
             saith
          
           a
           Che
           la
           felicità
           del
           suo
           ingegno
           non
           la
           fà
           bisognosa
           dell
           '
           opera
           suo
           .
           
             And
             again
             ,
             submitting
             a
             certain
             Demonstration
             ,
             which
             he
             intended
             to
             divulge
             ,
             to
             the
             Judgment
             of
             this
             our
             Abbot
             ,
             he
             writes
             to
             him
             in
             this
             manner
             :
          
           b
           Questo
           lo
           comunico
           a
           V.
           S.
           per
           lettera
           prima
           che
           ad
           alcun
           altro
           ,
           con
           attenderne
           principalmente
           il
           parer
           suo
           ,
           e
           doppo
           quello
           de'
           
           nostri
           Amici
           discosti
           ,
           conpensiero
           d'
           inviarne
           poi
           altre
           Copie
           ad
           altri
           Amici
           d'
           Italia
           ,
           e
           di
           Francia
           ,
           quando
           io
           ne
           venga
           da
           lei
           configliato
           :
           e
           qui
           pregandola
           a
           farci
           parte
           d'
           alcuna
           delle
           sue
           peregrine
           speculationi
           ;
           con
           sincerissimo
           affetto
           ,
           &c.
           
           
             And
             the
             most
             acute
             Mathematician
          
           Signore
           Evangelista
           Terricelli
           ,
           
             late
             Professour
             to
             the
             Grand
             Duke
             in
             immediate
             Succession
             after
          
           GALILEO
           ,
           
             maketh
             this
             Honourable
             and
             Grateful
             Mention
             of
             him
             ,
             and
             his
             Book
             :
          
           c
           Omitto
           magnum
           illum
           nutantis
           Maris
           motum
           ;
           Praetereo
           etiam
           omnem
           Fluminum
           ,
           Aquarumque
           Currentium
           tum
           mensurum
           ,
           tum
           usum
           ,
           quarum
           omnis
           doctrina
           reperta
           primum
           fuit
           ab
           Abbate
           BENEDICTO
           CASTELLIO
           Preceptore
           meo
           .
           Scripsit
           ille
           Scientiam
           suam
           ,
           &
           illam
           non
           solum
           demonstratione
           ,
           verum
           etiam
           opere
           confirmavit
           ,
           maxima
           cum
           Principum
           &
           populorum
           utilitate
           ,
           majore
           cum
           admiratione
           Phylosophorum
           .
           Extat
           illius
           Liber
           ,
           vere
           aureus
           .
        
         
           §
           .
           I
           have
           onely
           two
           particulars
           more
           to
           offer
           the
           English
           Reader
           :
           The
           one
           concerns
           the
           Book
           ,
           and
           it
           is
           this
           ,
           That
           after
           the
           general
           Aprobation
           it
           hath
           had
           in
           Italy
           ,
           I
           cannot
           but
           think
           it
           deserveth
           the
           same
           Civil
           Entertainment
           with
           us
           ,
           in
           regard
           that
           it
           cometh
           with
           no
           lesse
           
             Novelty
             ,
             Facility
             ,
             Verity
             ,
             and
             Utility
          
           to
           us
           than
           to
           those
           whom
           the
           Authour
           favoured
           with
           the
           Original
           .
           Our
           Rivers
           and
           Sewers
           through
           Publique
           Distractions
           and
           Private
           Incroachments
           are
           in
           great
           disorder
           ,
           as
           those
           Channels
           for
           instance
           which
           formerly
           were
           Navigable
           unto
           the
           very
           Walls
           of
           
           York
           and
           Salisbury
           ,
           &c
           :
           Our
           Ports
           are
           choaked
           and
           obstructed
           by
           Shelfes
           and
           Setlements
           :
           Our
           Fenns
           do
           in
           a
           great
           part
           lie
           waste
           and
           unimproved
           :
           Now
           all
           these
           may
           be
           (
           and
           ,
           as
           I
           find
           by
           the
           Confession
           of
           some
           whose
           Practises
           upon
           the
           Copy
           of
           the
           First
           Book
           onely
           of
           our
           Authour
           hath
           got
           them
           both
           Money
           and
           Reputation
           ,
           in
           part
           have
           been
           )
           remedied
           by
           the
           Ways
           and
           Means
           he
           here
           sets
           down
           .
           The
           truth
           is
           the
           Argument
           hath
           been
           past
           over
           with
           an
           Vniversal
           Silence
           ;
           so
           that
           to
           this
           day
           I
           have
           not
           seen
           any
           thing
           that
           hath
           been
           written
           Demonstratively
           and
           with
           Mathematical
           Certainty
           concerning
           the
           same
           ,
           save
           onely
           what
           this
           Learned
           Prelate
           hath
           delivered
           of
           his
           Own
           Invention
           in
           these
           Treatises
           :
           who
           yet
           hath
           so
           fully
           and
           plainly
           handled
           the
           Whole
           Doctrine
           ,
           that
           I
           may
           affirm
           his
           Work
           to
           be
           every
           way
           absolute
           .
           It
           must
           be
           confest
           the
           Demonstration
           of
           the
           Second
           Proposition
           of
           the
           Second
           Book
           did
           not
           well
           please
           the
           Authour
           ,
           and
           had
           he
           lived
           he
           would
           have
           supplyed
           that
           defect
           ,
           but
           being
           prevented
           by
           Death
           ,
           the
           Reader
           must
           content
           himself
           with
           the
           Mechanical
           Proof
           that
           he
           giveth
           you
           of
           the
           truth
           of
           so
           Excellent
           a
           Conclusion
           .
        
         
           §
           .
           The
           other
           particular
           that
           I
           am
           to
           offer
           is
           ,
           that
           out
           of
           my
           desire
           to
           contribute
           what
           lyeth
           in
           me
           to
           the
           compleating
           of
           this
           Piece
           for
           English
           Practice
           ,
           I
           have
           exeeded
           my
           promise
           not
           onely
           in
           giving
           you
           the
           Second
           and
           following
           Books
           which
           were
           not
           extant
           at
           the
           time
           of
           tendering
           my
           Overtures
           ,
           but
           also
           in
           that
           I
           have
           added
           a
           Map
           or
           Plat
           of
           all
           the
           Rivers
           ,
           Lakes
           ,
           Fenns
           ,
           &c.
           mentioned
           thorowout
           the
           Work.
           And
           if
           I
           have
           not
           kept
           touch
           in
           point
           of
           Time
           ,
           let
           it
           be
           considered
           that
           I
           am
           the
           Translator
           and
           not
           the
           Printer
           .
           To
           conclude
           ,
           according
           to
           your
           acceptance
           of
           these
           my
           endeavours
           ,
           you
           may
           expect
           some
           other
           Tracts
           of
           no
           lesse
           Profit
           and
           Delight
           .
           Farewell
           .
        
         
           
             T.
             S.
             
          
        
      
       
         
         
           ERRATA
           of
           the
           second
           PART
           of
           the
           first
           TOME
           .
        
         
           In
           PREFACE
           ,
           read
           
             Ferdinando
             II.
          
           ibid.
           l'Aqua
           .
        
         
           Page
           2.
           
           LINE
           26
           ,
           for
           must
           read
           much
           .
           P.
           3.
           l.
           22
           ,
           r.
           and
           let
           .
           l.
           25.
           r.
           water
           ,
           〈…〉
           .
           41.
           r.
           Tappe
           ,
           (
           
             as
             every
             where
             else
          
           )
           .
           Page
           4.
           l.
           18.
           r.
           cords
           .
           Page
           6.
           l.
           9.
           r.
           acquire
           ,
           or
           ▪
           Page
           9.
           l.
           1.
           r.
           irreperable
           .
           P.
           10.
           l.
           13.
           r.
           dissimboguement
           .
           For
           Page
           17.
           r.
           P.
           15.
           
           P.
           15.
           l.
           27
           ,
           r.
           in
           .
           l.
           36
           ,
           r.
           is
           as
           .
           l.
           38
           ,
           r.
           〈◊〉
           .
           P.
           17.
           l.
           12
           ,
           Giuli●
           .
           l.
           ●7
           .
           r.
           Measurers
           .
           l.
           25
           ,
           r.
           measured
           it
           ,
           r.
           necessarily
           .
           P.
           23.
           l.
           19.
           r.
           for
           help
           .
           for
           Page
           31.
           r.
           P.
           32.
           
           P.
           24
           ▪
           l.
           14
           ,
           r.
           to
           .
           l.
           17
           ,
           r.
           namly
           ,
           of
           the.
           l.
           23
           ,
           r.
           easie
           .
           P.
           25.
           l.
           38.
           r.
           Cock.
           p.
           29.
           l.
           7.
           r.
           lasted
           ,
           p.
           31.
           l.
           32.
           r.
           Soe
           .
           p.
           41.
           l.
           20.
           r.
           to
           the
           line
           .
           p.
           48.
           l.
           19.
           r.
           us
           the
           *
           .
           id
           .
           
             Figure
             false
          
           p.
           52.
           l.
           30
           ,
           and
           31.
           for
           Theorem
           r.
           Proposition
           .
           p.
           53.
           l.
           29.
           r.
           again
           .
           p.
           57.
           l.
           19
           ,
           r.
           same
           if
           ▪
           l.
           44.
           r.
           bodily
           .
           p.
           58.
           l.
           9.
           r.
           gathering
           .
           l.
           40.
           
             omit
             ;
          
           .
           p.
           60.
           l.
           2.
           omit
           ,
           if
           .
           p.
           65.
           l.
           1.
           r.
           tid●
           
             dele
             ;
          
           .
           p.
           66.
           l.
           35.
           r.
           Stoppage
           of
           .
           p.
           68.
           l.
           12
           ,
           for
           Lords
           the
           r.
           Lords
           .
           l.
           
             ult
             .
             for
          
           they
           r.
           it
           .
           p.
           69.
           l.
           14.
           r.
           to
           one
           .
           id
           .
           carried
           dele
           to
           .
           p.
           71.
           l.
           20
           ,
           r.
           and
           that
           .
           l.
           25
           ,
           r.
           Braces
           ;
           it
           .
           l.
           29.
           r.
           Braces
           .
           l.
           44
           ,
           r.
           the
           Brent
           .
           p.
           72.
           l.
           23.
           
             r.
             Serene
             Highnesse
          
           .
           p.
           73.
           l.
           24
           ,
           r.
           deliberation
           :
           l.
           26
           ,
           for
           summe
           r.
           Moddel
           .
           l.
           40.
           r.
           Months
           .
           p.
           79.
           l.
           18.
           r.
           that
           into
           .
           p.
           82.
           l.
           22.
           
             dele
             ;
          
           .
           p
           ▪
           85.
           l.
           9
           ,
           10.
           dele
           a
           free
           drame
           .
           p.
           88.
           l.
           5.
           r.
           Palmes
           .
           p.
           89.
           l.
           8.
           r.
           Princes
           .
           p.
           92.
           l.
           3.
           r.
           Discourses
           .
           p.
           93.
           l.
           31.
           r.
           Tautologie
           .
           p.
           94.
           l.
           9.
           r.
           miracle
           ;
           .
           p.
           97.
           l.
           13.
           r.
           weighty
           .
           p.
           101.
           l.
           21.
           r.
           Marrara
           .
           p.
           107.
           l.
           28
           ,
           r.
           Patrimony
           .
           l.
           40.
           r.
           above
           .
           p.
           111.
           l.
           16.
           r.
           said
           .
           For
           p.
           432.
           r.
           p.
           114.
           p.
           114.
           l.
           35.
           r.
           of
           200.
           l.
           41.
           r.
           closed
           .
           p.
           115.
           l.
           29.
           r.
           constant
           ;
           .
        
      
    
     
       
         
           
             
             
               OF
               THE
               MENSURATION
               OF
               Running
               Waters
               .
            
             
               LIB
               .
               I.
               
            
             
               WHat
               ,
               and
               of
               how
               great
               moment
               the
               consideration
               of
               Motion
               is
               in
               natural
               things
               ,
               is
               so
               manifest
               ,
               that
               the
               Prince
               of
               Peripateticks
               pronounced
               that
               in
               his
               Schools
               now
               much
               used
               Sentence
               :
               
                 Ignorato
                 motu
                 ,
                 ignoratur
                 natura
              
               .
               Thence
               it
               is
               that
               true
               Philosophers
               have
               so
               travailed
               in
               the
               contemplation
               of
               the
               Celestial
               motions
               ,
               and
               in
               the
               speculation
               of
               the
               motions
               of
               Animals
               ,
               that
               they
               have
               arrived
               to
               a
               wonderful
               height
               and
               sublimity
               of
               understanding
               .
               Under
               the
               same
               Science
               of
               Motion
               is
               comprehended
               all
               that
               which
               is
               written
               by
               Mechanitians
               concerning
               Engines
               moving
               of
               themselves
               ,
               Machins
               moving
               by
               the
               force
               of
               Air
               ,
               and
               those
               which
               serve
               to
               move
               weights
               and
               immense
               magnitudes
               with
               small
               force
               .
               There
               appertaineth
               to
               the
               Science
               of
               Motion
               all
               that
               which
               hath
               been
               written
               of
               the
               alteration
               not
               onely
               of
               Bodies
               ,
               but
               of
               our
               Minds
               also
               ;
               and
               in
               sum
               ,
               this
               ample
               matter
               of
               Motion
               is
               so
               extended
               and
               dilated
               ,
               that
               there
               are
               few
               things
               which
               fall
               under
               mans
               notice
               ,
               which
               are
               not
               conjoyned
               with
               Motion
               ,
               or
               at
               least
               depending
               thereupon
               ,
               or
               to
               the
               knowledge
               thereof
               directed
               ;
               and
               of
               almost
               every
               of
               them
               ,
               there
               hath
               been
               written
               and
               composed
               by
               sublime
               wits
               ,
               learned
               Treatises
               and
               Instructions
               .
               
               And
               because
               that
               in
               the
               years
               past
               I
               had
               occasion
               by
               Order
               of
               our
               Lord
               Pope
               Vrban
               8.
               to
               apply
               my
               thoughts
               to
               the
               motion
               of
               the
               Waters
               of
               Rivers
               ,
               (
               a
               matter
               difficult
               ,
               most
               important
               ,
               and
               little
               handled
               by
               others
               )
               having
               concerning
               the
               same
               observed
               some
               particulars
               not
               well
               observed
               ,
               or
               considered
               till
               now
               ,
               but
               of
               great
               moment
               both
               in
               publick
               and
               private
               affairs
               ;
               I
               have
               thought
               good
               to
               publish
               them
               ,
               to
               the
               end
               that
               ingenious
               spirits
               might
               have
               occasion
               to
               discusse
               more
               exactly
               then
               hitherto
               hath
               been
               done
               ,
               so
               necessary
               and
               profitable
               a
               matter
               ,
               and
               to
               supply
               also
               my
               defects
               in
               this
               short
               and
               difficult
               Tractate
               .
               Difficult
               I
               say
               ,
               for
               the
               truth
               is
               ,
               these
               knowledges
               ,
               though
               of
               things
               next
               our
               senses
               ,
               are
               sometimes
               more
               abstruce
               and
               hidden
               ,
               then
               the
               knowledge
               of
               things
               more
               remote
               ;
               and
               much
               better
               ,
               and
               with
               greater
               exquisitness
               are
               known
               the
               motions
               of
               the
               Planets
               ,
               and
               Periods
               of
               the
               Stars
               ,
               than
               those
               of
               Rivers
               and
               Seas
               :
               As
               that
               singular
               light
               of
               Philosophie
               of
               our
               times
               ,
               and
               my
               Master
               
                 Signore
                 Galileo
                 Galilei
              
               wisely
               observeth
               in
               his
               Book
               concerning
               the
               Solar
               spots
               .
               And
               to
               proceed
               with
               a
               due
               order
               in
               Sciences
               ,
               I
               will
               take
               some
               suppositions
               and
               cognitions
               sufficiently
               clear
               ;
               from
               which
               I
               will
               afterwards
               proceed
               to
               the
               deducing
               of
               the
               principal
               conclusions
               .
               But
               to
               the
               end
               that
               what
               I
               have
               written
               at
               the
               end
               of
               this
               discourse
               in
               a
               demonstrative
               and
               Geometrical
               method
               ,
               may
               also
               be
               understood
               of
               those
               which
               never
               have
               applyed
               their
               thoughts
               to
               the
               study
               of
               Geometry
               ;
               I
               have
               endeavoured
               to
               explain
               my
               conceit
               by
               an
               example
               ,
               and
               with
               the
               consideration
               of
               the
               natural
               things
               themselves
               ,
               must
               after
               the
               same
               order
               in
               which
               I
               began
               to
               doubt
               in
               this
               matter
               ;
               and
               have
               placed
               this
               particular
               Treatise
               here
               in
               the
               beginning
               ,
               adverting
               nevertheless
               ,
               that
               he
               who
               desires
               more
               full
               and
               absolute
               solidity
               of
               Reasons
               ,
               may
               overpass
               this
               prefatory
               discourse
               ,
               and
               onely
               consider
               what
               is
               treated
               of
               in
               the
               demonstrations
               placed
               towards
               the
               end
               ,
               and
               return
               afterwards
               to
               the
               consideration
               of
               the
               things
               collected
               in
               the
               Corollaries
               and
               Appendices
               ;
               which
               demonstrations
               notwithstanding
               ,
               may
               be
               pretermitted
               by
               him
               that
               hath
               not
               seen
               at
               least
               the
               first
               six
               Books
               of
               the
               Elements
               of
               Euclid
               ;
               so
               that
               he
               diligently
               observeth
               that
               which
               followeth
               .
            
             
               I
               say
               therefore
               ,
               that
               having
               in
               times
               past
               ,
               on
               divers
               occasions
               heard
               speak
               of
               the
               measures
               of
               the
               waters
               of
               Rivers
               ,
               and
               Fountains
               ,
               saying
               ,
               such
               a
               River
               is
               two
               or
               three
               thousand
               feet
               of
               water
               ;
               such
               a
               spring-water
               is
               twenty
               ,
               thirty
               ,
               or
               forty
               inches
               ,
               &c.
               
               Although
               in
               such
               manner
               I
               have
               found
               all
               to
               treat
               thereof
               in
               word
               and
               writing
               ,
               without
               variety
               ,
               and
               as
               we
               are
               wont
               to
               say
               ,
               
                 constanti
                 sermone
              
               ,
               yea
               even
               Artists
               and
               Ingeneers
               ,
               as
               if
               it
               were
               a
               thing
               that
               admitted
               not
               of
               any
               doubt
               ,
               yet
               howsoever
               I
               remained
               still
               infolded
               in
               such
               an
               obscurity
               ,
               that
               I
               well
               knew
               I
               understood
               
               nothing
               at
               all
               ,
               of
               that
               which
               others
               pretended
               full
               and
               clearly
               to
               understand
               .
               And
               my
               doubt
               arose
               from
               my
               frequent
               observation
               of
               many
               Trenches
               and
               Channels
               ,
               which
               carry
               water
               to
               turn
               Mills
               ,
               in
               which
               Trenches
               ,
               and
               Channels
               ,
               the
               water
               being
               measured
               ,
               was
               found
               pretty
               deep
               ;
               but
               if
               afterwards
               the
               same
               water
               was
               measured
               in
               the
               fall
               it
               made
               to
               turn
               the
               Wheel
               of
               the
               Mill
               ,
               it
               was
               much
               lesse
               ,
               not
               amounting
               often
               to
               the
               tenth
               part
               ,
               nor
               sometimes
               to
               the
               twentieth
               ,
               insomuch
               ,
               that
               the
               same
               running
               water
               came
               to
               be
               one
               while
               more
               ,
               another
               while
               less
               in
               measure
               ,
               in
               divers
               parts
               of
               its
               Channel
               ;
               and
               for
               that
               reason
               this
               vulgar
               manner
               of
               measuring
               running
               Waters
               ,
               as
               indeterminate
               and
               uncertain
               ,
               was
               by
               me
               justly
               suspected
               ,
               the
               measure
               being
               to
               be
               determinate
               ,
               and
               the
               same
               .
               And
               here
               I
               freely
               confesse
               that
               I
               had
               singular
               help
               to
               resolve
               this
               difficulty
               from
               the
               excellent
               &
               accurate
               way
               of
               discoursing
               ,
               as
               in
               allother
               matters
               ,
               so
               also
               in
               this
               ,
               of
               the
               Right
               Honourable
               and
               Truly
               Noble
               Signior
               Ciampoli
               ,
               Secretary
               of
               the
               Popes
               secret
               affairs
               .
               Who
               moreover
               ,
               not
               sparing
               for
               the
               costs
               of
               the
               same
               ,
               generously
               gave
               me
               occasion
               a
               few
               years
               past
               to
               try
               by
               exact
               experiments
               that
               which
               past
               concerning
               this
               particular
               .
               And
               to
               explain
               all
               more
               clearly
               with
               an
               example
               ;
               we
               suppose
               a
               Vessel
               filled
               with
               Water
               ,
               as
               for
               instance
               a
               Butt
               ,
               which
               is
               kept
               full
               ,
               though
               still
               water
               runneth
               out
               ,
               and
               the
               Water
               run
               out
               by
               two
               Taps
               equal
               of
               bignesse
               ,
               one
               put
               in
               the
               bottom
               of
               the
               Vessel
               ,
               and
               the
               other
               in
               the
               upper
               part
               ;
               it
               is
               manifest
               that
               in
               the
               time
               wherein
               from
               the
               upper
               part
               shall
               issue
               a
               determinate
               measure
               of
               water
               from
               the
               inferiour
               part
               there
               shall
               issue
               four
               ,
               five
               ,
               and
               many
               more
               of
               the
               same
               measures
               ,
               according
               to
               the
               difference
               of
               the
               height
               of
               the
               Taps
               ,
               and
               the
               distance
               of
               the
               upper
               Tap
               from
               the
               Superficies
               and
               level
               of
               the
               water
               of
               the
               Vessel
               :
               and
               all
               this
               will
               alwayes
               follow
               ,
               though
               ,
               as
               hath
               been
               said
               ,
               the
               Taps
               be
               equal
               ,
               and
               the
               water
               in
               discharging
               keep
               the
               said
               Taps
               alwayes
               full
               .
               Where
               first
               we
               note
               ,
               that
               ,
               although
               the
               measure
               of
               the
               Taps
               be
               equal
               ,
               neverthelesse
               there
               issueth
               from
               them
               in
               equal
               times
               unequal
               quantities
               of
               water
               ,
               And
               if
               we
               should
               more
               attentively
               consider
               this
               businesse
               ,
               we
               should
               find
               ,
               that
               the
               water
               by
               the
               lower
               Tap
               ,
               runneth
               and
               passeth
               with
               much
               greater
               velocity
               ,
               then
               it
               doth
               by
               the
               upper
               ,
               whatever
               is
               the
               reason
               .
               If
               therefore
               we
               would
               have
               such
               a
               quantity
               of
               Water
               discharge
               from
               the
               upper
               tap
               ,
               as
               would
               discharge
               from
               the
               neather
               in
               the
               same
               time
               ,
               it
               is
               plain
               ,
               that
               either
               the
               upper
               Tap●
               must
               be
               multiplyed
               in
               such
               sort
               ,
               that
               so
               many
               more
               Taps
               in
               number
               be
               placed
               above
               than
               below
               ,
               as
               the
               neather
               tap
               shall
               be
               more
               swift
               than
               the
               upper
               ,
               or
               the
               upper
               Tap
               made
               so
               much
               bigger
               than
               the
               nether
               ,
               by
               how
               much
               that
               beneath
               shall
               be
               more
               swift
               than
               that
               above
               ;
               and
               so
               then
               in
               equal
               times
               ,
               the
               same
               quantity
               of
               Water
               shall
               discharge
               from
               the
               upper
               ,
               as
               doth
               from
               the
               neather
               part
               .
            
             
             
               I
               will
               declare
               my self
               by
               another
               example
               .
               If
               we
               should
               imagine
               ,
               that
               two
               cords
               or
               lines
               of
               equal
               thickness
               ,
               be
               drawn
               through
               two
               holes
               of
               equal
               bore
               ;
               but
               so
               that
               the
               first
               pass
               with
               quadruple
               velocity
               to
               the
               second
               :
               It
               is
               manifest
               ,
               that
               if
               in
               a
               determinate
               time
               ,
               we
               shall
               by
               the
               first
               bore
               have
               drawn
               four
               Ells
               of
               the
               line
               ,
               in
               the
               same
               time
               ,
               by
               the
               second
               hole
               we
               shall
               have
               drawn
               but
               one
               Ell
               of
               cord
               onely
               ;
               and
               if
               by
               the
               first
               there
               passe
               twelve
               Ells
               ,
               then
               through
               the
               second
               there
               shall
               passe
               onely
               three
               Ells
               ;
               and
               in
               short
               the
               quantity
               of
               cord
               shall
               have
               the
               same
               proportion
               to
               the
               cord
               ,
               that
               the
               volocity
               hath
               to
               the
               velocity
               .
               And
               therefore
               we
               desiring
               to
               compensate
               the
               tardity
               of
               the
               second
               cord
               ,
               and
               maintaining
               the
               same
               tardity
               to
               draw
               through
               the
               second
               hole
               as
               much
               cord
               as
               through
               the
               first
               ,
               it
               will
               be
               necessary
               to
               draw
               through
               the
               second
               bore
               four
               ends
               of
               cord
               ;
               so
               that
               the
               thickness
               of
               all
               the
               cords
               by
               the
               second
               hole
               ,
               have
               the
               same
               proportion
               to
               the
               thickness
               of
               the
               cord
               which
               passeth
               onely
               by
               the
               first
               ,
               as
               the
               velocity
               of
               the
               cord
               by
               the
               first
               hole
               hath
               reciprocally
               to
               the
               velocity
               of
               the
               cod's
               by
               the
               second
               hole
               .
               And
               thus
               its
               clear
               ,
               that
               when
               there
               is
               drawn
               through
               two
               holes
               equal
               quantity
               of
               cords
               in
               equal
               time
               ,
               but
               with
               unequal
               velocity
               ,
               it
               will
               be
               necessary
               ,
               that
               the
               thickness
               of
               all
               the
               four
               cords
               shall
               have
               the
               same
               reciprocal
               proportion
               to
               the
               thickness
               of
               the
               swifter
               cord
               ,
               that
               the
               velocity
               of
               the
               swifter
               cord
               hath
               to
               the
               velocity
               of
               the
               slower
               .
               The
               which
               is
               verified
               likewise
               in
               the
               fluid
               Element
               of
               Water
               .
            
             
               And
               to
               the
               end
               that
               this
               principal
               fundamental
               be
               well
               understood
               ,
               I
               will
               also
               note
               a
               certain
               observation
               made
               my
               me
               in
               the
               Art
               of
               Wyer-drawing
               ,
               or
               spinning
               Gold
               ,
               Silver
               ,
               Brass
               ,
               and
               Iron
               ,
               and
               it
               is
               this
               ;
               That
               such
               Artificers
               desiring
               more
               and
               more
               to
               disgrosse
               and
               subtillize
               the
               said
               Metals
               ,
               having
               wound
               about
               a
               Rocket
               or
               Barrel
               ,
               the
               thread
               of
               the
               Metal
               ,
               they
               place
               the
               Rocket
               in
               a
               frame
               upon
               a
               stedfast
               Axis
               ,
               in
               such
               sort
               that
               the
               Rocket
               may
               turn
               about
               in
               it self
               ;
               then
               making
               one
               end
               of
               the
               thread
               to
               passe
               by
               force
               through
               a
               Plate
               of
               Steel
               pierced
               with
               divers
               holes
               ,
               greater
               and
               lesser
               ,
               as
               need
               requireth
               ,
               fastning
               the
               same
               end
               of
               the
               thread
               to
               another
               Rocket
               ,
               they
               wind
               up
               the
               thread
               ,
               which
               passing
               through
               a
               bore
               less
               than
               the
               thicknesse
               of
               the
               thread
               ,
               is
               of
               force
               constrained
               to
               disgrosse
               and
               subtillize
               .
               Now
               that
               which
               is
               intensly
               to
               be
               observed
               in
               this
               business
               ,
               is
               this
               ,
               That
               the
               parts
               of
               the
               thread
               before
               the
               hole
               ,
               are
               of
               such
               a
               thicknesse
               ,
               but
               the
               parts
               of
               the
               same
               thread
               after
               it
               is
               passed
               the
               hole
               ,
               are
               of
               a
               lesser
               thicknesse
               :
               and
               yet
               neverthelesse
               the
               masse
               and
               weight
               of
               the
               thread
               which
               is
               drawn
               forth
               ,
               is
               ever
               equal
               to
               the
               masse
               and
               weight
               of
               the
               thread
               which
               is
               winded
               up
               .
               But
               if
               we
               should
               well
               consider
               the
               matter
               ,
               we
               should
               finde
               ,
               that
               the
               thicker
               the
               thread
               before
               the
               hole
               is
               ,
               than
               the
               thread
               passed
               the
               hole
               ,
               the
               greater
               reciprocally
               is
               the
               
               velocity
               of
               the
               parts
               of
               the
               thread
               passed
               the
               hole
               ,
               than
               the
               volocity
               of
               the
               parts
               before
               the
               hole
               :
               Insomuch
               that
               if
               
                 v●rbi
                 gratia
              
               the
               thicknesse
               of
               the
               thread
               before
               the
               hole
               ,
               were
               double
               to
               the
               thicknesse
               after
               the
               hole
               ,
               in
               such
               case
               the
               velocity
               of
               the
               parts
               of
               the
               thread
               passed
               the
               hole
               ,
               should
               be
               double
               to
               the
               velocity
               of
               the
               parts
               of
               the
               thread
               before
               the
               hole
               ;
               and
               thus
               the
               thicknesse
               compensates
               the
               velocity
               ,
               and
               the
               velocity
               compensates
               the
               thicknesse
               .
               So
               that
               the
               same
               occurreth
               in
               the
               solid
               Metals
               of
               Gold
               ,
               Silver
               ,
               Brass
               ,
               Iron
               ,
               &c.
               that
               eveneth
               also
               in
               the
               fluid
               Element
               of
               Water
               ,
               and
               other
               liquids
               ,
               namely
               ,
               That
               the
               velocity
               beareth
               the
               same
               proportion
               to
               the
               velocity
               ,
               that
               the
               thicknesse
               of
               the
               Metal
               ,
               or
               Water
               ,
               hath
               to
               the
               thicknesse
               .
            
             
               And
               therefore
               granting
               this
               discourse
               ,
               we
               may
               say
               ,
               that
               as
               often
               as
               two
               Taps
               with
               different
               velocity
               discharge
               equal
               quantities
               of
               Water
               in
               equal
               times
               ,
               it
               will
               be
               necessary
               that
               the
               Tap
               lesse
               swift
               be
               so
               much
               greater
               ,
               and
               larger
               ,
               than
               the
               Tap
               more
               swift
               ,
               by
               how
               much
               the
               swifter
               superates
               in
               velocity
               the
               slower
               ;
               and
               to
               pronounce
               the
               Proposition
               in
               more
               proper
               terms
               ,
               we
               say
               ;
               That
               if
               two
               Taps
               of
               unequal
               velocity
               ,
               discharge
               in
               equal
               times
               equal
               quantities
               of
               Water
               ,
               the
               greatnesse
               of
               the
               first
               shall
               be
               to
               the
               greatnesse
               of
               the
               second
               ,
               in
               reciprocal
               proportion
               ,
               as
               the
               velocity
               of
               the
               second
               to
               the
               velocity
               of
               the
               first
               .
               As
               for
               example
               ,
               if
               the
               first
               Tap
               shall
               be
               ten
               times
               swifter
               than
               the
               second
               Tap
               ,
               it
               will
               be
               necessary
               ,
               that
               the
               second
               be
               ten
               times
               bigger
               and
               larger
               than
               the
               first
               ;
               and
               in
               such
               case
               the
               Taps
               shall
               discharge
               equall
               quantities
               of
               water
               in
               equal
               times
               ;
               and
               this
               is
               the
               principal
               and
               most
               important
               point
               ,
               which
               ought
               to
               be
               kept
               alwayes
               in
               minde
               ,
               for
               that
               on
               it
               well
               understood
               depend
               many
               things
               profitable
               ,
               and
               worthy
               of
               our
               knowledge
               .
            
             
               Now
               applying
               all
               that
               hath
               been
               said
               neerer
               to
               our
               purpose
               ,
               I
               consider
               ,
               that
               it
               being
               most
               true
               ,
               that
               in
               divers
               parts
               of
               the
               same
               River
               or
               Current
               of
               running
               water
               ,
               there
               doth
               always
               passe
               equal
               quantity
               of
               Water
               in
               equal
               time
               (
               which
               thing
               is
               also
               demonstrated
               in
               our
               first
               Proposition
               )
               and
               it
               being
               also
               true
               ,
               that
               in
               divers
               parts
               the
               same
               River
               may
               have
               various
               and
               different
               velocity
               ;
               it
               follows
               of
               necessary
               consequence
               ,
               that
               where
               the
               River
               hath
               lesse
               velocity
               ,
               it
               shall
               be
               of
               greater
               measure
               ,
               and
               in
               those
               parts
               ,
               in
               which
               it
               hath
               greater
               velocity
               ,
               it
               shall
               be
               of
               lesse
               measure
               ;
               and
               in
               sum
               ,
               the
               velocity
               of
               several
               parts
               of
               the
               said
               River
               ,
               shall
               have
               eternally
               reciprocall
               and
               like
               proportion
               with
               their
               measures
               .
               This
               principle
               and
               fundamental
               well
               established
               ,
               that
               the
               same
               Current
               of
               Water
               changeth
               measure
               ,
               according
               to
               its
               varying
               of
               velocity
               ;
               that
               is
               ,
               lessening
               the
               measure
               ,
               when
               the
               velocity
               encreaseth
               ,
               and
               encreasing
               the
               measure
               ,
               when
               the
               velocity
               decreaseth
               ;
               I
               passe
               to
               the
               consideration
               of
               many
               
               particular
               accidents
               in
               this
               admirable
               matter
               ,
               and
               all
               depending
               on
               this
               sole
               Proposition
               ,
               the
               sense
               of
               which
               I
               have
               oft
               repeated
               ,
               that
               it
               might
               be
               well
               understood
               .
            
             
               
                 COROLLARIE
                 I.
                 
              
               
                 ANd
                 first
                 ,
                 we
                 hence
                 conclude
                 ,
                 that
                 the
                 same
                 Streams
                 of
                 a
                 Torrent
                 ,
                 namely
                 ,
                 those
                 streams
                 which
                 carry
                 equal
                 quantity
                 of
                 Water
                 in
                 equal
                 times
                 ,
                 make
                 not
                 the
                 same
                 depths
                 or
                 measures
                 in
                 the
                 River
                 ,
                 in
                 which
                 they
                 enter
                 ,
                 unlesse
                 when
                 in
                 the
                 entrance
                 into
                 the
                 River
                 they
                 acquired
                 ;
                 or
                 to
                 say
                 better
                 ,
                 keep
                 the
                 same
                 velocity
                 ;
                 because
                 if
                 the
                 velocicities
                 acquired
                 in
                 the
                 River
                 shall
                 be
                 different
                 ,
                 also
                 the
                 measures
                 shall
                 be
                 diverse
                 ;
                 and
                 consequently
                 the
                 depths
                 ,
                 as
                 is
                 demonstrated
                 .
              
            
             
               
                 COROLLARIE
                 II.
                 
              
               
                 ANd
                 because
                 successively
                 ,
                 as
                 the
                 River
                 is
                 more
                 and
                 more
                 full
                 ,
                 it
                 is
                 constituted
                 ordinarily
                 in
                 greater
                 &
                 greater
                 velocity
                 :
                 hence
                 it
                 is
                 that
                 the
                 same
                 streams
                 of
                 the
                 Torrent
                 ,
                 that
                 enter
                 into
                 the
                 River
                 ,
                 make
                 lesse
                 and
                 lesse
                 depths
                 ,
                 as
                 the
                 River
                 grows
                 more
                 and
                 more
                 full
                 ;
                 since
                 that
                 also
                 the
                 Waters
                 of
                 the
                 Torrent
                 being
                 entered
                 into
                 the
                 River
                 ,
                 go
                 acquiring
                 greater
                 and
                 greater
                 velocities
                 ,
                 and
                 therefore
                 diminish
                 in
                 measure
                 and
                 height
                 .
              
            
             
               
                 COROLLARIE
                 III.
                 
              
               
                 WE
                 observe
                 also
                 ,
                 that
                 while
                 the
                 main
                 River
                 is
                 shallow
                 ,
                 if
                 there
                 fall
                 but
                 a
                 gentle
                 rain
                 ,
                 it
                 suddenly
                 much
                 increaseth
                 and
                 riseth
                 ;
                 but
                 when
                 the
                 River
                 is
                 already
                 swelled
                 ,
                 though
                 there
                 fall
                 again
                 another
                 new
                 violent
                 shower
                 ,
                 yet
                 it
                 increaseth
                 not
                 at
                 the
                 same
                 rate
                 as
                 before
                 ,
                 proportionably
                 to
                 the
                 rain
                 which
                 fell
                 :
                 which
                 thing
                 we
                 may
                 affirm
                 particularly
                 to
                 depend
                 on
                 this
                 ,
                 that
                 in
                 the
                 first
                 case
                 ,
                 while
                 the
                 River
                 is
                 low
                 ,
                 it
                 is
                 found
                 also
                 very
                 slow
                 ,
                 and
                 therefore
                 the
                 little
                 water
                 which
                 entereth
                 into
                 it
                 ,
                 passeth
                 and
                 runs
                 with
                 little
                 velocity
                 ,
                 and
                 consequently
                 occupieth
                 a
                 great
                 measure
                 :
                 But
                 when
                 the
                 River
                 is
                 once
                 augmented
                 ,
                 by
                 new
                 water
                 being
                 also
                 made
                 more
                 swift
                 ,
                 it
                 causeth
                 the
                 great
                 Flood
                 of
                 water
                 which
                 falleth
                 ,
                 to
                 bear
                 a
                 lesse
                 measure
                 ,
                 and
                 not
                 to
                 make
                 such
                 a
                 depth
                 .
              
            
             
               
                 COROLLARIE
                 IV.
                 
              
               
                 FRom
                 the
                 things
                 demonstrated
                 is
                 manifest
                 also
                 ,
                 that
                 whilst
                 a
                 Torrent
                 entereth
                 into
                 a
                 River
                 ,
                 at
                 the
                 time
                 of
                 Ebbe
                 ,
                 then
                 the
                 Torrent
                 moveth
                 with
                 such
                 a
                 certain
                 velocity
                 ,
                 what
                 ever
                 it
                 be
                 ,
                 
                 passing
                 by
                 its
                 extreamest
                 parts
                 ,
                 wherewith
                 it
                 communicateth
                 with
                 the
                 River
                 ;
                 in
                 which
                 parts
                 ,
                 the
                 Torrent
                 being
                 measured
                 ,
                 shall
                 have
                 such
                 a
                 certain
                 measure
                 :
                 but
                 the
                 River
                 swelling
                 and
                 rising
                 ,
                 also
                 those
                 parts
                 of
                 the
                 Torrent
                 augment
                 in
                 greatnesse
                 and
                 measure
                 ,
                 though
                 the
                 Torrent
                 ,
                 in
                 that
                 instant
                 ,
                 dis-imbogue
                 no
                 more
                 water
                 than
                 it
                 did
                 before
                 :
                 so
                 that
                 the
                 River
                 being
                 swelled
                 ,
                 we
                 are
                 to
                 consider
                 two
                 mouths
                 of
                 the
                 same
                 Torrent
                 ,
                 one
                 lesse
                 before
                 the
                 rising
                 ,
                 the
                 other
                 greater
                 after
                 the
                 rising
                 ,
                 which
                 mouths
                 discharge
                 equal
                 quantities
                 of
                 water
                 in
                 equal
                 times
                 ;
                 therefore
                 the
                 velocity
                 by
                 the
                 lesser
                 mouth
                 shall
                 be
                 greater
                 than
                 the
                 velocity
                 by
                 the
                 greater
                 mouth
                 ;
                 and
                 thus
                 the
                 Torrent
                 shall
                 be
                 retarded
                 from
                 its
                 ordinary
                 course
                 .
              
            
             
               
                 COROLLARIE
                 V.
                 
              
               
                 FRom
                 which
                 operation
                 of
                 Nature
                 proceedeth
                 another
                 effect
                 worthy
                 of
                 consideration
                 ;
                 and
                 it
                 is
                 ,
                 that
                 the
                 course
                 of
                 the
                 water
                 retarding
                 ,
                 as
                 hath
                 been
                 said
                 in
                 those
                 ultimate
                 parts
                 of
                 the
                 Torrent
                 ,
                 if
                 it
                 shall
                 happen
                 that
                 the
                 Torrent
                 grow
                 torbid
                 and
                 muddy
                 ,
                 and
                 its
                 streame
                 be
                 retarded
                 in
                 such
                 a
                 degree
                 ,
                 that
                 it
                 is
                 not
                 able
                 to
                 carry
                 away
                 those
                 minute
                 grains
                 of
                 Earth
                 ,
                 which
                 compose
                 the
                 muddinesse
                 ;
                 in
                 this
                 case
                 the
                 Torrent
                 shall
                 clear
                 away
                 the
                 mud
                 ,
                 and
                 carry
                 away
                 the
                 Sand
                 at
                 the
                 bottome
                 of
                 its
                 own
                 Chanel
                 ,
                 in
                 the
                 extream
                 parts
                 of
                 its
                 mouth
                 ,
                 which
                 raised
                 and
                 voided
                 Sand
                 ,
                 shall
                 again
                 afterwards
                 be
                 carried
                 away
                 ,
                 when
                 the
                 River
                 abating
                 ,
                 the
                 Torrent
                 shall
                 return
                 to
                 move
                 with
                 its
                 primitive
                 velocity
                 .
              
            
             
               
                 COROLLARIE
                 VI.
                 
              
               
                 WHilst
                 it
                 is
                 demonstrated
                 ,
                 that
                 the
                 same
                 water
                 hath
                 different
                 measures
                 in
                 its
                 Chanel
                 or
                 course
                 ,
                 according
                 as
                 it
                 varieth
                 in
                 velocity
                 ;
                 so
                 that
                 the
                 measure
                 of
                 the
                 water
                 is
                 alwayes
                 greater
                 ,
                 where
                 the
                 velocity
                 is
                 lesser
                 ;
                 and
                 on
                 the
                 contrary
                 ,
                 the
                 measure
                 lesser
                 ,
                 where
                 the
                 velocity
                 is
                 greater
                 :
                 from
                 hence
                 we
                 may
                 most
                 elegantly
                 render
                 the
                 reason
                 of
                 the
                 usual
                 Proverb
                 ,
                 
                   Take
                   heed
                   of
                   the
                   still
                   waters
                   :
                
                 For
                 that
                 if
                 we
                 consider
                 the
                 self
                 same
                 water
                 of
                 a
                 River
                 in
                 those
                 parts
                 ,
                 wherein
                 it
                 is
                 less
                 swift
                 ,
                 and
                 thence
                 called
                 still
                 or
                 smooth
                 water
                 ,
                 it
                 shall
                 be
                 ,
                 of
                 necessity
                 ,
                 of
                 greater
                 measure
                 than
                 in
                 those
                 parts
                 ,
                 in
                 which
                 it
                 is
                 more
                 swift
                 ,
                 and
                 therefore
                 ordinarily
                 shall
                 be
                 also
                 more
                 deep
                 and
                 dangerous
                 for
                 passengers
                 ;
                 whence
                 it
                 is
                 well
                 said
                 ,
                 
                   Take
                   heed
                   of
                   the
                   still
                   Waters
                
                 ;
                 and
                 this
                 saying
                 hath
                 been
                 since
                 applied
                 to
                 things
                 moral
                 .
              
            
             
               
               
                 COROLLARIE
                 VII
                 .
              
               
                 LIkewise
                 ,
                 from
                 the
                 things
                 demonstrated
                 may
                 be
                 concluded
                 ,
                 that
                 the
                 windes
                 ,
                 which
                 stop
                 a
                 River
                 ,
                 and
                 blowing
                 against
                 the
                 Current
                 ,
                 retard
                 its
                 course
                 and
                 ordinary
                 velocity
                 shall
                 necessarily
                 amplifie
                 the
                 measure
                 of
                 the
                 same
                 River
                 ,
                 and
                 consequently
                 shall
                 be
                 ,
                 in
                 great
                 part
                 ,
                 causes
                 ;
                 or
                 we
                 may
                 say
                 ,
                 potent
                 con-causes
                 of
                 making
                 the
                 extraordinary
                 inundations
                 which
                 Rivers
                 use
                 to
                 make
                 .
                 And
                 it
                 s
                 most
                 certain
                 ,
                 that
                 as
                 often
                 as
                 a
                 strong
                 and
                 continual
                 wind
                 shall
                 blow
                 against
                 the
                 Current
                 of
                 a
                 River
                 ,
                 and
                 shall
                 reduce
                 the
                 water
                 of
                 the
                 River
                 to
                 such
                 tardity
                 of
                 motion
                 ,
                 that
                 in
                 the
                 time
                 wherein
                 before
                 it
                 run
                 five
                 miles
                 ,
                 it
                 now
                 moveth
                 but
                 one
                 ,
                 such
                 a
                 River
                 will
                 increase
                 to
                 five
                 times
                 the
                 measure
                 ,
                 though
                 there
                 should
                 not
                 be
                 added
                 any
                 other
                 quantity
                 of
                 water
                 ;
                 which
                 thing
                 indeed
                 hath
                 in
                 it
                 something
                 of
                 strange
                 ,
                 but
                 it
                 is
                 most
                 certain
                 ,
                 for
                 that
                 look
                 what
                 proportion
                 the
                 waters
                 velocity
                 before
                 the
                 winde
                 ,
                 hath
                 to
                 the
                 velocity
                 after
                 the
                 winde
                 ,
                 and
                 such
                 reciprocally
                 is
                 the
                 measure
                 of
                 the
                 same
                 water
                 after
                 the
                 winde
                 ,
                 to
                 the
                 measure
                 before
                 the
                 winde
                 ;
                 and
                 because
                 it
                 hath
                 been
                 supposed
                 in
                 our
                 case
                 that
                 the
                 velocity
                 is
                 diminished
                 to
                 a
                 fifth
                 part
                 ,
                 therefore
                 the
                 measure
                 shall
                 be
                 increased
                 five
                 times
                 more
                 than
                 that
                 ,
                 which
                 it
                 was
                 before
                 .
              
            
             
               
                 COROLLARIE
                 VIII
                 .
              
               
                 WE
                 have
                 also
                 probable
                 the
                 cause
                 of
                 the
                 inundations
                 of
                 Tyber
                 ,
                 which
                 befel
                 at
                 Rome
                 ,
                 in
                 the
                 time
                 of
                 Alexander
                 the
                 Sixth
                 ,
                 &
                 of
                 Clement
                 the
                 Seventh
                 ;
                 which
                 innundations
                 came
                 in
                 a
                 serene
                 time
                 ,
                 and
                 without
                 great
                 thaws
                 of
                 the
                 Snows
                 ;
                 which
                 therefore
                 much
                 puzzled
                 the
                 wits
                 of
                 those
                 times
                 .
                 But
                 we
                 may
                 with
                 much
                 probability
                 affirm
                 ,
                 That
                 the
                 River
                 rose
                 to
                 such
                 a
                 height
                 and
                 excresence
                 ,
                 by
                 the
                 retardation
                 of
                 the
                 Waters
                 dependant
                 on
                 the
                 boistrous
                 and
                 constant
                 Winds
                 ,
                 that
                 blew
                 in
                 those
                 times
                 ,
                 as
                 is
                 noted
                 in
                 the
                 memorials
                 .
              
            
             
               
                 COROLLARIE
                 .
                 IX
                 .
              
               
                 IT
                 being
                 most
                 manifest
                 ,
                 that
                 by
                 the
                 great
                 abundance
                 of
                 Water
                 the
                 Torrents
                 may
                 increase
                 ,
                 and
                 of
                 themselves
                 alone
                 exorbitantly
                 swell
                 the
                 River
                 ;
                 and
                 having
                 demonstrated
                 that
                 also
                 without
                 new
                 Water
                 ,
                 but
                 onely
                 by
                 the
                 notable
                 retardment
                 the
                 River
                 riseth
                 and
                 increaseth
                 in
                 measure
                 ,
                 in
                 proportion
                 as
                 the
                 velocity
                 decreaseth
                 :
                 hence
                 it
                 is
                 apparent
                 ,
                 that
                 each
                 of
                 these
                 causes
                 being
                 able
                 of
                 it self
                 ,
                 and
                 separate
                 from
                 the
                 other
                 to
                 swell
                 the
                 River
                 ;
                 when
                 it
                 shall
                 happen
                 that
                 both
                 these
                 two
                 causes
                 conspire
                 the
                 augmentation
                 of
                 
                 the
                 River
                 ,
                 in
                 such
                 a
                 case
                 there
                 must
                 follow
                 very
                 great
                 and
                 irrepable
                 innundations
                 .
              
            
             
               
                 COROLLARIE
                 X.
                 
              
               
                 FRom
                 what
                 hath
                 been
                 demonstrated
                 ,
                 we
                 may
                 with
                 facility
                 resolve
                 the
                 doubt
                 which
                 hath
                 troubled
                 ,
                 and
                 still
                 poseth
                 the
                 most
                 diligent
                 ,
                 but
                 incautelous
                 observers
                 of
                 Rivers
                 ,
                 who
                 measuring
                 the
                 Streams
                 and
                 Torrents
                 which
                 fall
                 into
                 another
                 River
                 ;
                 as
                 those
                 for
                 instance
                 ,
                 which
                 enter
                 into
                 the
                 Po
                 ,
                 or
                 those
                 which
                 fall
                 into
                 Tiber
                 ;
                 and
                 having
                 summed
                 the
                 total
                 of
                 these
                 measures
                 ,
                 and
                 conferring
                 the
                 measures
                 of
                 the
                 Rivers
                 and
                 Brooks
                 ,
                 which
                 fall
                 into
                 Tiber
                 ,
                 with
                 the
                 measure
                 of
                 Tiber
                 ,
                 and
                 the
                 measures
                 of
                 those
                 which
                 disimbogue
                 into
                 Po
                 ,
                 with
                 the
                 measure
                 of
                 Po
                 ,
                 they
                 find
                 them
                 not
                 equal
                 ,
                 as
                 ,
                 it
                 seems
                 to
                 them
                 ,
                 they
                 ought
                 to
                 be
                 ,
                 and
                 this
                 is
                 because
                 they
                 have
                 not
                 well
                 noted
                 the
                 most
                 important
                 point
                 of
                 the
                 variation
                 of
                 velocity
                 ,
                 and
                 how
                 that
                 it
                 is
                 the
                 most
                 potent
                 cause
                 of
                 wonderfully
                 altering
                 the
                 measures
                 of
                 running
                 Waters
                 ;
                 but
                 we
                 most
                 facilly
                 resolving
                 the
                 doubt
                 ,
                 may
                 say
                 that
                 these
                 Waters
                 diminish
                 the
                 measure
                 ,
                 being
                 once
                 entered
                 the
                 principal
                 Channel
                 ,
                 because
                 they
                 increase
                 in
                 velocity
                 .
              
            
             
               
                 COROLLARIE
                 XI
                 .
              
               
                 THrough
                 the
                 ignorance
                 of
                 the
                 force
                 of
                 the
                 velocity
                 of
                 the
                 Water
                 ,
                 in
                 altering
                 its
                 measure
                 ,
                 &
                 augmenting
                 it
                 when
                 the
                 velocity
                 diminisheth
                 ;
                 and
                 diminishing
                 it
                 when
                 the
                 velocity
                 augmenteth
                 :
                 The
                 Architect
                 
                   Giovanni
                   Fontana
                
                 ,
                 endeavoured
                 to
                 measure
                 ,
                 and
                 and
                 to
                 cause
                 to
                 be
                 measured
                 by
                 his
                 Nephew
                 ,
                 all
                 the
                 Brooks
                 and
                 Rivers
                 which
                 discharged
                 their
                 Waters
                 into
                 Tiber
                 ,
                 at
                 the
                 time
                 of
                 the
                 Innundation
                 ;
                 which
                 happened
                 at
                 Rome
                 in
                 the
                 year
                 1598
                 ,
                 and
                 published
                 a
                 small
                 Treatise
                 thereof
                 ,
                 wherein
                 he
                 summeth
                 up
                 the
                 measures
                 of
                 the
                 extraordinary
                 Water
                 which
                 fell
                 into
                 Tiber
                 ,
                 and
                 made
                 account
                 that
                 it
                 was
                 about
                 five
                 hundred
                 Ells
                 more
                 than
                 ordinary
                 ;
                 and
                 in
                 the
                 end
                 of
                 that
                 Treatise
                 concludeth
                 ,
                 that
                 to
                 remove
                 the
                 Innundation
                 wholly
                 from
                 Rome
                 ,
                 it
                 would
                 be
                 necessary
                 to
                 make
                 two
                 other
                 Channels
                 ,
                 equal
                 to
                 that
                 at
                 present
                 ,
                 and
                 that
                 lesse
                 would
                 not
                 suffice
                 ;
                 and
                 finding
                 afterwards
                 that
                 the
                 whole
                 Stream
                 passed
                 under
                 the
                 Bridge
                 Quattro-Capi
                 ,
                 (
                 the
                 Arch
                 whereof
                 is
                 of
                 a
                 far
                 less
                 measure
                 then
                 five
                 hundred
                 Ells
                 )
                 concludeth
                 ,
                 that
                 under
                 the
                 said
                 Bridge
                 past
                 a
                 hundred
                 fifty
                 one
                 Ells
                 of
                 Water
                 compressed
                 ,
                 (
                 I
                 have
                 set
                 down
                 the
                 precise
                 term
                 of
                 comprest
                 Water
                 ,
                 written
                 by
                 Fontana
                 )
                 wherein
                 I
                 finde
                 many
                 errors
                 .
              
               
                 The
                 first
                 of
                 which
                 is
                 to
                 think
                 that
                 the
                 measures
                 of
                 these
                 Waters
                 compressed
                 in
                 the
                 Channels
                 of
                 those
                 Brooks
                 and
                 Rivers
                 ,
                 
                 should
                 maintain
                 themselves
                 the
                 same
                 in
                 Tiber
                 ,
                 which
                 by
                 his
                 leave
                 ,
                 is
                 most
                 false
                 ,
                 when
                 ever
                 those
                 waters
                 reduced
                 into
                 Tiber
                 ,
                 retain
                 not
                 the
                 same
                 velocity
                 which
                 they
                 had
                 in
                 the
                 place
                 in
                 which
                 Fontana
                 and
                 his
                 Nephew
                 measured
                 them
                 :
                 And
                 all
                 this
                 is
                 manifest
                 from
                 the
                 things
                 which
                 we
                 have
                 above
                 explained
                 ;
                 for
                 ,
                 if
                 the
                 Waters
                 reduced
                 into
                 Tiber
                 increase
                 in
                 velocity
                 ,
                 they
                 decrease
                 in
                 measure
                 ;
                 and
                 if
                 they
                 decrease
                 in
                 velocity
                 ,
                 they
                 increase
                 in
                 measure
                 .
              
               
                 Secondly
                 ,
                 I
                 consider
                 that
                 the
                 measures
                 of
                 those
                 Brooks
                 and
                 Rivers
                 ,
                 which
                 enter
                 into
                 Tiber
                 at
                 the
                 time
                 of
                 Innundation
                 ,
                 are
                 not
                 between
                 themselves
                 really
                 the
                 same
                 ,
                 when
                 their
                 velocities
                 are
                 not
                 equal
                 ,
                 though
                 they
                 have
                 the
                 same
                 names
                 of
                 Ells
                 and
                 Feet
                 ;
                 for
                 that
                 its
                 possible
                 that
                 a
                 disinboguement
                 of
                 ten
                 Ells
                 requadrated
                 (
                 to
                 speak
                 in
                 the
                 phrase
                 of
                 Fontana
                 )
                 of
                 one
                 of
                 those
                 Brooks
                 ,
                 might
                 discharge
                 into
                 Tiber
                 at
                 the
                 time
                 of
                 Innundation
                 ,
                 four
                 ,
                 ten
                 ,
                 and
                 twenty
                 times
                 less
                 Water
                 ,
                 than
                 another
                 mouth
                 equal
                 to
                 the
                 first
                 in
                 greatness
                 ,
                 as
                 would
                 occur
                 when
                 the
                 first
                 mouth
                 were
                 four
                 ,
                 ten
                 ,
                 or
                 twenty
                 times
                 less
                 swift
                 than
                 the
                 second
                 .
                 Whereupon
                 ,
                 whilst
                 Fontana
                 summes
                 up
                 the
                 Ells
                 and
                 Feet
                 of
                 the
                 measures
                 of
                 those
                 Brooks
                 and
                 Rivers
                 into
                 a
                 total
                 aggregate
                 ,
                 he
                 commits
                 the
                 same
                 error
                 with
                 him
                 ,
                 which
                 would
                 add
                 into
                 one
                 summe
                 diverse
                 moneys
                 of
                 diverse
                 values
                 ,
                 and
                 diverse
                 places
                 ,
                 but
                 that
                 had
                 the
                 same
                 name
                 ;
                 as
                 if
                 one
                 should
                 say
                 ten
                 Crowns
                 of
                 Roman
                 money
                 ,
                 four
                 Crowns
                 of
                 Gold
                 ,
                 thirteen
                 Crowns
                 of
                 Florence
                 ,
                 five
                 Crowns
                 of
                 Venice
                 ,
                 and
                 eight
                 Crowns
                 of
                 Mantua
                 ,
                 should
                 make
                 the
                 same
                 summe
                 with
                 forty
                 Crowns
                 of
                 Gold
                 ,
                 or
                 forty
                 Crowns
                 of
                 Mantua
                 .
              
               
                 Thirdly
                 ,
                 It
                 might
                 happen
                 that
                 some
                 River
                 or
                 Current
                 in
                 the
                 parts
                 nearer
                 Rome
                 ,
                 in
                 the
                 time
                 of
                 its
                 flowing
                 ,
                 did
                 not
                 send
                 forth
                 more
                 Water
                 than
                 ordinary
                 ;
                 and
                 however
                 ,
                 it
                 s
                 a
                 thing
                 very
                 clear
                 ,
                 that
                 whilst
                 the
                 stream
                 came
                 from
                 the
                 superior
                 parts
                 ,
                 that
                 same
                 Brook
                 or
                 River
                 would
                 be
                 augmented
                 in
                 measure
                 ,
                 as
                 hath
                 been
                 noted
                 in
                 the
                 fourth
                 Corollary
                 ;
                 in
                 such
                 sort
                 ,
                 that
                 Fontana
                 might
                 have
                 inculcated
                 ,
                 and
                 noted
                 that
                 same
                 River
                 or
                 Current
                 as
                 concurring
                 to
                 the
                 Innundation
                 ,
                 although
                 it
                 were
                 therein
                 altogether
                 unconcerned
                 .
              
               
                 Moreover
                 ,
                 in
                 the
                 fourth
                 place
                 we
                 must
                 note
                 ,
                 That
                 it
                 might
                 so
                 fall
                 out
                 ,
                 that
                 such
                 a
                 River
                 not
                 onely
                 was
                 uninteressed
                 in
                 the
                 Innundation
                 ,
                 though
                 augmented
                 in
                 measure
                 ,
                 but
                 it
                 might
                 I
                 say
                 happen
                 ,
                 that
                 it
                 was
                 instrumental
                 to
                 the
                 asswaging
                 the
                 Innundation
                 ,
                 by
                 augmenting
                 in
                 the
                 measure
                 of
                 its
                 own
                 Channel
                 ;
                 which
                 matter
                 is
                 sufficiently
                 evident
                 ;
                 for
                 if
                 it
                 be
                 supposed
                 that
                 the
                 River
                 in
                 the
                 time
                 of
                 flood
                 ,
                 had
                 not
                 had
                 of
                 it self
                 ,
                 and
                 from
                 its
                 proper
                 springs
                 more
                 Water
                 than
                 ordinary
                 ,
                 it
                 s
                 a
                 thing
                 certain
                 ,
                 that
                 the
                 Water
                 of
                 Tiber
                 rising
                 and
                 increasing
                 ;
                 also
                 that
                 River
                 ,
                 to
                 level
                 it self
                 with
                 the
                 Water
                 of
                 Tiber
                 ,
                 would
                 have
                 retained
                 some
                 of
                 
                 its
                 Waters
                 in
                 its
                 own
                 Chanel
                 ,
                 without
                 discharging
                 them
                 into
                 Tyber
                 ,
                 or
                 else
                 would
                 have
                 ingorged
                 and
                 swallowed
                 (
                 if
                 I
                 may
                 so
                 say
                 )
                 some
                 of
                 the
                 water
                 of
                 Tyber
                 ;
                 and
                 in
                 this
                 case
                 ,
                 at
                 the
                 time
                 of
                 Inundation
                 ,
                 lesse
                 abundance
                 of
                 water
                 would
                 have
                 come
                 to
                 Rome
                 ,
                 and
                 yet
                 neverthelesse
                 the
                 measure
                 of
                 that
                 River
                 would
                 have
                 been
                 increased
                 .
              
               
                 Fifthly
                 ,
                 Fontana
                 deceiveth
                 himself
                 ,
                 when
                 he
                 concludeth
                 ,
                 that
                 to
                 remove
                 the
                 Inundation
                 from
                 Rome
                 ,
                 it
                 would
                 be
                 necessary
                 to
                 make
                 two
                 other
                 Chanels
                 of
                 Rivers
                 ,
                 that
                 were
                 as
                 large
                 as
                 that
                 ,
                 which
                 is
                 the
                 present
                 one
                 ,
                 and
                 that
                 less
                 would
                 not
                 suffice
                 ,
                 which
                 ,
                 I
                 say
                 ,
                 is
                 a
                 fallacy
                 :
                 and
                 to
                 convince
                 him
                 easily
                 of
                 his
                 errour
                 ,
                 it
                 sufficeth
                 to
                 say
                 ,
                 that
                 all
                 the
                 Streams
                 being
                 passed
                 under
                 the
                 Bridge
                 Quattro-Capi
                 ,
                 as
                 he
                 himself
                 attests
                 ,
                 a
                 Channel
                 would
                 suffice
                 only
                 of
                 the
                 capacity
                 of
                 the
                 said
                 Bridge
                 ,
                 provided
                 that
                 the
                 water
                 there
                 might
                 run
                 with
                 the
                 same
                 velocity
                 ,
                 as
                 it
                 did
                 under
                 the
                 Bridge
                 at
                 the
                 time
                 of
                 Inundation
                 ;
                 and
                 on
                 the
                 contrary
                 ,
                 twenty
                 Currents
                 of
                 capacity
                 equal
                 to
                 the
                 present
                 one
                 ,
                 would
                 not
                 suffice
                 ,
                 if
                 the
                 water
                 should
                 run
                 with
                 twenty
                 times
                 less
                 velocity
                 ,
                 than
                 it
                 made
                 at
                 the
                 time
                 of
                 the
                 Inundation
                 .
              
               
                 Sixthly
                 ,
                 to
                 me
                 it
                 seemeth
                 a
                 great
                 weaknesse
                 to
                 say
                 ,
                 that
                 there
                 should
                 passe
                 under
                 the
                 Bridge
                 Quattro-Capi
                 ,
                 an
                 hundred
                 fifty
                 one
                 ells
                 of
                 water
                 compressed
                 ;
                 for
                 that
                 I
                 do
                 not
                 understand
                 that
                 water
                 is
                 like
                 Cotton
                 or
                 Wool
                 ,
                 which
                 matters
                 may
                 be
                 prest
                 and
                 trod
                 ,
                 as
                 it
                 happeneth
                 also
                 to
                 the
                 air
                 ,
                 which
                 receiveth
                 compression
                 in
                 such
                 sort
                 ,
                 that
                 after
                 that
                 in
                 some
                 certain
                 place
                 a
                 quantity
                 of
                 air
                 shall
                 be
                 reduced
                 to
                 its
                 natural
                 constitution
                 ;
                 and
                 having
                 taken
                 up
                 all
                 the
                 said
                 place
                 ,
                 yet
                 neverthelesse
                 compressing
                 the
                 first
                 Air
                 with
                 force
                 and
                 violence
                 ,
                 it
                 is
                 reduced
                 into
                 far
                 less
                 room
                 ,
                 and
                 will
                 admit
                 four
                 or
                 six
                 times
                 as
                 much
                 air
                 ,
                 as
                 before
                 ,
                 as
                 is
                 experimentally
                 *
                 seen
                 in
                 the
                 Wind-Gun
                 ,
                 invented
                 in
                 our
                 dayes
                 by
                 
                   M.
                   Vincenzo
                   Vincenti
                
                 of
                 Vrbin
                 ,
                 which
                 property
                 of
                 the
                 Air
                 of
                 admitting
                 condensation
                 ,
                 is
                 also
                 seen
                 in
                 the
                 portable
                 Fountains
                 of
                 the
                 same
                 
                   M.
                   Vincenzo
                
                 :
                 which
                 Fountains
                 spirt
                 the
                 Water
                 on
                 high
                 ,
                 by
                 force
                 of
                 the
                 Air
                 compressed
                 ,
                 which
                 whilst
                 it
                 seeks
                 to
                 reduce
                 its
                 self
                 to
                 its
                 natural
                 constitution
                 ,
                 in
                 the
                 dilation
                 causeth
                 that
                 violence
                 .
                 But
                 the
                 water
                 can
                 never
                 ,
                 for
                 any
                 thing
                 I
                 know
                 ,
                 crowd
                 ,
                 or
                 press
                 so
                 ,
                 as
                 that
                 if
                 before
                 the
                 compression
                 it
                 held
                 or
                 possest
                 a
                 place
                 ,
                 being
                 in
                 its
                 natural
                 constitution
                 ,
                 I
                 believe
                 not
                 ,
                 I
                 say
                 ,
                 that
                 it
                 is
                 possible
                 ,
                 by
                 pressing
                 and
                 crowding
                 to
                 make
                 it
                 possess
                 less
                 room
                 ,
                 for
                 if
                 it
                 were
                 possible
                 to
                 compress
                 the
                 Water
                 ,
                 and
                 make
                 it
                 to
                 occupy
                 a
                 less
                 place
                 ,
                 it
                 would
                 thence
                 follow
                 ,
                 that
                 two
                 Vessels
                 of
                 equal
                 measure
                 ,
                 but
                 of
                 unequal
                 height
                 ,
                 should
                 be
                 of
                 unequal
                 capacity
                 ,
                 and
                 that
                 should
                 hold
                 more
                 water
                 which
                 was
                 higher
                 ;
                 also
                 a
                 Cylinder
                 ,
                 or
                 other
                 Vessel
                 more
                 high
                 than
                 broad
                 ,
                 would
                 containe
                 more
                 water
                 erected
                 ,
                 than
                 being
                 laid
                 along
                 ;
                 for
                 that
                 being
                 erected
                 ,
                 
                 the
                 water
                 put
                 therein
                 would
                 be
                 more
                 pressed
                 and
                 crowded
                 .
              
               
                 And
                 therefore
                 ,
                 in
                 our
                 case
                 ,
                 according
                 to
                 our
                 principles
                 we
                 will
                 say
                 ,
                 that
                 the
                 water
                 of
                 that
                 Stream
                 passeth
                 all
                 under
                 the
                 said
                 Bridge
                 Quattro-Capi
                 ,
                 for
                 that
                 being
                 there
                 most
                 swift
                 ,
                 it
                 ought
                 of
                 consequence
                 to
                 be
                 less
                 in
                 measure
                 .
              
               
                 And
                 here
                 one
                 may
                 see
                 ,
                 into
                 how
                 many
                 errours
                 a
                 man
                 may
                 run
                 through
                 ignorance
                 of
                 a
                 true
                 and
                 real
                 Principle
                 ,
                 which
                 once
                 known
                 and
                 well
                 understood
                 ,
                 takes
                 away
                 all
                 mists
                 of
                 doubting
                 ,
                 and
                 easily
                 resolveth
                 all
                 difficulties
                 .
              
            
             
               
                 COROLLARIE
                 .
                 XII
                 .
              
               
                 THrough
                 the
                 same
                 inadvertency
                 of
                 not
                 regarding
                 the
                 variation
                 of
                 velocity
                 in
                 the
                 same
                 Current
                 ,
                 there
                 are
                 committed
                 by
                 Ingineers
                 and
                 Learned
                 men
                 ,
                 errours
                 of
                 very
                 great
                 moment
                 (
                 and
                 I
                 could
                 thereof
                 produce
                 examples
                 ,
                 but
                 for
                 good
                 reasons
                 I
                 pass
                 them
                 over
                 in
                 silence
                 )
                 when
                 they
                 think
                 ,
                 and
                 propose
                 ,
                 by
                 deriving
                 new
                 Channels
                 from
                 great
                 Rivers
                 ,
                 to
                 diminish
                 the
                 measure
                 of
                 the
                 water
                 in
                 the
                 River
                 ,
                 and
                 to
                 diminish
                 it
                 proportionally
                 ,
                 according
                 to
                 the
                 measure
                 of
                 the
                 Water
                 which
                 they
                 make
                 to
                 pass
                 through
                 the
                 Channel
                 ,
                 as
                 making
                 v.g.
                 a
                 Channel
                 fifty
                 foot
                 broad
                 ,
                 in
                 which
                 the
                 derived
                 water
                 is
                 to
                 run
                 waste
                 ,
                 ten
                 foot
                 deep
                 ,
                 they
                 think
                 they
                 have
                 diminished
                 the
                 measure
                 of
                 the
                 Water
                 in
                 the
                 River
                 five
                 hundred
                 feet
                 ,
                 which
                 thing
                 doth
                 not
                 indeed
                 so
                 fall
                 out
                 ;
                 and
                 the
                 reason
                 is
                 plain
                 ;
                 for
                 that
                 the
                 Chanel
                 being
                 derived
                 ,
                 the
                 rest
                 of
                 the
                 main
                 River
                 ,
                 diminisheth
                 in
                 velocity
                 ,
                 and
                 therefore
                 retains
                 a
                 greater
                 measure
                 than
                 it
                 had
                 at
                 first
                 before
                 the
                 derivation
                 of
                 the
                 Chanel
                 ;
                 and
                 moreover
                 ,
                 if
                 the
                 Chanel
                 being
                 derived
                 ,
                 it
                 shall
                 not
                 conserve
                 the
                 same
                 velocity
                 which
                 it
                 had
                 at
                 first
                 in
                 the
                 main
                 River
                 ,
                 but
                 shall
                 diminish
                 it
                 ,
                 it
                 will
                 be
                 necessary
                 ,
                 that
                 it
                 hath
                 a
                 greater
                 measure
                 than
                 it
                 had
                 before
                 in
                 the
                 River
                 ;
                 and
                 therefore
                 to
                 accompt
                 aright
                 ,
                 there
                 shall
                 not
                 be
                 so
                 much
                 water
                 derived
                 into
                 the
                 Channel
                 ,
                 as
                 shall
                 diminish
                 the
                 River
                 ,
                 according
                 to
                 the
                 quantity
                 of
                 the
                 water
                 in
                 the
                 Channel
                 ,
                 as
                 is
                 pretended
                 .
              
            
             
               
                 COROLLARIE
                 .
                 XIII
                 .
              
               
                 THis
                 same
                 consideration
                 giveth
                 me
                 occasion
                 to
                 discover
                 a
                 most
                 ordinary
                 errour
                 ,
                 observed
                 by
                 me
                 in
                 the
                 businesse
                 of
                 the
                 water
                 of
                 Ferara
                 ,
                 when
                 I
                 was
                 in
                 those
                 parts
                 ,
                 in
                 service
                 of
                 the
                 most
                 Reverend
                 and
                 Illustrious
                 Monsignor
                 Corsini
                 ;
                 the
                 sublime
                 wit
                 of
                 whom
                 hath
                 been
                 a
                 very
                 great
                 help
                 to
                 me
                 in
                 these
                 contemplations
                 ;
                 it
                 s
                 very
                 true
                 ,
                 I
                 have
                 been
                 much
                 perplexed
                 ,
                 whether
                 I
                 should
                 commit
                 this
                 particular
                 to
                 paper
                 ,
                 or
                 passe
                 it
                 over
                 in
                 silence
                 ,
                 for
                 that
                 I
                 have
                 ever
                 doubted
                 ,
                 that
                 the
                 opinion
                 so
                 common
                 and
                 
                 moreover
                 confirmed
                 with
                 a
                 most
                 manifest
                 experiment
                 ,
                 may
                 not
                 onely
                 make
                 this
                 my
                 conjecture
                 to
                 be
                 esteemed
                 far
                 from
                 true
                 ,
                 but
                 also
                 to
                 discredit
                 with
                 the
                 World
                 the
                 rest
                 of
                 this
                 my
                 Treatise
                 :
                 Neverthelesse
                 I
                 have
                 at
                 last
                 resolved
                 not
                 to
                 be
                 wanting
                 to
                 my self
                 ,
                 and
                 to
                 truth
                 in
                 a
                 matter
                 of
                 it self
                 ,
                 and
                 for
                 other
                 consequences
                 most
                 important
                 ;
                 nor
                 doth
                 it
                 seem
                 to
                 me
                 requisite
                 in
                 difficult
                 matters
                 ,
                 such
                 as
                 these
                 we
                 have
                 in
                 hand
                 ,
                 to
                 resigne
                 our selves
                 to
                 the
                 common
                 opinion
                 ,
                 since
                 it
                 would
                 be
                 very
                 strange
                 if
                 the
                 multitude
                 in
                 such
                 matters
                 should
                 hit
                 on
                 the
                 truth
                 ,
                 nor
                 ought
                 that
                 to
                 be
                 held
                 difficult
                 ,
                 in
                 which
                 even
                 the
                 vulgar
                 do
                 know
                 the
                 truth
                 and
                 right
                 ;
                 besides
                 that
                 I
                 hope
                 moreover
                 to
                 prove
                 all
                 in
                 such
                 sort
                 ,
                 that
                 persons
                 of
                 solid
                 judgment
                 ,
                 shall
                 rest
                 fully
                 perswaded
                 ,
                 so
                 that
                 they
                 but
                 keep
                 in
                 mind
                 the
                 principal
                 ground
                 and
                 foundation
                 of
                 all
                 this
                 Treatise
                 ;
                 and
                 though
                 that
                 which
                 I
                 will
                 propose
                 ,
                 be
                 a
                 particular
                 ,
                 as
                 I
                 have
                 said
                 ,
                 pertaining
                 onely
                 to
                 the
                 interests
                 of
                 Ferara
                 ;
                 yet
                 neverthelesse
                 from
                 this
                 particular
                 Doctrine
                 well
                 understood
                 ,
                 good
                 judgement
                 may
                 be
                 made
                 of
                 other
                 the
                 like
                 cases
                 in
                 general
                 .
              
               
                 I
                 say
                 then
                 ,
                 for
                 greater
                 perspecuity
                 ,
                 and
                 better
                 understanding
                 of
                 the
                 whole
                 ,
                 That
                 about
                 thirteen
                 miles
                 above
                 Ferara
                 ,
                 near
                 to
                 Stellata
                 ,
                 the
                 main
                 of
                 Po
                 ,
                 branching
                 it self
                 into
                 two
                 parts
                 ,
                 with
                 one
                 of
                 its
                 Arms
                 it
                 cometh
                 close
                 to
                 Ferara
                 ,
                 retaining
                 the
                 name
                 of
                 the
                 Po
                 of
                 Ferara
                 ;
                 and
                 here
                 again
                 it
                 divideth
                 it self
                 into
                 two
                 other
                 branches
                 ,
                 and
                 that
                 which
                 continueth
                 on
                 the
                 right
                 hand
                 ,
                 is
                 called
                 the
                 Po
                 of
                 Argenta
                 ,
                 and
                 of
                 Primaro
                 ;
                 and
                 that
                 on
                 the
                 left
                 the
                 Po
                 of
                 Volana
                 .
                 But
                 for
                 that
                 the
                 bed
                 of
                 the
                 Po
                 of
                 Ferara
                 being
                 heretofore
                 augmented
                 and
                 raised
                 ,
                 it
                 followeth
                 that
                 it
                 resteth
                 wholly
                 deprived
                 of
                 the
                 Water
                 of
                 the
                 great
                 Po
                 ,
                 except
                 in
                 the
                 time
                 of
                 its
                 greater
                 swelling
                 ;
                 for
                 in
                 that
                 case
                 ,
                 this
                 Po
                 of
                 Ferara
                 being
                 restrained
                 with
                 a
                 Bank
                 near
                 to
                 Bondeno
                 ,
                 would
                 come
                 also
                 in
                 the
                 overflowings
                 of
                 the
                 main
                 Po
                 ,
                 to
                 be
                 free
                 from
                 its
                 Waters
                 :
                 But
                 the
                 Lords
                 of
                 Ferara
                 are
                 wont
                 at
                 such
                 time
                 as
                 the
                 Po
                 threateneth
                 to
                 break
                 out
                 ,
                 to
                 cut
                 the
                 bank
                 ;
                 by
                 which
                 cutting
                 ,
                 there
                 disgorgeth
                 such
                 a
                 Torrent
                 of
                 Water
                 ,
                 that
                 it
                 is
                 observed
                 ,
                 that
                 the
                 main
                 Po
                 in
                 the
                 space
                 of
                 some
                 few
                 hours
                 abateth
                 near
                 a
                 foot
                 ,
                 and
                 all
                 persons
                 that
                 I
                 have
                 spoken
                 with
                 hitherto
                 ,
                 moved
                 by
                 this
                 experiment
                 ,
                 think
                 that
                 it
                 is
                 of
                 great
                 profit
                 and
                 benefit
                 to
                 keep
                 ready
                 this
                 Vent
                 ,
                 and
                 to
                 make
                 use
                 of
                 it
                 in
                 the
                 time
                 of
                 its
                 fullnesse
                 .
                 And
                 indeed
                 ,
                 the
                 thing
                 considered
                 simply
                 ,
                 and
                 at
                 the
                 first
                 appearance
                 ,
                 it
                 seemeth
                 that
                 none
                 can
                 think
                 otherwise
                 ;
                 the
                 rather
                 ,
                 for
                 that
                 many
                 examining
                 the
                 matter
                 narrowly
                 ,
                 measure
                 that
                 body
                 of
                 Water
                 which
                 runneth
                 by
                 the
                 Channel
                 ,
                 or
                 Bed
                 of
                 the
                 Po
                 of
                 Ferara
                 ,
                 and
                 make
                 account
                 ,
                 that
                 the
                 body
                 of
                 the
                 Water
                 of
                 the
                 great
                 Po
                 ,
                 is
                 diminished
                 the
                 quantity
                 of
                 the
                 body
                 of
                 the
                 Water
                 which
                 runneth
                 by
                 the
                 Po
                 of
                 Ferara
                 .
                 But
                 if
                 we
                 well
                 remember
                 what
                 hath
                 been
                 said
                 in
                 the
                 beginning
                 of
                 the
                 Treatise
                 ,
                 and
                 how
                 much
                 
                 the
                 variety
                 of
                 the
                 velocities
                 of
                 the
                 said
                 Water
                 importeth
                 ,
                 and
                 the
                 knowledge
                 of
                 them
                 is
                 necessary
                 to
                 conclude
                 the
                 true
                 quantity
                 of
                 the
                 running
                 Water
                 ,
                 we
                 shall
                 finde
                 it
                 manifest
                 ,
                 that
                 the
                 benefit
                 of
                 this
                 Vent
                 is
                 far
                 lesse
                 than
                 it
                 is
                 generally
                 thought
                 :
                 And
                 mereover
                 ,
                 we
                 shall
                 finde
                 ,
                 if
                 I
                 deceive
                 not
                 my self
                 ,
                 that
                 there
                 follow
                 from
                 thence
                 so
                 many
                 mischiefs
                 ,
                 that
                 I
                 could
                 greatly
                 incline
                 to
                 believe
                 ,
                 that
                 it
                 were
                 more
                 to
                 the
                 purpose
                 wholly
                 to
                 stop
                 it
                 up
                 ,
                 than
                 to
                 maintain
                 it
                 open
                 :
                 yet
                 I
                 am
                 not
                 so
                 wedded
                 to
                 my
                 opinion
                 ,
                 but
                 that
                 I
                 am
                 ready
                 to
                 change
                 my
                 judgement
                 upon
                 strength
                 of
                 better
                 reasons
                 ;
                 especially
                 of
                 one
                 that
                 shall
                 have
                 first
                 well
                 understood
                 the
                 beginning
                 of
                 this
                 my
                 discourse
                 ,
                 which
                 I
                 frequently
                 inculcate
                 ,
                 because
                 it
                 s
                 absolutely
                 impossible
                 without
                 this
                 advertisement
                 to
                 treat
                 of
                 these
                 matters
                 ,
                 and
                 not
                 commit
                 very
                 great
                 errours
                 .
              
               
                 I
                 propose
                 therefore
                 to
                 consideration
                 ,
                 that
                 although
                 it
                 be
                 true
                 ,
                 that
                 whilst
                 the
                 water
                 of
                 the
                 main
                 Po
                 is
                 at
                 its
                 greatest
                 height
                 ,
                 the
                 Bank
                 and
                 Dam
                 then
                 cut
                 of
                 the
                 Po
                 of
                 Ferara
                 ,
                 and
                 the
                 superior
                 waters
                 having
                 a
                 very
                 great
                 fall
                 into
                 the
                 Channel
                 of
                 Ferara
                 ,
                 they
                 precipitate
                 into
                 the
                 same
                 with
                 great
                 violence
                 and
                 velocity
                 ,
                 and
                 with
                 the
                 same
                 in
                 the
                 beginning
                 ,
                 or
                 little
                 lesse
                 ,
                 they
                 run
                 towards
                 the
                 Po
                 of
                 Volana
                 ,
                 and
                 of
                 Argenta
                 on
                 the
                 sea
                 coasts
                 ;
                 yet
                 after
                 the
                 space
                 of
                 some
                 few
                 hours
                 ,
                 the
                 Po
                 of
                 Ferara
                 being
                 full
                 ,
                 and
                 the
                 superior
                 Waters
                 not
                 finding
                 so
                 great
                 a
                 diclivity
                 there
                 ,
                 as
                 they
                 had
                 at
                 the
                 beginning
                 of
                 the
                 cutting
                 ,
                 they
                 fall
                 not
                 into
                 the
                 same
                 with
                 the
                 former
                 velocity
                 ,
                 but
                 with
                 far
                 lesse
                 ,
                 and
                 thereby
                 a
                 great
                 deal
                 lesse
                 Water
                 begins
                 to
                 issue
                 from
                 the
                 great
                 Po
                 ;
                 and
                 if
                 we
                 diligently
                 compare
                 the
                 velocity
                 at
                 the
                 first
                 cutting
                 ,
                 with
                 the
                 velocity
                 of
                 the
                 Water
                 after
                 the
                 cutting
                 made
                 ,
                 and
                 when
                 the
                 Po
                 of
                 Ferara
                 shall
                 be
                 full
                 of
                 Water
                 ,
                 we
                 shall
                 finde
                 perhaps
                 that
                 to
                 be
                 fifteen
                 or
                 twenty
                 times
                 greater
                 than
                 this
                 ,
                 and
                 consequently
                 the
                 Water
                 which
                 issues
                 from
                 the
                 great
                 Po
                 ,
                 that
                 first
                 impetuosity
                 being
                 past
                 ,
                 shall
                 be
                 onely
                 the
                 fifteenth
                 or
                 twentieth
                 part
                 of
                 that
                 which
                 issued
                 at
                 the
                 beginning
                 ;
                 and
                 therefore
                 the
                 Waters
                 of
                 the
                 main
                 Po
                 will
                 return
                 in
                 a
                 small
                 time
                 almost
                 to
                 the
                 first
                 height
                 .
                 And
                 here
                 I
                 will
                 pray
                 those
                 who
                 rest
                 not
                 wholly
                 satisfied
                 with
                 what
                 hath
                 been
                 said
                 ,
                 that
                 for
                 the
                 love
                 of
                 truth
                 ,
                 and
                 the
                 common
                 good
                 ,
                 they
                 would
                 please
                 to
                 make
                 diligent
                 observation
                 whether
                 in
                 the
                 time
                 of
                 great
                 Floods
                 ,
                 the
                 said
                 Bank
                 or
                 Dam
                 at
                 Bondeno
                 is
                 cut
                 ,
                 and
                 that
                 in
                 few
                 hours
                 the
                 main
                 Po
                 diminisheth
                 ,
                 as
                 hath
                 been
                 said
                 about
                 a
                 foot
                 in
                 its
                 height
                 ;
                 that
                 they
                 would
                 observe
                 I
                 say
                 ,
                 whether
                 ,
                 a
                 day
                 or
                 two
                 being
                 past
                 ,
                 the
                 Waters
                 of
                 the
                 main
                 Po
                 return
                 almost
                 to
                 their
                 first
                 height
                 ;
                 for
                 if
                 this
                 should
                 follow
                 ,
                 it
                 would
                 be
                 very
                 clear
                 ,
                 that
                 the
                 benefit
                 which
                 resulteth
                 from
                 this
                 diversion
                 or
                 Vent
                 ,
                 is
                 not
                 so
                 great
                 as
                 is
                 universally
                 presumed
                 ;
                 I
                 say
                 ,
                 it
                 is
                 not
                 so
                 great
                 as
                 is
                 presumed
                 ;
                 because
                 ,
                 though
                 it
                 be
                 granted
                 for
                 true
                 ,
                 that
                 the
                 Waters
                 of
                 the
                 main
                 Po
                 ,
                 abate
                 at
                 the
                 beginning
                 of
                 
                 the
                 Vent
                 ,
                 yet
                 this
                 benefit
                 happens
                 to
                 be
                 but
                 temporary
                 and
                 for
                 a
                 few
                 hours
                 :
                 If
                 the
                 rising
                 of
                 Po
                 ,
                 and
                 the
                 dangers
                 of
                 breaking
                 forth
                 were
                 of
                 short
                 duration
                 ,
                 as
                 it
                 ordinarily
                 befalleth
                 in
                 the
                 overflowings
                 of
                 Torrents
                 ,
                 in
                 such
                 a
                 case
                 the
                 profit
                 of
                 the
                 Vent
                 would
                 be
                 of
                 some
                 esteem
                 :
                 But
                 because
                 the
                 swellings
                 of
                 Po
                 continue
                 for
                 thirty
                 ,
                 or
                 sometimes
                 for
                 forty
                 dayes
                 ,
                 therefore
                 the
                 gain
                 which
                 results
                 from
                 the
                 Vent
                 proveth
                 to
                 be
                 inconsiderable
                 .
                 It
                 remaineth
                 now
                 to
                 consider
                 the
                 notable
                 harms
                 which
                 follow
                 the
                 said
                 Sluice
                 or
                 Vent
                 ,
                 that
                 so
                 reflection
                 being
                 made
                 ,
                 and
                 the
                 profit
                 and
                 the
                 detriment
                 compared
                 ,
                 one
                 may
                 rightly
                 judge
                 ,
                 and
                 choose
                 that
                 which
                 shall
                 be
                 most
                 convenient
                 .
                 The
                 first
                 prejudice
                 therefore
                 which
                 ariseth
                 from
                 this
                 Vent
                 or
                 Sluice
                 ,
                 is
                 ;
                 That
                 the
                 Channels
                 of
                 
                   Ferara
                   ,
                   Primaro
                
                 ,
                 and
                 Volana
                 filling
                 with
                 Water
                 ,
                 all
                 those
                 parts
                 from
                 Bondeno
                 to
                 the
                 Sea
                 side
                 are
                 allarmed
                 and
                 endangered
                 thereby
                 .
                 Secondly
                 ,
                 The
                 Waters
                 of
                 the
                 Po
                 of
                 Primaro
                 having
                 free
                 ingresse
                 into
                 the
                 upper
                 Valleys
                 ,
                 they
                 fill
                 them
                 to
                 the
                 great
                 damage
                 of
                 the
                 Fields
                 adjacent
                 ,
                 and
                 obstruct
                 the
                 course
                 of
                 the
                 ordinary
                 Trenches
                 in
                 the
                 same
                 Valleys
                 ;
                 insomuch
                 that
                 all
                 the
                 care
                 ,
                 cost
                 ,
                 and
                 labour
                 about
                 the
                 draining
                 ,
                 and
                 freeing
                 the
                 upper
                 Valleys
                 from
                 Water
                 ,
                 would
                 also
                 become
                 vain
                 and
                 ineffectual
                 .
                 Thirdly
                 ,
                 I
                 consider
                 that
                 these
                 Waters
                 of
                 the
                 Po
                 of
                 Ferara
                 being
                 passed
                 downwards
                 towards
                 the
                 Sea
                 ,
                 at
                 the
                 time
                 that
                 the
                 main
                 Po
                 was
                 in
                 its
                 greater
                 excrescences
                 and
                 heights
                 ,
                 it
                 is
                 manifest
                 by
                 experience
                 ,
                 that
                 when
                 the
                 great
                 Po
                 diminisheth
                 ,
                 then
                 these
                 Waters
                 passed
                 by
                 the
                 Po
                 of
                 Ferara
                 begin
                 to
                 retard
                 in
                 their
                 course
                 ,
                 and
                 finally
                 come
                 to
                 turn
                 the
                 current
                 upwards
                 towards
                 Stellata
                 ,
                 resting
                 first
                 in
                 the
                 intermediate
                 time
                 ,
                 almost
                 fixed
                 and
                 standing
                 ,
                 and
                 therefore
                 deposing
                 the
                 muddinesse
                 ,
                 they
                 fill
                 up
                 the
                 Channel
                 of
                 the
                 River
                 or
                 Current
                 of
                 Ferara
                 .
                 Fourthly
                 and
                 lastly
                 ,
                 There
                 followeth
                 from
                 this
                 same
                 diversion
                 another
                 notable
                 damage
                 ,
                 and
                 it
                 is
                 like
                 to
                 that
                 which
                 followeth
                 the
                 breaches
                 made
                 by
                 Rivers
                 ;
                 near
                 to
                 which
                 breaches
                 in
                 the
                 lower
                 parts
                 ,
                 namely
                 below
                 the
                 breach
                 ,
                 there
                 is
                 begot
                 in
                 the
                 Channel
                 of
                 the
                 River
                 ,
                 a
                 certain
                 ridge
                 or
                 shelf
                 ,
                 that
                 is
                 ,
                 the
                 bottom
                 of
                 the
                 River
                 is
                 raised
                 ,
                 as
                 is
                 sufficiently
                 manifest
                 by
                 experience
                 ;
                 and
                 thus
                 just
                 in
                 the
                 same
                 manner
                 cutting
                 the
                 Bank
                 at
                 Bondeno
                 ,
                 there
                 is
                 at
                 it
                 were
                 a
                 breach
                 made
                 ,
                 from
                 which
                 followeth
                 the
                 rising
                 in
                 the
                 lower
                 parts
                 of
                 the
                 main
                 Po
                 ,
                 being
                 past
                 the
                 mouth
                 of
                 Pamaro
                 ;
                 which
                 thing
                 ,
                 how
                 pernitious
                 it
                 is
                 ,
                 let
                 any
                 one
                 judge
                 that
                 understandeth
                 these
                 matters
                 .
                 And
                 therefore
                 both
                 for
                 the
                 small
                 benefit
                 ,
                 and
                 so
                 many
                 harms
                 that
                 ensue
                 from
                 maintaining
                 this
                 diversion
                 ,
                 I
                 should
                 think
                 it
                 were
                 more
                 sound
                 advice
                 to
                 keep
                 that
                 Bank
                 alwaies
                 whole
                 at
                 Bondeno
                 ,
                 or
                 in
                 any
                 other
                 convenient
                 place
                 ,
                 and
                 not
                 to
                 permit
                 that
                 the
                 Water
                 of
                 the
                 Grand
                 Po
                 should
                 ever
                 come
                 near
                 to
                 Ferara
                 .
              
            
             
               
               
                 COROLLARIE
                 XIV
                 .
              
               
                 IN
                 the
                 Grand
                 Rivers
                 ,
                 which
                 fall
                 into
                 the
                 Sea
                 ,
                 as
                 here
                 in
                 
                   Italy
                   Po
                   ,
                   Adige
                
                 ,
                 *
                 and
                 Arno
                 ,
                 which
                 are
                 armed
                 with
                 Banks
                 against
                 their
                 excrescencies
                 ,
                 it
                 s
                 observed
                 that
                 far
                 from
                 the
                 Sea
                 ,
                 they
                 need
                 Banks
                 of
                 a
                 notable
                 height
                 ;
                 which
                 height
                 goeth
                 afterwards
                 by
                 degrees
                 diminishing
                 ,
                 the
                 more
                 it
                 approacheth
                 to
                 the
                 Sea-coasts
                 :
                 in
                 such
                 sort
                 ,
                 that
                 the
                 Po
                 ,
                 distant
                 from
                 the
                 Sea
                 about
                 fifty
                 or
                 sixty
                 miles
                 at
                 Ferara
                 ,
                 shall
                 have
                 Banks
                 that
                 be
                 above
                 twenty
                 feet
                 higher
                 than
                 the
                 ordinary
                 Water-marks
                 ;
                 but
                 ten
                 or
                 twelve
                 miles
                 from
                 the
                 Sea
                 ,
                 the
                 Banks
                 are
                 not
                 twelve
                 feet
                 higher
                 than
                 the
                 said
                 ordinary
                 Water-marks
                 ,
                 though
                 the
                 breadth
                 of
                 the
                 River
                 be
                 the
                 same
                 ,
                 so
                 that
                 the
                 excrescence
                 of
                 the
                 same
                 Innundation
                 happens
                 to
                 be
                 far
                 greater
                 in
                 measure
                 remote
                 from
                 the
                 Sea
                 ,
                 then
                 near
                 ;
                 and
                 yet
                 it
                 should
                 seem
                 ,
                 that
                 the
                 same
                 quantity
                 of
                 Water
                 passing
                 by
                 every
                 place
                 ,
                 the
                 River
                 should
                 need
                 to
                 have
                 the
                 same
                 altitude
                 of
                 Banks
                 in
                 all
                 places
                 :
                 But
                 we
                 by
                 our
                 Principles
                 and
                 fundamentals
                 may
                 be
                 able
                 to
                 render
                 the
                 reason
                 of
                 that
                 effect
                 ,
                 and
                 say
                 ;
                 That
                 that
                 excesse
                 of
                 quantity
                 of
                 Water
                 ,
                 above
                 the
                 ordinary
                 Water
                 ,
                 goeth
                 alwaies
                 acquiring
                 greater
                 velocity
                 ;
                 the
                 nearer
                 it
                 approacheth
                 the
                 Sea
                 ,
                 and
                 therefore
                 decreaseth
                 in
                 measure
                 ,
                 and
                 consequenly
                 in
                 height
                 .
                 And
                 this
                 perhaps
                 might
                 have
                 been
                 the
                 cause
                 in
                 great
                 part
                 ,
                 why
                 the
                 Tyber
                 in
                 the
                 Innundation
                 Anno
                 1578.
                 issued
                 not
                 forth
                 of
                 its
                 Channel
                 below
                 Rome
                 towards
                 the
                 Sea.
                 
              
            
             
               
                 COROLLARIE
                 XV.
                 
              
               
                 FRom
                 the
                 same
                 Doctrine
                 may
                 be
                 rendred
                 a
                 most
                 manifest
                 reason
                 why
                 the
                 falling
                 Waters
                 go
                 lessening
                 in
                 their
                 descent
                 ,
                 so
                 that
                 the
                 same
                 falling
                 Water
                 ,
                 measured
                 at
                 the
                 beginning
                 of
                 its
                 fall
                 ,
                 is
                 greater
                 ,
                 and
                 bigger
                 ,
                 and
                 afterwards
                 by
                 degrees
                 lesseneth
                 in
                 measure
                 the
                 more
                 it
                 is
                 remote
                 from
                 the
                 beginning
                 of
                 the
                 fall
                 .
                 Which
                 dependeth
                 on
                 no
                 other
                 ,
                 than
                 on
                 the
                 acquisition
                 ,
                 which
                 it
                 successively
                 makes
                 of
                 greater
                 velocity
                 ;
                 it
                 being
                 a
                 most
                 familiar
                 conclusion
                 among
                 Philosophers
                 ,
                 that
                 grave
                 bodies
                 falling
                 ,
                 the
                 more
                 they
                 remove
                 from
                 the
                 beginning
                 of
                 their
                 motion
                 ,
                 the
                 more
                 they
                 acquire
                 of
                 swiftnesse
                 ;
                 and
                 therefore
                 the
                 Water
                 ,
                 as
                 a
                 grave
                 body
                 ,
                 falling
                 ,
                 gradually
                 velocitates
                 ,
                 and
                 therefore
                 decreaseth
                 in
                 measure
                 ,
                 and
                 lesseneth
                 .
              
            
             
               
                 COROLLARIE
                 XVI
                 .
              
               
                 ANd
                 on
                 the
                 contrary
                 ,
                 the
                 spirtings
                 of
                 a
                 Fountain
                 of
                 Water
                 ,
                 which
                 spring
                 on
                 high
                 ,
                 work
                 a
                 contrary
                 effect
                 ;
                 namely
                 
                 in
                 the
                 beginning
                 they
                 are
                 small
                 ,
                 and
                 afterwards
                 become
                 greater
                 and
                 bigge
                 ;
                 and
                 the
                 reason
                 is
                 most
                 manifest
                 ,
                 because
                 in
                 the
                 beginning
                 they
                 are
                 very
                 swift
                 ,
                 and
                 afterwards
                 gradually
                 relent
                 their
                 impetuosity
                 ,
                 and
                 motion
                 ,
                 so
                 that
                 in
                 the
                 beginning
                 of
                 the
                 excursion
                 that
                 they
                 make
                 ,
                 they
                 ought
                 to
                 be
                 small
                 ,
                 and
                 afterwards
                 to
                 grow
                 bigger
                 ,
                 as
                 in
                 the
                 effect
                 is
                 seen
                 .
              
            
             
               
                 APPENDIX
                 I.
                 
              
               
                 INto
                 the
                 errour
                 of
                 not
                 considering
                 how
                 much
                 the
                 different
                 velocities
                 of
                 the
                 same
                 running
                 water
                 in
                 several
                 places
                 of
                 its
                 current
                 ,
                 are
                 able
                 to
                 change
                 the
                 measure
                 of
                 the
                 same
                 water
                 ,
                 and
                 to
                 make
                 it
                 greater
                 ;
                 or
                 lesse
                 ,
                 I
                 think
                 ,
                 if
                 I
                 be
                 not
                 deceived
                 ,
                 that
                 
                   Giulio
                   Frontino
                
                 a
                 noble
                 antient
                 Writer
                 ,
                 may
                 have
                 faln
                 in
                 the
                 Second
                 Book
                 which
                 he
                 writ
                 ,
                 of
                 the
                 Aqueducts
                 of
                 the
                 City
                 of
                 Rome
                 :
                 Whilst
                 finding
                 the
                 measure
                 of
                 the
                 Water
                 *
                 Commentariis
                 lesse
                 than
                 it
                 was
                 
                   in
                   erogatione
                
                 1263.
                 
                 Quinaries
                 ,
                 he
                 thought
                 that
                 so
                 much
                 difference
                 might
                 proceed
                 from
                 the
                 negligence
                 of
                 the
                 Measures
                 ,
                 and
                 when
                 afterwards
                 with
                 his
                 own
                 industry
                 he
                 measured
                 the
                 same
                 water
                 at
                 the
                 beginnings
                 of
                 the
                 Aqueducts
                 ,
                 finding
                 it
                 neer
                 10000.
                 
                 Quinaries
                 bigger
                 than
                 it
                 was
                 
                   in
                   Commentariis
                
                 he
                 judged
                 ,
                 that
                 the
                 overplus
                 was
                 imbeziled
                 by
                 Ministers
                 and
                 Partakers
                 ;
                 which
                 in
                 part
                 might
                 be
                 so
                 ,
                 for
                 it
                 is
                 but
                 too
                 true
                 ,
                 that
                 the
                 publique
                 is
                 almost
                 alwayes
                 defrauded
                 ;
                 yet
                 neverthelesse
                 ,
                 I
                 verily
                 believe
                 withal
                 ,
                 that
                 besides
                 the
                 frauds
                 of
                 these
                 Officers
                 ,
                 the
                 velocities
                 of
                 the
                 water
                 in
                 the
                 place
                 wherein
                 Frontino
                 measured
                 ,
                 it
                 might
                 be
                 different
                 from
                 those
                 velocities
                 ,
                 which
                 are
                 found
                 in
                 other
                 places
                 before
                 measured
                 by
                 others
                 ;
                 and
                 therefore
                 the
                 measures
                 of
                 the
                 waters
                 might
                 ,
                 yea
                 ought
                 necessarily
                 to
                 be
                 different
                 ,
                 it
                 having
                 been
                 by
                 us
                 demonstrated
                 ,
                 that
                 the
                 measures
                 of
                 the
                 same
                 running
                 water
                 have
                 reciprocal
                 proportion
                 to
                 their
                 velocities
                 .
                 Which
                 Frontino
                 not
                 well
                 considering
                 ,
                 and
                 finding
                 the
                 water
                 
                   in
                   Commentariis
                
                 12755.
                 
                 
                   Quinaries
                   in
                   erogatione
                
                 14018
                 ,
                 and
                 in
                 his
                 own
                 measure
                 
                   ad
                   capita
                   ductuum
                
                 ,
                 at
                 the
                 head
                 of
                 the
                 fountain
                 22755.
                 
                 Quinaries
                 ,
                 or
                 thereabouts
                 ,
                 he
                 thought
                 ,
                 that
                 in
                 all
                 these
                 places
                 there
                 past
                 different
                 quantities
                 of
                 water
                 ;
                 namely
                 ,
                 greater
                 at
                 the
                 fountain
                 head
                 then
                 that
                 which
                 was
                 
                   in
                   Erogatione
                
                 ,
                 and
                 this
                 he
                 judged
                 greater
                 than
                 that
                 which
                 was
                 
                   in
                   Commentariis
                
                 .
              
            
             
               
                 APPENDIX
                 II.
                 
              
               
                 A
                 Like
                 mistake
                 chanced
                 lately
                 in
                 the
                 Aqueduct
                 of
                 Acqua-Paola
                 ,
                 which
                 Water
                 should
                 be
                 2000
                 Inches
                 ,
                 and
                 so
                 many
                 effectively
                 ought
                 to
                 be
                 allowed
                 ;
                 and
                 it
                 hath
                 been
                 given
                 in
                 
                 so
                 to
                 be
                 by
                 the
                 Signors
                 of
                 Bracciano
                 to
                 the
                 Apostolick-Chamber
                 ;
                 and
                 there
                 was
                 a
                 measure
                 thereof
                 made
                 at
                 the
                 beginning
                 of
                 the
                 Aqueduct
                 ;
                 which
                 measure
                 proved
                 afterwards
                 much
                 lesse
                 and
                 short
                 ,
                 considered
                 and
                 taken
                 in
                 Rome
                 ,
                 and
                 thence
                 followed
                 discontents
                 and
                 great
                 disorders
                 ,
                 and
                 all
                 because
                 this
                 property
                 of
                 Running-Waters
                 ,
                 of
                 increasing
                 in
                 measure
                 ,
                 where
                 the
                 velocity
                 decreased
                 ;
                 and
                 of
                 diminishing
                 in
                 measure
                 ,
                 where
                 the
                 velocity
                 augmented
                 ,
                 was
                 not
                 lookt
                 into
                 .
              
            
             
               
                 APPENDIX
                 III.
                 
              
               
                 A
                 Like
                 errour
                 ,
                 in
                 my
                 judgement
                 ,
                 hath
                 been
                 committed
                 by
                 all
                 those
                 learned
                 men
                 ,
                 which
                 to
                 prevent
                 the
                 diversion
                 of
                 the
                 Reno
                 of
                 Bologna
                 into
                 Po
                 by
                 the
                 Channels
                 ,
                 through
                 which
                 it
                 at
                 present
                 runneth
                 ,
                 judged
                 ,
                 that
                 the
                 Reno
                 being
                 in
                 its
                 greater
                 excrescence
                 about
                 2000
                 ▪
                 feet
                 ,
                 and
                 the
                 Po
                 being
                 near
                 1000.
                 feet
                 broad
                 ,
                 they
                 judged
                 ,
                 I
                 say
                 ,
                 that
                 letting
                 the
                 Reno
                 into
                 Po
                 ,
                 it
                 would
                 have
                 raised
                 the
                 Water
                 of
                 Po
                 two
                 feet
                 ;
                 from
                 which
                 rise
                 ,
                 they
                 concluded
                 afterwards
                 most
                 exorbitant
                 disorders
                 ,
                 either
                 of
                 extraordinary
                 Inundations
                 ,
                 or
                 else
                 of
                 immense
                 and
                 intolerable
                 expences
                 to
                 the
                 people
                 in
                 raising
                 the
                 Banks
                 of
                 Po
                 and
                 Reno
                 ,
                 and
                 with
                 such
                 like
                 weaknesses
                 ,
                 often
                 vainly
                 disturbed
                 the
                 minds
                 of
                 the
                 persons
                 concerned
                 :
                 But
                 now
                 from
                 the
                 things
                 demonstrated
                 ,
                 it
                 is
                 manifest
                 ,
                 That
                 the
                 measure
                 of
                 the
                 Reno
                 in
                 Reno
                 ,
                 would
                 be
                 different
                 from
                 the
                 measure
                 of
                 Reno
                 in
                 Po
                 ;
                 in
                 case
                 that
                 the
                 velocity
                 of
                 the
                 Reno
                 in
                 Po
                 ,
                 should
                 differ
                 from
                 the
                 velocity
                 of
                 Reno
                 in
                 Reno
                 ,
                 as
                 is
                 more
                 exactly
                 determined
                 in
                 the
                 fourth
                 Proposition
                 .
              
            
             
               
                 APPENDIX
                 IV.
                 
              
               
                 NO
                 less
                 likewise
                 are
                 those
                 Ingeneers
                 and
                 Artists
                 deceived
                 ,
                 that
                 have
                 affirmed
                 ,
                 That
                 letting
                 the
                 Reno
                 into
                 Po
                 ,
                 there
                 would
                 be
                 no
                 rise
                 at
                 all
                 in
                 the
                 Water
                 of
                 Po
                 :
                 For
                 the
                 truth
                 is
                 ,
                 That
                 letting
                 Reno
                 into
                 Po
                 ,
                 there
                 would
                 alwaies
                 be
                 a
                 rising
                 ;
                 but
                 sometimes
                 greater
                 ,
                 sometimes
                 lesse
                 ,
                 as
                 the
                 Po
                 shall
                 have
                 a
                 swifter
                 or
                 slower
                 Current
                 ;
                 so
                 that
                 if
                 the
                 Po
                 shall
                 be
                 constituted
                 in
                 a
                 great
                 velocity
                 ,
                 the
                 rise
                 will
                 be
                 very
                 small
                 ;
                 and
                 if
                 the
                 said
                 Po
                 shall
                 be
                 slow
                 in
                 its
                 course
                 ,
                 then
                 the
                 rise
                 will
                 be
                 notable
                 .
              
            
             
               
                 APPENDIX
                 V.
                 
              
               
                 ANd
                 here
                 it
                 will
                 not
                 be
                 besides
                 the
                 purpose
                 to
                 advertise
                 ,
                 That
                 the
                 measures
                 ,
                 partments
                 ,
                 and
                 distributions
                 of
                 the
                 Waters
                 of
                 Fountains
                 ,
                 cannot
                 be
                 made
                 exactly
                 ,
                 unless
                 there
                 be
                 considered
                 ,
                 
                 besides
                 the
                 measure
                 ,
                 the
                 velocity
                 also
                 of
                 the
                 Water
                 ;
                 which
                 particular
                 not
                 being
                 thorowly
                 observed
                 ,
                 is
                 the
                 cause
                 of
                 continual
                 miscariages
                 in
                 such
                 like
                 affairs
                 .
              
            
             
               
                 APPENDIX
                 VI.
                 
              
               
                 LIke
                 consideration
                 ought
                 to
                 be
                 had
                 with
                 the
                 greater
                 diligence
                 ,
                 for
                 that
                 an
                 errour
                 therein
                 is
                 more
                 prejudicial
                 ;
                 I
                 say
                 ,
                 ought
                 to
                 be
                 had
                 by
                 those
                 which
                 part
                 and
                 divide
                 VVaters
                 ;
                 for
                 the
                 watering
                 of
                 fields
                 ,
                 as
                 is
                 done
                 in
                 the
                 Territories
                 of
                 
                   Brescia
                   ,
                   Bergama
                   ,
                   Crema
                   ,
                   Pavia
                   ,
                   Lodigiano
                   ,
                   Cremona
                   ,
                
                 and
                 other
                 places
                 :
                 For
                 if
                 they
                 have
                 not
                 regard
                 to
                 the
                 most
                 important
                 point
                 of
                 the
                 variation
                 of
                 the
                 velocity
                 of
                 the
                 VVater
                 ,
                 but
                 onely
                 to
                 the
                 bare
                 Vulgar
                 measure
                 ,
                 there
                 will
                 alwaies
                 very
                 great
                 disorders
                 and
                 prejudices
                 ensue
                 to
                 the
                 persons
                 concerned
                 .
              
            
             
               
                 APPENDIX
                 VII
                 .
              
               
                 IT
                 seemeth
                 that
                 one
                 may
                 observe
                 ,
                 that
                 whilst
                 the
                 Water
                 runneth
                 along
                 a
                 Channel
                 ,
                 Current
                 ,
                 or
                 Conduit
                 ,
                 its
                 velocity
                 is
                 retarded
                 ,
                 withheld
                 ,
                 and
                 impeded
                 by
                 its
                 touching
                 the
                 Bank
                 of
                 side
                 of
                 the
                 said
                 Channel
                 or
                 Current
                 ;
                 which
                 ,
                 as
                 immoveable
                 ,
                 not
                 following
                 the
                 motion
                 of
                 the
                 VVater
                 ,
                 interrupteth
                 its
                 velocity
                 :
                 From
                 which
                 particular
                 ,
                 being
                 true
                 ,
                 as
                 I
                 believe
                 it
                 to
                 be
                 most
                 true
                 ,
                 and
                 from
                 our
                 considerations
                 ,
                 we
                 have
                 an
                 occasion
                 of
                 discovering
                 a
                 very
                 nice
                 mistake
                 ,
                 into
                 which
                 those
                 commonly
                 fall
                 who
                 divide
                 the
                 VVaters
                 of
                 Fountains
                 .
                 VVhich
                 division
                 is
                 wont
                 to
                 be
                 ,
                 by
                 what
                 I
                 have
                 seen
                 here
                 in
                 Rome
                 ,
                 performed
                 two
                 wayes
                 ;
                 The
                 first
                 of
                 which
                 is
                 with
                 the
                 measures
                 of
                 like
                 figures
                 ,
                 as
                 Circles
                 ,
                 or
                 Squares
                 ,
                 having
                 cut
                 through
                 a
                 Plate
                 of
                 metal
                 several
                 Circles
                 or
                 Squares
                 ,
                 one
                 of
                 half
                 〈◊〉
                 inch
                 ,
                 another
                 of
                 one
                 inch
                 ,
                 another
                 of
                 two
                 ,
                 of
                 three
                 ,
                 of
                 four
                 ,
                 &c.
                 with
                 which
                 they
                 afterwards
                 adjust
                 the
                 Cocks
                 to
                 dispence
                 the
                 VVaters
                 .
                 The
                 other
                 manner
                 of
                 dividing
                 the
                 VVaters
                 of
                 Fountains
                 ,
                 is
                 with
                 rectangle
                 paralellograms
                 ,
                 of
                 the
                 same
                 height
                 ,
                 but
                 of
                 different
                 Bases
                 ,
                 in
                 such
                 sort
                 likewise
                 ,
                 that
                 one
                 paralellogram
                 be
                 of
                 half
                 an
                 inch
                 ,
                 another
                 of
                 one
                 ,
                 two
                 ,
                 three
                 ,
                 &c.
                 
                 In
                 which
                 manner
                 of
                 measuring
                 and
                 dividing
                 the
                 Water
                 it
                 should
                 seem
                 that
                 the
                 Cocks
                 being
                 placed
                 in
                 one
                 and
                 the
                 same
                 plain
                 ,
                 equidistant
                 from
                 the
                 level
                 ,
                 or
                 superior
                 superficies
                 of
                 the
                 water
                 of
                 the
                 Well
                 ;
                 and
                 the
                 said
                 measures
                 being
                 most
                 exactly
                 made
                 ,
                 the
                 VVater
                 ought
                 consequently
                 also
                 to
                 be
                 equally
                 divided
                 ,
                 and
                 parted
                 according
                 to
                 the
                 proportion
                 of
                 the
                 measures
                 .
                 But
                 if
                 we
                 well
                 consider
                 every
                 particular
                 ,
                 we
                 shall
                 finde
                 ,
                 that
                 the
                 Cocks
                 ,
                 as
                 they
                 successively
                 are
                 greater
                 ,
                 discharge
                 alwaies
                 more
                 VVater
                 than
                 the
                 just
                 quantity
                 ,
                 in
                 comparison
                 of
                 
                 the
                 lesser
                 ;
                 that
                 is
                 ,
                 to
                 speak
                 more
                 properly
                 ,
                 The
                 VVater
                 which
                 passeth
                 through
                 the
                 greater
                 Cock
                 ,
                 hath
                 alwaies
                 a
                 greater
                 proportion
                 to
                 that
                 which
                 passeth
                 through
                 the
                 lesser
                 ,
                 than
                 the
                 greater
                 Cock
                 hath
                 to
                 the
                 lesser
                 .
                 All
                 which
                 I
                 will
                 declare
                 by
                 an
                 example
                 .
              
               
               
                 The
                 like
                 errour
                 occurreth
                 also
                 in
                 the
                 other
                 manner
                 of
                 measuring
                 the
                 VVater
                 of
                 a
                 Fountain
                 ,
                 as
                 may
                 easily
                 be
                 collected
                 from
                 what
                 hath
                 been
                 said
                 and
                 observed
                 above
                 .
              
            
             
               
                 APPENDIX
                 VIII
                 .
              
               
                 THe
                 same
                 contemplation
                 discovereth
                 the
                 errour
                 of
                 those
                 Architects
                 ,
                 who
                 being
                 to
                 erect
                 a
                 Bridge
                 of
                 sundry
                 Arches
                 over
                 a
                 River
                 ,
                 consider
                 the
                 ordinary
                 breadth
                 of
                 the
                 River
                 ;
                 which
                 being
                 
                   v.
                   g.
                
                 fourty
                 fathom
                 ,
                 and
                 the
                 Bridge
                 being
                 to
                 consist
                 of
                 four
                 Arches
                 ,
                 it
                 sufficeth
                 them
                 ,
                 that
                 the
                 breadth
                 of
                 all
                 the
                 four
                 Arches
                 taken
                 together
                 ,
                 be
                 fourty
                 fathom
                 ;
                 not
                 considering
                 that
                 in
                 the
                 ordinary
                 Channel
                 of
                 the
                 River
                 ,
                 the
                 Water
                 hath
                 onely
                 two
                 impediments
                 which
                 retard
                 its
                 velocity
                 ;
                 namely
                 ,
                 the
                 touching
                 and
                 gliding
                 along
                 the
                 two
                 sides
                 or
                 shores
                 of
                 the
                 River
                 :
                 but
                 
                 the
                 same
                 water
                 in
                 passing
                 under
                 the
                 Bridge
                 ,
                 in
                 our
                 case
                 meeteth
                 with
                 eight
                 of
                 the
                 same
                 impediments
                 ,
                 bearing
                 ,
                 and
                 thrusting
                 upon
                 two
                 sides
                 of
                 each
                 Arch
                 (
                 to
                 omit
                 the
                 impediment
                 of
                 the
                 bottom
                 ,
                 for
                 that
                 it
                 is
                 the
                 same
                 in
                 the
                 River
                 ,
                 and
                 under
                 the
                 Bridge
                 )
                 from
                 which
                 inadvertency
                 sometimes
                 follow
                 very
                 great
                 disorders
                 ,
                 as
                 quotidian
                 practice
                 shews
                 us
                 .
              
            
             
               
                 APPENDIX
                 IX
                 .
              
               
                 IT
                 is
                 also
                 worthy
                 to
                 consider
                 the
                 great
                 and
                 admirable
                 benefit
                 that
                 those
                 fields
                 receive
                 ,
                 which
                 are
                 wont
                 to
                 drink
                 up
                 the
                 Rain-water
                 with
                 difficulty
                 ,
                 through
                 the
                 height
                 of
                 the
                 water
                 in
                 the
                 principal
                 Ditches
                 ;
                 in
                 which
                 case
                 the
                 careful
                 Husbandman
                 cutteth
                 away
                 the
                 reeds
                 and
                 rushes
                 in
                 the
                 Ditches
                 ,
                 through
                 which
                 the
                 waters
                 pass
                 ;
                 whereupon
                 may
                 be
                 presently
                 seen
                 ,
                 so
                 soon
                 as
                 the
                 reeds
                 and
                 rushes
                 are
                 cut
                 ,
                 a
                 notable
                 Ebb
                 in
                 the
                 level
                 of
                 the
                 water
                 in
                 the
                 Ditches
                 ;
                 insomuch
                 that
                 sometimes
                 it
                 is
                 observed
                 ,
                 that
                 the
                 water
                 is
                 abated
                 after
                 the
                 said
                 cutting
                 a
                 third
                 and
                 more
                 ,
                 of
                 what
                 it
                 was
                 before
                 the
                 cutting
                 .
                 The
                 which
                 effect
                 seemingly
                 might
                 depend
                 on
                 this
                 ,
                 That
                 ,
                 before
                 those
                 weeds
                 took
                 up
                 room
                 in
                 the
                 Ditch
                 ,
                 and
                 for
                 that
                 cause
                 the
                 water
                 kept
                 a
                 higher
                 level
                 ,
                 and
                 the
                 said
                 Plants
                 being
                 afterwards
                 cut
                 and
                 removed
                 ,
                 the
                 water
                 came
                 to
                 abate
                 ,
                 possessing
                 the
                 place
                 that
                 before
                 was
                 occupied
                 by
                 the
                 weeds
                 :
                 Which
                 opinion
                 ,
                 though
                 probable
                 ,
                 and
                 at
                 first
                 sight
                 satisfactory
                 ,
                 is
                 nevertheless
                 insufficient
                 to
                 give
                 the
                 total
                 reason
                 of
                 that
                 notable
                 abatement
                 which
                 hath
                 been
                 spoken
                 of
                 :
                 But
                 it
                 is
                 necessary
                 to
                 have
                 recourse
                 to
                 our
                 consideration
                 of
                 the
                 velocity
                 in
                 the
                 course
                 of
                 the
                 water
                 ,
                 the
                 chiefest
                 and
                 true
                 cause
                 of
                 the
                 variation
                 of
                 the
                 measure
                 of
                 the
                 same
                 Running-Water
                 ;
                 for
                 ,
                 that
                 multitudes
                 of
                 reeds
                 ,
                 weeds
                 ,
                 and
                 plants
                 dispersed
                 through
                 the
                 current
                 of
                 the
                 Ditch
                 ,
                 do
                 chance
                 notably
                 to
                 retard
                 the
                 course
                 of
                 the
                 water
                 ,
                 and
                 therefore
                 the
                 measure
                 of
                 the
                 water
                 increaseth
                 ;
                 and
                 those
                 impediments
                 removed
                 ,
                 the
                 same
                 water
                 gaineth
                 velocity
                 ,
                 and
                 therefore
                 decreaseth
                 in
                 measure
                 ,
                 and
                 consequently
                 in
                 height
                 .
              
               
                 And
                 perhaps
                 this
                 point
                 well
                 understood
                 ,
                 may
                 be
                 of
                 great
                 profit
                 to
                 the
                 fields
                 adjacent
                 to
                 the
                 Pontine
                 Fens
                 ,
                 and
                 I
                 doubt
                 not
                 but
                 if
                 the
                 River
                 Ninfa
                 ,
                 and
                 the
                 other
                 principal
                 Brooks
                 of
                 those
                 Territories
                 were
                 kept
                 well
                 cleansed
                 from
                 weeds
                 ,
                 their
                 waters
                 would
                 be
                 at
                 a
                 lower
                 level
                 ,
                 and
                 consequently
                 the
                 drains
                 of
                 the
                 fields
                 would
                 run
                 into
                 them
                 more
                 readily
                 ;
                 it
                 being
                 alwayes
                 to
                 be
                 held
                 for
                 undoubted
                 ,
                 that
                 the
                 measure
                 of
                 the
                 water
                 before
                 the
                 cleansing
                 ,
                 hath
                 the
                 same
                 proportion
                 to
                 the
                 measure
                 after
                 cleansing
                 ,
                 that
                 the
                 velocity
                 after
                 the
                 cleansing
                 hath
                 to
                 the
                 velocity
                 before
                 the
                 cleansing
                 :
                 And
                 because
                 those
                 weeds
                 being
                 cleansed
                 
                 away
                 ,
                 the
                 course
                 of
                 the
                 water
                 notably
                 increaseth
                 ,
                 it
                 is
                 therefore
                 necessary
                 that
                 the
                 said
                 water
                 abate
                 in
                 measure
                 ,
                 and
                 become
                 lower
                 .
              
            
             
               
                 APPENDIX
                 .
                 X.
                 
              
               
                 WE
                 having
                 above
                 observed
                 some
                 errors
                 that
                 are
                 committed
                 in
                 distributing
                 the
                 waters
                 of
                 Fountains
                 ,
                 and
                 those
                 that
                 serve
                 to
                 water
                 fields
                 ;
                 it
                 seemeth
                 now
                 fit
                 ,
                 by
                 way
                 of
                 a
                 close
                 to
                 this
                 discourse
                 ,
                 to
                 advertise
                 by
                 what
                 means
                 these
                 divisions
                 may
                 be
                 made
                 justly
                 and
                 without
                 error
                 .
                 I
                 therefore
                 think
                 that
                 one
                 might
                 two
                 several
                 wayes
                 exquisitly
                 divide
                 the
                 water
                 of
                 Fountains
                 ;
                 The
                 first
                 would
                 be
                 by
                 diligently
                 examining
                 ,
                 First
                 ,
                 how
                 much
                 water
                 the
                 whole
                 Fountain
                 dischargeth
                 in
                 a
                 determinate
                 time
                 ,
                 as
                 for
                 instance
                 :
                 How
                 many
                 Barrels
                 ,
                 or
                 Tuns
                 it
                 carrieth
                 in
                 a
                 set
                 time
                 ;
                 and
                 in
                 case
                 you
                 are
                 afterwards
                 to
                 distribute
                 the
                 water
                 ,
                 distribute
                 it
                 at
                 the
                 rate
                 of
                 somany
                 Barrels
                 or
                 Tuns
                 ,
                 in
                 that
                 same
                 time
                 ;
                 and
                 in
                 this
                 case
                 the
                 participants
                 would
                 have
                 their
                 punctual
                 shares
                 :
                 Nor
                 could
                 it
                 ever
                 happen
                 to
                 send
                 out
                 more
                 water
                 ,
                 than
                 is
                 reckoned
                 to
                 be
                 in
                 the
                 principal
                 Fountain
                 ;
                 as
                 befel
                 
                   Giulio
                   Frontino
                
                 ,
                 and
                 as
                 also
                 it
                 frequently
                 happeneth
                 in
                 the
                 Modern
                 Aqueducts
                 ,
                 to
                 the
                 publick
                 and
                 private
                 detriment
                 .
              
               
                 The
                 other
                 way
                 of
                 dividing
                 the
                 same
                 waters
                 of
                 a
                 Fountain
                 ,
                 is
                 also
                 sufficiently
                 exact
                 and
                 easie
                 ;
                 and
                 may
                 be
                 ,
                 by
                 having
                 one
                 onely
                 size
                 for
                 the
                 Cock
                 or
                 Pipe
                 ,
                 as
                 suppose
                 of
                 an
                 inch
                 ,
                 or
                 of
                 half
                 an
                 inch
                 ;
                 and
                 when
                 the
                 case
                 requireth
                 to
                 dispence
                 two
                 ,
                 three
                 ,
                 and
                 more
                 inches
                 ,
                 take
                 so
                 many
                 Cocks
                 of
                 the
                 said
                 measure
                 as
                 do
                 evacuate
                 the
                 water
                 ,
                 which
                 is
                 to
                 be
                 emitted
                 ;
                 and
                 if
                 we
                 are
                 to
                 make
                 use
                 onely
                 of
                 one
                 greater
                 Cock
                 ,
                 we
                 being
                 to
                 place
                 one
                 to
                 discharge
                 for
                 example
                 four
                 inches
                 ;
                 and
                 having
                 the
                 former
                 sole
                 measure
                 of
                 an
                 inch
                 ,
                 we
                 must
                 make
                 a
                 Cock
                 that
                 is
                 bigger
                 ,
                 its
                 true
                 ,
                 than
                 the
                 Cock
                 of
                 one
                 inch
                 ;
                 but
                 not
                 simply
                 in
                 a
                 quadruple
                 proportion
                 ,
                 for
                 that
                 it
                 would
                 discharge
                 more
                 than
                 just
                 so
                 much
                 water
                 ,
                 as
                 hath
                 been
                 said
                 above
                 ;
                 but
                 we
                 ought
                 to
                 examine
                 diligently
                 how
                 much
                 water
                 the
                 little
                 Cock
                 emitteth
                 in
                 an
                 hour
                 ;
                 and
                 then
                 enlarge
                 ,
                 and
                 contract
                 the
                 greater
                 Cock
                 ,
                 so
                 ,
                 that
                 it
                 may
                 discharge
                 four
                 times
                 as
                 much
                 water
                 as
                 the
                 lesser
                 in
                 the
                 same
                 time
                 ;
                 and
                 by
                 this
                 means
                 we
                 shall
                 avoid
                 the
                 disorder
                 hinted
                 in
                 the
                 seventh
                 Appendix
                 .
                 It
                 would
                 be
                 necessary
                 nevertheless
                 ,
                 to
                 accommodate
                 the
                 Cocks
                 of
                 the
                 Cistern
                 so
                 ,
                 that
                 the
                 level
                 of
                 the
                 water
                 in
                 the
                 Cistern
                 may
                 alwayes
                 rest
                 at
                 one
                 determinate
                 mark
                 above
                 the
                 Cock
                 ,
                 otherwise
                 the
                 Cocks
                 will
                 emit
                 sometimes
                 greater
                 ,
                 and
                 sometimes
                 lesse
                 abundance
                 of
                 water
                 ▪
                 And
                 because
                 it
                 may
                 be
                 that
                 the
                 same
                 water
                 of
                 the
                 Fountain
                 may
                 be
                 some
                 times
                 more
                 abundant
                 ,
                 sometimes
                 less
                 ;
                 in
                 such
                 case
                 it
                 will
                 be
                 necessary
                 
                 to
                 adjust
                 the
                 Cistern
                 so
                 ,
                 that
                 the
                 excess
                 above
                 the
                 ordinary
                 water
                 ,
                 discharge
                 into
                 the
                 publick
                 Fountains
                 ,
                 that
                 so
                 the
                 particular
                 participants
                 may
                 have
                 alwayes
                 the
                 same
                 abundance
                 of
                 water
                 .
              
            
             
               
                 APPENDIX
                 XI
                 .
              
               
                 MUch
                 more
                 difficult
                 is
                 the
                 division
                 of
                 the
                 waters
                 which
                 serve
                 to
                 water
                 the
                 fields
                 ,
                 it
                 not
                 being
                 possible
                 to
                 observe
                 so
                 commodiously
                 ,
                 what
                 quantity
                 of
                 water
                 the
                 whole
                 Ditch
                 sends
                 forth
                 in
                 one
                 determinate
                 time
                 ,
                 as
                 may
                 be
                 done
                 in
                 Fountains
                 :
                 Yet
                 nevertheless
                 ,
                 if
                 the
                 second
                 proposition
                 by
                 us
                 a
                 little
                 below
                 demonstrated
                 ,
                 be
                 well
                 understood
                 ,
                 there
                 may
                 be
                 thence
                 taken
                 a
                 very
                 safe
                 and
                 just
                 way
                 to
                 distribute
                 such
                 waters
                 .
                 The
                 Proposition
                 therefore
                 by
                 us
                 demonstrated
                 is
                 this
                 :
                 If
                 there
                 be
                 two
                 Sections
                 ,
                 (
                 namely
                 two
                 mouths
                 of
                 Rivers
                 )
                 the
                 quantity
                 of
                 the
                 water
                 which
                 passeth
                 by
                 the
                 first
                 ,
                 hath
                 a
                 proportion
                 to
                 that
                 which
                 passeth
                 by
                 the
                 second
                 ,
                 compounded
                 of
                 the
                 proportions
                 of
                 the
                 first
                 Section
                 to
                 the
                 second
                 ,
                 and
                 of
                 the
                 velocity
                 through
                 the
                 first
                 ,
                 to
                 the
                 velocity
                 through
                 the
                 second
                 :
                 As
                 I
                 will
                 declare
                 for
                 example
                 by
                 help
                 of
                 practice
                 ,
                 that
                 I
                 may
                 be
                 understood
                 by
                 all
                 ,
                 in
                 a
                 matter
                 so
                 important
                 .
                 Let
                 the
                 two
                 mouths
                 of
                 the
                 Rivers
                 be
                 A
                 ,
                 and
                 B
                 ,
                 and
                 let
                 
                 the
                 mouth
                 A
                 be
                 in
                 measure
                 and
                 content
                 thirty
                 two
                 feet
                 ,
                 and
                 the
                 mouth
                 B
                 ,
                 eight
                 feet
                 .
                 Here
                 you
                 must
                 take
                 notice
                 ,
                 that
                 it
                 is
                 not
                 alwayes
                 true
                 ,
                 that
                 the
                 Water
                 which
                 passeth
                 by
                 A
                 ,
                 hath
                 the
                 same
                 proportion
                 to
                 that
                 which
                 passeth
                 by
                 B
                 ,
                 that
                 the
                 mouth
                 A
                 hath
                 to
                 the
                 mouth
                 B
                 ;
                 but
                 onely
                 when
                 the
                 velocityes
                 by
                 each
                 of
                 those
                 passages
                 are
                 equal
                 :
                 But
                 if
                 the
                 velocityes
                 shall
                 be
                 unequal
                 ,
                 it
                 may
                 be
                 that
                 the
                 said
                 mouths
                 may
                 emit
                 equal
                 quantity
                 of
                 Water
                 in
                 equal
                 times
                 ,
                 though
                 their
                 measure
                 be
                 unequal
                 ;
                 and
                 it
                 may
                 be
                 also
                 ,
                 that
                 the
                 bigger
                 doth
                 discharge
                 a
                 greater
                 quantity
                 of
                 Water
                 :
                 And
                 lastly
                 ,
                 it
                 may
                 be
                 ,
                 that
                 the
                 less
                 mouth
                 dischargeth
                 more
                 Water
                 than
                 the
                 greater
                 ;
                 and
                 all
                 this
                 is
                 manifest
                 by
                 the
                 things
                 noted
                 in
                 the
                 beginning
                 of
                 this
                 discourse
                 ,
                 and
                 by
                 the
                 said
                 second
                 Proposition
                 .
                 Now
                 to
                 examine
                 the
                 proportion
                 of
                 the
                 Water
                 that
                 passeth
                 by
                 one
                 Ditch
                 ,
                 to
                 that
                 which
                 passeth
                 by
                 another
                 ,
                 that
                 this
                 being
                 known
                 ,
                 the
                 same
                 Waters
                 and
                 mouths
                 of
                 Ditches
                 may
                 be
                 then
                 adjusted
                 ;
                 we
                 are
                 to
                 keep
                 account
                 not
                 onely
                 of
                 the
                 greatness
                 of
                 the
                 mouths
                 or
                 passages
                 of
                 the
                 Water
                 ,
                 but
                 of
                 the
                 velocity
                 also
                 ;
                 which
                 we
                 will
                 do
                 ,
                 by
                 first
                 finding
                 two
                 numbers
                 that
                 have
                 the
                 same
                 proportion
                 between
                 themselves
                 ,
                 
                 as
                 have
                 the
                 mouths
                 ,
                 which
                 are
                 the
                 numbers
                 32
                 and
                 8
                 in
                 our
                 example
                 :
                 Then
                 this
                 
                 being
                 done
                 ,
                 let
                 the
                 velocity
                 of
                 the
                 Water
                 by
                 the
                 passages
                 A
                 and
                 B
                 ,
                 be
                 examined
                 (
                 which
                 may
                 be
                 done
                 keeping
                 account
                 what
                 space
                 a
                 piece
                 of
                 Wood
                 ,
                 or
                 other
                 body
                 that
                 swimmeth
                 ,
                 is
                 carried
                 by
                 the
                 stream
                 in
                 one
                 determinate
                 time
                 ;
                 as
                 for
                 instance
                 in
                 50
                 pulses
                 )
                 and
                 then
                 work
                 by
                 the
                 golden
                 Rule
                 ,
                 as
                 the
                 velocity
                 by
                 A
                 ,
                 is
                 to
                 the
                 velocity
                 by
                 B
                 ,
                 so
                 is
                 the
                 number
                 8
                 ,
                 to
                 another
                 number
                 ,
                 which
                 is
                 4.
                 
                 It
                 is
                 clear
                 by
                 what
                 is
                 demonstrated
                 in
                 the
                 said
                 second
                 Proposition
                 ,
                 that
                 the
                 quantity
                 of
                 water
                 ,
                 which
                 passeth
                 by
                 the
                 mouth
                 A
                 ,
                 shall
                 have
                 the
                 same
                 proportion
                 of
                 that
                 which
                 passeth
                 by
                 the
                 mouth
                 B
                 ,
                 that
                 8
                 hath
                 to
                 1.
                 
                 Such
                 proportion
                 being
                 composed
                 of
                 the
                 proportions
                 of
                 32
                 to
                 8
                 ,
                 and
                 of
                 8
                 to
                 4
                 ;
                 namely
                 ,
                 to
                 the
                 greatness
                 of
                 the
                 mouth
                 A
                 ,
                 to
                 the
                 greatness
                 of
                 the
                 mouth
                 B
                 ,
                 and
                 of
                 the
                 velocity
                 in
                 A
                 ,
                 to
                 the
                 velocity
                 in
                 B.
                 This
                 being
                 done
                 ,
                 we
                 must
                 then
                 contract
                 the
                 mouth
                 which
                 dischargeth
                 more
                 then
                 its
                 just
                 quantity
                 of
                 water
                 ,
                 or
                 enlarge
                 the
                 other
                 which
                 dischargeth
                 less
                 ,
                 as
                 shal
                 be
                 most
                 commodious
                 in
                 practice
                 ,
                 which
                 to
                 him
                 that
                 hath
                 understood
                 this
                 little
                 that
                 hath
                 been
                 delivered
                 ,
                 will
                 be
                 very
                 easie
                 .
              
            
             
               
                 APPENDIX
                 XII
                 .
              
               
                 THese
                 opperations
                 about
                 Water
                 ,
                 as
                 I
                 have
                 hitherto
                 on
                 sundry
                 occasions
                 observed
                 ,
                 are
                 involved
                 in
                 so
                 many
                 difficulties
                 ,
                 and
                 such
                 a
                 multiplicity
                 of
                 most
                 extravagant
                 accidents
                 ,
                 that
                 it
                 is
                 no
                 marvel
                 if
                 continually
                 many
                 ,
                 and
                 very
                 important
                 errours
                 be
                 therein
                 committed
                 by
                 many
                 ,
                 and
                 even
                 by
                 Ingeneers
                 themselves
                 ,
                 and
                 Learned-men
                 ;
                 and
                 because
                 many
                 times
                 they
                 concern
                 not
                 onely
                 the
                 publique
                 ,
                 but
                 private
                 interests
                 :
                 Hence
                 it
                 is
                 ,
                 that
                 it
                 not
                 onely
                 belongeth
                 to
                 Artists
                 to
                 treat
                 thereof
                 ,
                 but
                 very
                 oft
                 even
                 the
                 vulgar
                 themselves
                 pretend
                 to
                 give
                 their
                 judgement
                 therein
                 :
                 And
                 I
                 have
                 been
                 troubled
                 many
                 times
                 with
                 a
                 necessity
                 of
                 treating
                 ,
                 not
                 onely
                 with
                 those
                 ,
                 which
                 either
                 by
                 practice
                 ,
                 or
                 particular
                 study
                 ,
                 understood
                 somewhat
                 in
                 these
                 matters
                 ;
                 but
                 also
                 with
                 people
                 wholly
                 void
                 of
                 those
                 notions
                 ,
                 which
                 are
                 necessary
                 for
                 one
                 that
                 would
                 on
                 good
                 grounds
                 discourse
                 about
                 this
                 particular
                 ;
                 and
                 thus
                 many
                 times
                 have
                 met
                 with
                 more
                 difficulty
                 in
                 the
                 thick
                 skulls
                 of
                 men
                 ,
                 than
                 in
                 precipitous
                 Torrents
                 ,
                 and
                 vast
                 Fennes
                 .
                 And
                 in
                 particular
                 ,
                 I
                 had
                 occasion
                 some
                 years
                 past
                 to
                 go
                 see
                 the
                 Cave
                 or
                 Emissary
                 of
                 the
                 Lake
                 of
                 Perugia
                 ,
                 made
                 many
                 years
                 agon
                 by
                 
                   Braccio
                   Fortobraccio
                
                 ,
                 but
                 for
                 that
                 it
                 was
                 with
                 great
                 ruines
                 by
                 Time
                 decayed
                 ,
                 and
                 rendred
                 unuseful
                 ,
                 it
                 was
                 repaired
                 with
                 industry
                 
                 truly
                 heroicall
                 and
                 admirable
                 ,
                 by
                 Monsignor
                 
                   Maffei
                   Barberino
                
                 ,
                 then
                 Prefect
                 for
                 the
                 Wayes
                 ,
                 and
                 now
                 Pope
                 .
                 And
                 being
                 necessitated
                 ,
                 that
                 I
                 might
                 be
                 able
                 to
                 walk
                 in
                 the
                 Cave
                 ,
                 and
                 for
                 other
                 causes
                 ,
                 I
                 let
                 down
                 the
                 Sluices
                 of
                 the
                 said
                 Cave
                 ,
                 at
                 the
                 mouth
                 of
                 the
                 Lake
                 :
                 No
                 sooner
                 were
                 they
                 stopt
                 ,
                 but
                 a
                 great
                 many
                 of
                 the
                 people
                 of
                 the
                 Towns
                 and
                 Villages
                 coasting
                 upon
                 the
                 Lake
                 flocking
                 thither
                 ,
                 began
                 to
                 make
                 grievous
                 complaints
                 ,
                 that
                 if
                 those
                 Sluices
                 were
                 kept
                 shut
                 ,
                 not
                 onely
                 the
                 Lake
                 would
                 want
                 its
                 due
                 Vent
                 ,
                 but
                 also
                 the
                 parts
                 adjacent
                 to
                 the
                 Lake
                 would
                 be
                 over
                 flown
                 to
                 their
                 very
                 great
                 detriment
                 .
                 And
                 because
                 at
                 first
                 appearance
                 their
                 motion
                 seemed
                 very
                 reasonable
                 ,
                 I
                 found
                 my self
                 hard
                 put
                 to
                 it
                 ,
                 seeing
                 no
                 way
                 to
                 perswade
                 such
                 a
                 multitude
                 ,
                 that
                 the
                 prejudice
                 which
                 they
                 pretended
                 I
                 should
                 do
                 them
                 by
                 keeping
                 the
                 Sluices
                 shut
                 for
                 two
                 dayes
                 ,
                 was
                 absolutely
                 insensible
                 ;
                 and
                 that
                 by
                 keeping
                 them
                 open
                 ,
                 the
                 Lake
                 did
                 not
                 ebb
                 in
                 the
                 same
                 time
                 so
                 much
                 as
                 the
                 thickness
                 of
                 a
                 sheet
                 of
                 Paper
                 :
                 And
                 therefore
                 I
                 was
                 necessitated
                 to
                 make
                 use
                 of
                 the
                 authority
                 I
                 had
                 ,
                 and
                 so
                 followed
                 my
                 business
                 as
                 cause
                 required
                 ,
                 without
                 any
                 regard
                 to
                 that
                 Rabble
                 tumultuously
                 assembled
                 .
                 Now
                 when
                 I
                 am
                 not
                 working
                 with
                 Mattock
                 or
                 Spade
                 ,
                 but
                 with
                 the
                 Pen
                 and
                 Discourse
                 ,
                 I
                 intend
                 to
                 demonstrate
                 clearly
                 to
                 those
                 that
                 are
                 capable
                 of
                 reason
                 ,
                 and
                 that
                 have
                 well
                 understood
                 the
                 ground
                 of
                 this
                 my
                 Treatise
                 ,
                 that
                 the
                 fear
                 was
                 altogether
                 vain
                 which
                 those
                 people
                 conceited
                 .
                 And
                 therefore
                 I
                 say
                 ,
                 that
                 the
                 Emissary
                 or
                 Sluice
                 of
                 the
                 Lake
                 of
                 Perugia
                 ,
                 standing
                 in
                 the
                 same
                 manner
                 as
                 at
                 present
                 ,
                 and
                 the
                 water
                 passing
                 thorow
                 it
                 with
                 the
                 same
                 velocity
                 as
                 now
                 ;
                 to
                 examine
                 how
                 much
                 the
                 Lake
                 may
                 abate
                 in
                 two
                 days
                 space
                 ,
                 we
                 ought
                 to
                 consider
                 ,
                 what
                 proportion
                 the
                 superficies
                 of
                 the
                 whole
                 Lake
                 hath
                 to
                 the
                 measure
                 of
                 the
                 Section
                 of
                 the
                 Emissary
                 ,
                 and
                 afterwards
                 to
                 infer
                 ,
                 that
                 the
                 velocity
                 of
                 the
                 water
                 by
                 the
                 Emissary
                 or
                 Sluice
                 ,
                 shall
                 have
                 the
                 same
                 proportion
                 to
                 the
                 abatement
                 of
                 the
                 Lake
                 ,
                 and
                 to
                 prove
                 thorowly
                 and
                 clearly
                 this
                 discourse
                 ,
                 I
                 intend
                 to
                 demonstrate
                 the
                 following
                 Proposition
                 .
              
               
               
                 That
                 which
                 hath
                 been
                 demonstrated
                 in
                 the
                 Vessel
                 ,
                 falls
                 out
                 exactly
                 also
                 in
                 our
                 Lake
                 of
                 Perugia
                 ,
                 and
                 its
                 Emissary
                 ;
                 and
                 because
                 the
                 immensity
                 of
                 the
                 superficies
                 of
                 the
                 Lake
                 is
                 in
                 proportion
                 to
                 the
                 superficies
                 of
                 the
                 Emissary
                 or
                 Sluice
                 ,
                 as
                 many
                 millions
                 to
                 one
                 ,
                 as
                 may
                 be
                 easily
                 calculated
                 ;
                 it
                 is
                 manifest
                 ,
                 that
                 such
                 abatement
                 shall
                 be
                 imperceptible
                 ,
                 and
                 almost
                 nothing
                 ,
                 in
                 two
                 dayes
                 space
                 ,
                 nay
                 in
                 four
                 or
                 six
                 :
                 and
                 all
                 this
                 will
                 be
                 true
                 ,
                 when
                 we
                 suppose
                 that
                 for
                 that
                 time
                 there
                 entreth
                 no
                 other
                 Water
                 into
                 the
                 Lake
                 from
                 Ditches
                 or
                 Rivolets
                 ,
                 which
                 falling
                 into
                 the
                 Lake
                 would
                 render
                 such
                 abatement
                 yet
                 less
                 .
              
               
                 Now
                 we
                 see
                 ,
                 that
                 it
                 's
                 necessary
                 to
                 examine
                 such
                 abatements
                 and
                 risings
                 ,
                 with
                 excellent
                 reasons
                 ,
                 or
                 at
                 least
                 ,
                 with
                 accurate
                 experiments
                 ,
                 before
                 we
                 resolve
                 and
                 conclude
                 any
                 thing
                 ;
                 and
                 how
                 farre
                 the
                 vulgar
                 are
                 distant
                 from
                 a
                 right
                 judgement
                 in
                 such
                 matters
                 .
              
            
             
               
                 APPENDIX
                 XIII
                 .
              
               
                 FOR
                 greater
                 confirmation
                 of
                 all
                 this
                 which
                 I
                 have
                 said
                 ,
                 I
                 will
                 instance
                 in
                 another
                 like
                 case
                 ,
                 which
                 also
                 I
                 met
                 with
                 heretofore
                 ,
                 wherein
                 ,
                 for
                 that
                 the
                 business
                 was
                 not
                 rightly
                 understood
                 ,
                 many
                 disorders
                 ,
                 vast
                 expences
                 ,
                 and
                 considerable
                 mischiefs
                 have
                 followed
                 .
                 There
                 was
                 heretofore
                 an
                 Emissary
                 or
                 Sluice
                 made
                 to
                 drain
                 the
                 Waters
                 ,
                 which
                 from
                 Rains
                 ,
                 Springs
                 ,
                 and
                 Rivolets
                 fall
                 into
                 a
                 Lake
                 ;
                 to
                 the
                 end
                 ,
                 the
                 shores
                 adjoyning
                 on
                 the
                 Lake
                 ,
                 should
                 be
                 free
                 from
                 the
                 overflowing
                 of
                 the
                 Waters
                 ;
                 but
                 because
                 perhaps
                 the
                 enterprize
                 was
                 not
                 well
                 managed
                 and
                 carried
                 on
                 ,
                 it
                 fell
                 out
                 ,
                 that
                 the
                 Fields
                 adjacent
                 to
                 the
                 said
                 Chanel
                 could
                 not
                 drain
                 ,
                 but
                 continued
                 under
                 water
                 ;
                 to
                 which
                 disorders
                 a
                 present
                 remedy
                 hath
                 been
                 used
                 ,
                 namely
                 ,
                 in
                 a
                 time
                 convenient
                 to
                 stop
                 up
                 the
                 Sluice
                 ,
                 by
                 meanes
                 of
                 certain
                 Floodgates
                 kept
                 on
                 purpose
                 for
                 that
                 end
                 ;
                 and
                 thus
                 abating
                 the
                 Level
                 of
                 the
                 Water
                 
                 in
                 the
                 Emissary
                 ,
                 in
                 the
                 space
                 of
                 three
                 or
                 four
                 dayes
                 ,
                 the
                 Fields
                 have
                 been
                 haply
                 drained
                 .
                 But
                 on
                 the
                 other
                 part
                 ,
                 the
                 proprietors
                 bordering
                 on
                 the
                 Lake
                 opposed
                 this
                 ,
                 grievously
                 complaining
                 ,
                 that
                 whilst
                 the
                 Floodgates
                 are
                 shut
                 ,
                 and
                 the
                 course
                 of
                 the
                 Water
                 of
                 the
                 Sluice
                 hindered
                 ,
                 the
                 Lake
                 overflowes
                 the
                 Lands
                 adjacent
                 ,
                 by
                 meanes
                 of
                 the
                 Rivers
                 that
                 fell
                 into
                 it
                 ,
                 to
                 their
                 very
                 great
                 damage
                 ;
                 and
                 so
                 continuing
                 their
                 suits
                 ,
                 they
                 got
                 more
                 of
                 vexation
                 than
                 satisfaction
                 .
                 Now
                 ,
                 being
                 asked
                 my
                 opinion
                 herein
                 ,
                 I
                 judged
                 it
                 requisite
                 (
                 since
                 the
                 point
                 in
                 controversie
                 was
                 about
                 the
                 rising
                 and
                 falling
                 of
                 the
                 Lake
                 )
                 that
                 the
                 said
                 abatement
                 ,
                 when
                 the
                 Floodgates
                 are
                 open
                 ,
                 and
                 increase
                 when
                 they
                 are
                 shut
                 should
                 be
                 exactly
                 measured
                 ,
                 and
                 told
                 them
                 ,
                 that
                 it
                 might
                 be
                 easily
                 done
                 at
                 a
                 time
                 when
                 no
                 extraordinary
                 Waters
                 fell
                 into
                 the
                 Lake
                 ,
                 neither
                 of
                 Rain
                 ,
                 or
                 otherwise
                 ;
                 and
                 the
                 Lake
                 was
                 undisturbed
                 by
                 winds
                 that
                 might
                 drive
                 the
                 Water
                 to
                 any
                 side
                 ,
                 by
                 planting
                 neer
                 to
                 an
                 Islet
                 ,
                 which
                 is
                 about
                 the
                 middle
                 of
                 the
                 Lake
                 ,
                 a
                 thick
                 post
                 ,
                 on
                 which
                 should
                 be
                 made
                 the
                 marks
                 of
                 the
                 Lakes
                 rising
                 and
                 falling
                 for
                 two
                 or
                 three
                 dayes
                 .
                 I
                 would
                 not
                 ,
                 at
                 that
                 time
                 ,
                 pawn
                 ,
                 or
                 resolutely
                 declare
                 ,
                 my
                 judgment
                 ,
                 in
                 regard
                 I
                 might
                 be
                 ,
                 by
                 divers
                 accidents
                 missed
                 .
                 But
                 this
                 I
                 told
                 them
                 ,
                 that
                 (
                 by
                 what
                 I
                 have
                 demonstrated
                 ,
                 and
                 particularly
                 that
                 which
                 I
                 have
                 said
                 above
                 touching
                 the
                 Lake
                 of
                 Perugia
                 )
                 I
                 inclined
                 greatly
                 to
                 think
                 ,
                 that
                 these
                 risings
                 and
                 fallings
                 would
                 prove
                 imperceptible
                 ,
                 and
                 inconsiderable
                 ;
                 and
                 therefore
                 ,
                 that
                 in
                 case
                 experience
                 should
                 make
                 good
                 my
                 reason
                 ,
                 it
                 would
                 be
                 to
                 no
                 purpose
                 for
                 them
                 to
                 continue
                 disputing
                 and
                 wrangling
                 ,
                 which
                 causeth
                 ,
                 (
                 according
                 to
                 the
                 Proverb
                 )
                 
                   A
                   great
                   deal
                   of
                   cry
                
                 ,
                 but
                 produceth
                 not
                 much
                 Wool.
                 
              
               
                 Lastly
                 ,
                 it
                 importing
                 very
                 much
                 to
                 know
                 what
                 a
                 Rain
                 continued
                 for
                 many
                 dayes
                 can
                 do
                 in
                 raising
                 these
                 Lakes
                 ,
                 I
                 will
                 here
                 insert
                 the
                 Copy
                 of
                 a
                 Letter
                 ,
                 which
                 I
                 writ
                 formerly
                 to
                 
                   Signior
                   Galilaeo
                   Galilaei
                
                 ,
                 chief
                 Philosopher
                 to
                 the
                 Grand
                 Duke
                 of
                 Tuscany
                 ,
                 wherein
                 I
                 have
                 delivered
                 one
                 of
                 my
                 conceits
                 in
                 this
                 businesse
                 ,
                 and
                 it
                 may
                 be
                 ,
                 by
                 this
                 Letter
                 ,
                 I
                 may
                 ,
                 more
                 strongly
                 ,
                 confirm
                 what
                 I
                 have
                 said
                 above
                 .
              
            
             
               
               
                 The
                 Copy
                 of
                 a
                 Letter
                 to
                 Signore
                 GALILAEO
                 GALILAEI
                 ,
                 Chief
                 Philosopher
                 to
                 the
                 most
                 Serene
                 Great
                 Duke
                 of
                 TVSCANY
                 .
              
               
                 
                   Worthy
                   and
                   most
                   Excellent
                   SIR
                   ,
                
              
               
                 IN
                 satisfaction
                 of
                 my
                 promise
                 ,
                 in
                 my
                 former
                 Letters
                 of
                 representing
                 unto
                 you
                 some
                 of
                 my
                 Considerations
                 made
                 upon
                 the
                 Lake
                 Thrasimeno
                 ,
                 I
                 say
                 ,
                 That
                 in
                 times
                 past
                 ,
                 being
                 in
                 Perugia
                 ,
                 where
                 we
                 held
                 our
                 General
                 Convention
                 ,
                 having
                 understood
                 that
                 the
                 Lake
                 Thrasimeno
                 ,
                 by
                 the
                 great
                 drought
                 of
                 many
                 Moneths
                 was
                 much
                 abated
                 ,
                 It
                 came
                 into
                 my
                 head
                 ,
                 to
                 go
                 privately
                 and
                 see
                 this
                 novelty
                 ,
                 both
                 for
                 my
                 particular
                 satisfaction
                 ,
                 as
                 also
                 that
                 I
                 might
                 be
                 able
                 to
                 relate
                 the
                 whole
                 to
                 my
                 Patrons
                 ,
                 upon
                 the
                 certitude
                 of
                 my
                 own
                 sight
                 of
                 the
                 place
                 .
                 And
                 so
                 being
                 come
                 to
                 the
                 Emissary
                 of
                 the
                 Lake
                 ,
                 I
                 found
                 that
                 the
                 Level
                 of
                 the
                 Lakes
                 surface
                 was
                 ebbed
                 about
                 five
                 Roman
                 Palmes
                 of
                 its
                 wonted
                 watermark
                 ,
                 insomuch
                 that
                 it
                 was
                 lower
                 than
                 the
                 transome
                 of
                 the
                 mouth
                 of
                 the
                 Emissary
                 ,
                 by
                 the
                 length
                 of
                 —
                 this
                 described
                 line
                 ,
                 and
                 therefore
                 no
                 Water
                 issued
                 out
                 of
                 the
                 Lake
                 ,
                 to
                 the
                 great
                 prejudice
                 of
                 all
                 the
                 places
                 and
                 villages
                 circumjacent
                 ,
                 in
                 regard
                 that
                 the
                 Water
                 which
                 used
                 to
                 run
                 from
                 the
                 said
                 Lake
                 turned
                 22
                 Mills
                 ,
                 which
                 not
                 going
                 ,
                 necessitated
                 the
                 inhabitants
                 of
                 those
                 parts
                 to
                 go
                 a
                 dayes
                 journey
                 and
                 more
                 ,
                 to
                 grinde
                 upon
                 the
                 Tiber.
                 Being
                 returned
                 to
                 Perugia
                 ,
                 there
                 followed
                 a
                 Rain
                 ,
                 not
                 very
                 great
                 ,
                 but
                 constant
                 ,
                 and
                 even
                 ,
                 which
                 lasted
                 for
                 the
                 space
                 of
                 eight
                 hours
                 ,
                 or
                 thereabouts
                 ;
                 and
                 it
                 came
                 into
                 my
                 thoughts
                 to
                 examine
                 ,
                 being
                 in
                 Perugia
                 ,
                 how
                 much
                 the
                 Lake
                 was
                 increased
                 and
                 raised
                 by
                 this
                 Rain
                 ,
                 supposing
                 (
                 as
                 it
                 was
                 probable
                 enough
                 )
                 that
                 the
                 Rain
                 had
                 been
                 universal
                 over
                 all
                 the
                 Lake
                 ;
                 and
                 like
                 to
                 that
                 which
                 fell
                 in
                 Perugia
                 ,
                 and
                 to
                 this
                 purpose
                 I
                 took
                 a
                 Glasse
                 formed
                 like
                 a
                 Cylinder
                 ,
                 about
                 a
                 palme
                 high
                 ,
                 and
                 half
                 a
                 palme
                 broad
                 ;
                 and
                 having
                 put
                 in
                 water
                 sufficient
                 to
                 cover
                 the
                 bottome
                 of
                 the
                 Glasse
                 ,
                 I
                 noted
                 diligently
                 the
                 mark
                 of
                 the
                 height
                 of
                 the
                 Water
                 in
                 the
                 Glasse
                 ,
                 and
                 afterwards
                 exposed
                 it
                 to
                 the
                 open
                 weather
                 ,
                 to
                 receive
                 the
                 Raine-water
                 ,
                 which
                 fell
                 into
                 it
                 ;
                 and
                 I
                 let
                 it
                 stand
                 for
                 the
                 space
                 of
                 an
                 hour
                 ;
                 and
                 having
                 observed
                 that
                 in
                 that
                 time
                 the
                 Water
                 was
                 risen
                 in
                 the
                 Vessel
                 the
                 height
                 of
                 the
                 following
                 line
                 —
                 ,
                 I
                 considered
                 that
                 if
                 I
                 had
                 exposed
                 to
                 the
                 same
                 rain
                 such
                 other
                 vessels
                 equal
                 to
                 that
                 ,
                 the
                 Water
                 would
                 have
                 risen
                 in
                 them
                 all
                 according
                 to
                 that
                 measure
                 :
                 And
                 thereupon
                 concluded
                 ,
                 that
                 also
                 in
                 all
                 
                 the
                 whole
                 extent
                 of
                 the
                 Lake
                 ,
                 it
                 was
                 necessary
                 the
                 Water
                 should
                 be
                 raised
                 in
                 the
                 space
                 of
                 an
                 hour
                 the
                 same
                 measure
                 .
                 Yet
                 here
                 I
                 considered
                 two
                 difficulties
                 that
                 might
                 disturb
                 and
                 altar
                 such
                 an
                 effect
                 ,
                 or
                 at
                 least
                 render
                 it
                 inobserveable
                 ,
                 which
                 afterwards
                 well
                 weighed
                 ,
                 and
                 resolved
                 ,
                 left
                 me
                 (
                 as
                 I
                 will
                 tell
                 you
                 anon
                 )
                 in
                 the
                 conclusion
                 the
                 more
                 confirmed
                 ;
                 that
                 the
                 Lake
                 ought
                 to
                 be
                 increased
                 in
                 the
                 space
                 of
                 eight
                 hours
                 ,
                 that
                 the
                 rain
                 lasted
                 eight
                 times
                 that
                 measure
                 .
                 And
                 whilst
                 I
                 again
                 exposed
                 the
                 Glass
                 to
                 repeat
                 the
                 experiment
                 ,
                 there
                 came
                 unto
                 me
                 an
                 Ingeneer
                 to
                 talk
                 with
                 me
                 touching
                 certain
                 affairs
                 of
                 our
                 Monastary
                 of
                 Perugia
                 ,
                 and
                 discoursing
                 with
                 him
                 ,
                 I
                 shewed
                 him
                 the
                 Glass
                 out
                 at
                 my
                 Chamber
                 window
                 ,
                 exposed
                 in
                 a
                 Court-yard
                 ;
                 and
                 communicated
                 to
                 him
                 my
                 fancy
                 ,
                 relating
                 unto
                 him
                 all
                 that
                 I
                 had
                 done
                 .
                 But
                 I
                 soon
                 perceived
                 that
                 this
                 brave
                 fellow
                 conceited
                 me
                 to
                 be
                 but
                 of
                 a
                 dull
                 brain
                 ,
                 for
                 he
                 smiling
                 said
                 unto
                 me
                 ;
                 Sir
                 ,
                 you
                 deceive
                 your self
                 :
                 I
                 am
                 of
                 opinion
                 that
                 the
                 Lake
                 will
                 not
                 be
                 increased
                 by
                 this
                 rain
                 ,
                 so
                 much
                 as
                 the
                 thicknesse
                 of
                 a
                 *
                 Julio
                 .
                 Hearing
                 him
                 pronounce
                 this
                 his
                 opinion
                 with
                 freeness
                 and
                 confidence
                 ,
                 I
                 urged
                 him
                 to
                 give
                 me
                 some
                 reason
                 for
                 what
                 he
                 said
                 ,
                 assuring
                 him
                 ,
                 that
                 I
                 would
                 change
                 my
                 judgement
                 ,
                 when
                 I
                 saw
                 the
                 strength
                 of
                 his
                 Arguments
                 :
                 To
                 which
                 he
                 answered
                 ,
                 that
                 he
                 had
                 been
                 very
                 conversant
                 about
                 the
                 Lake
                 ,
                 and
                 was
                 every
                 day
                 upon
                 it
                 ,
                 and
                 was
                 well
                 assured
                 that
                 it
                 was
                 not
                 at
                 all
                 increased
                 .
                 And
                 importuning
                 him
                 further
                 ,
                 that
                 he
                 would
                 give
                 me
                 some
                 reason
                 for
                 his
                 so
                 thinking
                 ,
                 he
                 proposed
                 to
                 my
                 consideration
                 the
                 great
                 drought
                 passed
                 ,
                 and
                 that
                 that
                 same
                 rain
                 was
                 nothing
                 for
                 the
                 great
                 parching
                 :
                 To
                 which
                 I
                 answered
                 ,
                 I
                 believe
                 Sir
                 that
                 the
                 surface
                 of
                 the
                 Lake
                 ,
                 on
                 which
                 the
                 rain
                 had
                 fallen
                 was
                 moistned
                 ▪
                 and
                 therefore
                 saw
                 not
                 how
                 its
                 drought
                 ,
                 which
                 was
                 nothing
                 at
                 all
                 ,
                 could
                 have
                 drunk
                 up
                 any
                 part
                 of
                 the
                 rain
                 .
                 For
                 all
                 this
                 he
                 persisting
                 in
                 his
                 conceit
                 ,
                 without
                 yielding
                 in
                 the
                 least
                 to
                 my
                 allegation
                 ;
                 he
                 granted
                 in
                 the
                 end
                 (
                 I
                 believe
                 in
                 civility
                 to
                 me
                 )
                 that
                 my
                 reason
                 was
                 plausible
                 and
                 good
                 ,
                 but
                 that
                 in
                 practise
                 it
                 could
                 not
                 hold
                 .
                 At
                 last
                 to
                 clear
                 up
                 all
                 ,
                 I
                 made
                 one
                 be
                 called
                 ,
                 and
                 sent
                 him
                 to
                 the
                 mouth
                 of
                 the
                 Emissary
                 of
                 the
                 Lake
                 ,
                 with
                 order
                 to
                 bring
                 me
                 an
                 exact
                 account
                 ,
                 how
                 he
                 found
                 the
                 water
                 of
                 the
                 Lake
                 ,
                 in
                 respect
                 of
                 the
                 Transome
                 of
                 the
                 Sluice
                 .
                 Now
                 here
                 ,
                 Signore
                 Galilaeo
                 ,
                 I
                 would
                 not
                 have
                 you
                 think
                 that
                 I
                 had
                 brought
                 the
                 matter
                 in
                 hand
                 to
                 concern
                 me
                 in
                 my
                 honour
                 ;
                 but
                 believe
                 me
                 (
                 and
                 there
                 are
                 witnesses
                 of
                 the
                 same
                 still
                 living
                 )
                 that
                 my
                 messenger
                 returning
                 in
                 the
                 evening
                 to
                 Perugia
                 ,
                 he
                 brought
                 me
                 word
                 ,
                 that
                 the
                 water
                 of
                 the
                 Lake
                 began
                 to
                 run
                 through
                 the
                 Cave
                 ;
                 and
                 that
                 it
                 was
                 risen
                 almost
                 a
                 fingers
                 breadth
                 above
                 the
                 Transome
                 :
                 Insomuch
                 ,
                 that
                 adding
                 this
                 measure
                 ,
                 to
                 that
                 of
                 the
                 lowness
                 of
                 the
                 surface
                 of
                 the
                 Lake
                 ,
                 beneath
                 the
                 Transome
                 before
                 the
                 rain
                 ,
                 
                 it
                 was
                 manifest
                 that
                 the
                 rising
                 of
                 the
                 Lake
                 caused
                 by
                 the
                 rain
                 ,
                 was
                 to
                 a
                 hair
                 those
                 four
                 fingers
                 breadth
                 that
                 I
                 had
                 judged
                 it
                 to
                 be
                 .
                 Two
                 dayes
                 after
                 I
                 had
                 another
                 bout
                 with
                 the
                 Ingeneer
                 ,
                 and
                 related
                 to
                 him
                 the
                 whole
                 business
                 ,
                 to
                 which
                 he
                 knew
                 not
                 what
                 to
                 answer
                 .
              
               
                 Now
                 the
                 two
                 difficulties
                 which
                 I
                 thought
                 of
                 ,
                 able
                 to
                 impede
                 my
                 conclusion
                 ,
                 were
                 these
                 following
                 :
                 First
                 ,
                 I
                 considered
                 that
                 it
                 might
                 be
                 ,
                 that
                 the
                 Wind
                 blowing
                 from
                 the
                 side
                 where
                 the
                 Sluice
                 stood
                 ,
                 to
                 the
                 Lake-ward
                 ;
                 the
                 mole
                 and
                 mass
                 of
                 the
                 Water
                 of
                 the
                 Lake
                 might
                 be
                 driven
                 to
                 the
                 contrary
                 shore
                 ;
                 on
                 which
                 the
                 Water
                 rising
                 ,
                 it
                 might
                 be
                 fallen
                 at
                 the
                 mouth
                 of
                 the
                 Emissary
                 ,
                 and
                 so
                 the
                 observation
                 might
                 be
                 much
                 obscured
                 .
                 But
                 this
                 difficulty
                 wholly
                 vanished
                 by
                 reason
                 of
                 the
                 Aires
                 great
                 tranquility
                 ;
                 which
                 it
                 kept
                 at
                 that
                 time
                 ,
                 for
                 no
                 Wind
                 was
                 stirring
                 on
                 any
                 side
                 ,
                 neither
                 whilst
                 it
                 rained
                 ,
                 nor
                 afterwards
                 .
              
               
                 The
                 second
                 difficulty
                 which
                 put
                 the
                 rising
                 in
                 doubt
                 ,
                 was
                 ,
                 That
                 having
                 observed
                 in
                 Florence
                 ,
                 and
                 elsewhere
                 ,
                 those
                 Ponds
                 into
                 which
                 the
                 rain-water
                 ,
                 falling
                 from
                 the
                 house
                 ,
                 is
                 conveyed
                 through
                 the
                 Common-shores
                 :
                 And
                 that
                 they
                 are
                 not
                 thereby
                 ever
                 filled
                 ,
                 but
                 that
                 they
                 swallow
                 all
                 that
                 abundance
                 of
                 water
                 ,
                 that
                 runs
                 into
                 them
                 by
                 those
                 conveyances
                 which
                 serve
                 them
                 with
                 water
                 ;
                 insomuch
                 that
                 those
                 conveyances
                 which
                 in
                 time
                 of
                 drought
                 maintain
                 the
                 Pond
                 ,
                 when
                 there
                 comes
                 new
                 abundance
                 of
                 water
                 into
                 the
                 Pond
                 ,
                 they
                 drink
                 it
                 up
                 ,
                 and
                 swallow
                 it
                 :
                 A
                 like
                 effect
                 might
                 also
                 fall
                 out
                 in
                 the
                 Lake
                 ,
                 in
                 which
                 there
                 being
                 many
                 veins
                 (
                 as
                 it
                 is
                 very
                 likely
                 )
                 that
                 maintain
                 and
                 feed
                 the
                 Lake
                 ;
                 these
                 veins
                 might
                 imbibe
                 the
                 new
                 addition
                 of
                 the
                 Rain-water
                 ,
                 and
                 so
                 by
                 that
                 means
                 annull
                 the
                 rising
                 ;
                 or
                 else
                 diminish
                 it
                 in
                 such
                 sort
                 ,
                 as
                 to
                 render
                 it
                 inobservable
                 .
                 But
                 this
                 difficulty
                 was
                 easily
                 resolved
                 by
                 considering
                 my
                 Treatise
                 of
                 the
                 measure
                 of
                 Running-Waters
                 ;
                 forasmuch
                 as
                 having
                 demonstrated
                 ,
                 that
                 the
                 abatement
                 of
                 a
                 Lake
                 beareth
                 the
                 reciprocal
                 proportion
                 to
                 the
                 velocity
                 of
                 the
                 Emissary
                 ,
                 which
                 the
                 measure
                 of
                 the
                 Section
                 of
                 the
                 Emissary
                 of
                 the
                 Lake
                 ,
                 hath
                 to
                 the
                 measure
                 of
                 the
                 surface
                 of
                 the
                 Lake
                 :
                 making
                 the
                 calculation
                 and
                 account
                 ,
                 though
                 in
                 gross
                 ;
                 by
                 supposing
                 that
                 its
                 veins
                 were
                 sufficiently
                 large
                 ,
                 and
                 that
                 the
                 velocity
                 in
                 them
                 were
                 notable
                 in
                 drinking
                 up
                 the
                 water
                 of
                 the
                 Lake
                 ;
                 yet
                 I
                 found
                 nevertheless
                 ,
                 that
                 many
                 weeks
                 and
                 moneths
                 would
                 be
                 spent
                 in
                 drinking
                 up
                 the
                 new-come
                 abundance
                 of
                 water
                 by
                 the
                 rain
                 ,
                 so
                 that
                 I
                 rested
                 sure
                 ,
                 that
                 the
                 rising
                 would
                 ensue
                 ,
                 as
                 in
                 effect
                 it
                 did
                 .
              
               
                 And
                 because
                 many
                 of
                 accurate
                 judgement
                 ,
                 have
                 again
                 caused
                 me
                 to
                 question
                 this
                 rising
                 ,
                 setting
                 before
                 me
                 ,
                 that
                 the
                 Earth
                 being
                 parched
                 by
                 the
                 great
                 drought
                 ,
                 that
                 had
                 so
                 long
                 continued
                 ,
                 it
                 might
                 be
                 ,
                 that
                 that
                 Bank
                 of
                 Earth
                 which
                 environed
                 the
                 brink
                 of
                 the
                 Lake
                 ,
                 being
                 dry
                 ,
                 and
                 imbibing
                 great
                 abundance
                 of
                 Water
                 
                 from
                 the
                 increasing
                 Lake
                 ,
                 would
                 not
                 suffer
                 it
                 to
                 increase
                 in
                 height
                 :
                 I
                 say
                 therefore
                 ,
                 that
                 if
                 we
                 would
                 rightly
                 consider
                 this
                 doubt
                 here
                 proposed
                 ,
                 we
                 should
                 ,
                 in
                 the
                 very
                 consideration
                 of
                 it
                 ,
                 see
                 it
                 resolved
                 ;
                 for
                 ,
                 it
                 being
                 supposed
                 that
                 that
                 list
                 or
                 border
                 of
                 Banks
                 which
                 was
                 to
                 be
                 occupied
                 by
                 the
                 increase
                 of
                 the
                 Lake
                 ,
                 be
                 a
                 Brace
                 in
                 breadth
                 quite
                 round
                 the
                 Lake
                 ,
                 and
                 that
                 by
                 reason
                 of
                 its
                 dryness
                 it
                 sucks
                 in
                 water
                 ,
                 and
                 that
                 by
                 that
                 means
                 this
                 proportion
                 of
                 water
                 co-operates
                 not
                 in
                 raising
                 of
                 the
                 Lake
                 :
                 It
                 is
                 absolutely
                 necessary
                 on
                 the
                 other
                 hand
                 ,
                 that
                 we
                 consider
                 ,
                 That
                 the
                 Circuit
                 of
                 the
                 water
                 of
                 the
                 Lake
                 being
                 thirty
                 miles
                 ,
                 as
                 it
                 s
                 commonly
                 held
                 ,
                 that
                 is
                 to
                 say
                 ,
                 Ninety
                 thousand
                 Braces
                 of
                 Florence
                 in
                 compass
                 ;
                 and
                 therefore
                 admitting
                 for
                 true
                 ,
                 that
                 each
                 Brace
                 of
                 this
                 Bank
                 drink
                 two
                 quarts
                 of
                 water
                 ,
                 and
                 that
                 for
                 the
                 spreading
                 it
                 require
                 three
                 quarts
                 more
                 ,
                 we
                 shall
                 finde
                 ,
                 that
                 the
                 whole
                 agregate
                 of
                 this
                 portion
                 of
                 water
                 ,
                 which
                 is
                 not
                 imployed
                 in
                 the
                 raising
                 of
                 the
                 Lake
                 ,
                 will
                 be
                 four
                 hundred
                 and
                 fifty
                 thousand
                 Quarts
                 of
                 water
                 ;
                 and
                 supposing
                 that
                 the
                 Lake
                 be
                 sixty
                 square
                 miles
                 ,
                 three
                 thousand
                 Braces
                 long
                 ,
                 we
                 shall
                 finde
                 ,
                 that
                 to
                 dispence
                 the
                 water
                 possest
                 by
                 the
                 Bank
                 about
                 the
                 Lake
                 ,
                 above
                 the
                 total
                 surface
                 of
                 the
                 Lake
                 ,
                 it
                 ought
                 to
                 be
                 spread
                 so
                 thin
                 ,
                 that
                 one
                 sole
                 quart
                 of
                 water
                 may
                 over-spread
                 ten
                 thousand
                 square
                 Braces
                 of
                 surface
                 :
                 such
                 a
                 thinness
                 ,
                 as
                 must
                 much
                 exceed
                 that
                 of
                 a
                 leaf
                 of
                 beaten
                 Gold
                 ,
                 and
                 also
                 less
                 than
                 that
                 skin
                 of
                 water
                 which
                 covers
                 the
                 Bubbles
                 of
                 it
                 :
                 and
                 such
                 would
                 that
                 be
                 ,
                 which
                 those
                 men
                 would
                 have
                 substracted
                 from
                 the
                 rising
                 of
                 the
                 Lake
                 :
                 But
                 again
                 ,
                 in
                 the
                 space
                 of
                 a
                 quarter
                 of
                 an
                 hour
                 at
                 the
                 beginning
                 of
                 the
                 rain
                 ,
                 all
                 that
                 Bank
                 is
                 soaked
                 by
                 the
                 said
                 rain
                 ,
                 so
                 that
                 we
                 need
                 not
                 for
                 the
                 moistning
                 of
                 it
                 ,
                 imploy
                 a
                 drop
                 of
                 that
                 water
                 which
                 falleth
                 into
                 the
                 Lake
                 .
                 Besides
                 we
                 have
                 not
                 brought
                 to
                 account
                 that
                 abundance
                 of
                 water
                 which
                 runs
                 in
                 time
                 of
                 rain
                 into
                 the
                 Lake
                 ,
                 from
                 the
                 steepness
                 of
                 the
                 adjacent
                 Hills
                 and
                 Mountains
                 ;
                 which
                 would
                 be
                 enough
                 to
                 supply
                 all
                 our
                 occasions
                 :
                 So
                 that
                 ,
                 neither
                 ought
                 we
                 for
                 this
                 reason
                 to
                 question
                 our
                 pretended
                 rising
                 .
                 And
                 this
                 is
                 what
                 hath
                 fallen
                 in
                 my
                 way
                 touching
                 the
                 consideration
                 of
                 the
                 Thrasimcnian
                 Lake
                 .
              
               
                 After
                 which
                 ,
                 perhaps
                 somewhat
                 rashly
                 ,
                 wandring
                 beyond
                 my
                 bounds
                 ,
                 I
                 proceeded
                 to
                 another
                 contemplation
                 ,
                 which
                 I
                 will
                 relate
                 to
                 you
                 ,
                 hoping
                 that
                 you
                 will
                 receive
                 it
                 ,
                 as
                 collected
                 with
                 these
                 cautions
                 requisite
                 in
                 such
                 like
                 affairs
                 ;
                 wherein
                 we
                 ought
                 not
                 too
                 positively
                 to
                 affirm
                 any
                 thing
                 of
                 our
                 own
                 heads
                 for
                 certain
                 ,
                 but
                 ought
                 to
                 submit
                 all
                 to
                 the
                 sound
                 and
                 secure
                 deliberation
                 of
                 the
                 Holy
                 Mother-Church
                 ,
                 as
                 I
                 do
                 this
                 of
                 mine
                 ,
                 and
                 all
                 others
                 ;
                 most
                 ready
                 to
                 change
                 my
                 judgement
                 ,
                 and
                 conform
                 my self
                 alwaies
                 to
                 the
                 deliberations
                 of
                 my
                 Superiors
                 .
                 Continuing
                 
                 therefore
                 my
                 above-said
                 conceit
                 about
                 the
                 rising
                 of
                 the
                 water
                 in
                 the
                 glass
                 tried
                 before
                 ,
                 it
                 came
                 into
                 my
                 minde
                 ,
                 that
                 the
                 forementioned
                 rain
                 having
                 been
                 very
                 gentle
                 ,
                 it
                 might
                 well
                 be
                 ,
                 that
                 if
                 there
                 should
                 have
                 faln
                 a
                 Rain
                 fifty
                 ,
                 an
                 hundred
                 ,
                 or
                 a
                 thousand
                 times
                 greater
                 than
                 this
                 ,
                 and
                 much
                 more
                 intense
                 (
                 which
                 would
                 insue
                 as
                 oft
                 as
                 those
                 falling
                 drops
                 were
                 four
                 ,
                 five
                 or
                 ten
                 times
                 bigger
                 than
                 those
                 of
                 the
                 above-mentioned
                 rain
                 ,
                 keeping
                 the
                 same
                 number
                 )
                 in
                 such
                 a
                 case
                 its
                 manifest
                 ,
                 that
                 in
                 the
                 space
                 of
                 an
                 hour
                 the
                 Water
                 would
                 rise
                 in
                 our
                 Glass
                 ,
                 two
                 ,
                 three
                 ,
                 and
                 perhaps
                 more
                 Yards
                 or
                 Braces
                 ;
                 and
                 consequently
                 ,
                 if
                 such
                 a
                 Raine
                 should
                 fall
                 upon
                 a
                 Lake
                 ,
                 that
                 the
                 said
                 Lake
                 would
                 rise
                 ,
                 according
                 to
                 the
                 same
                 rate
                 :
                 And
                 likewise
                 ,
                 if
                 such
                 a
                 Rain
                 were
                 universall
                 ,
                 over
                 the
                 whole
                 Terrestriall
                 Globe
                 ,
                 it
                 would
                 necessarily
                 ,
                 in
                 the
                 space
                 of
                 an
                 hour
                 ,
                 make
                 a
                 rising
                 of
                 two
                 ,
                 or
                 three
                 braces
                 round
                 about
                 the
                 said
                 Globe
                 .
                 And
                 because
                 we
                 have
                 from
                 Sacred
                 Records
                 ,
                 that
                 in
                 the
                 time
                 of
                 the
                 Deluge
                 ,
                 it
                 rained
                 fourty
                 dayes
                 and
                 fourty
                 nights
                 ;
                 namely
                 ,
                 for
                 the
                 space
                 of
                 960
                 houres
                 ;
                 its
                 clear
                 ,
                 that
                 if
                 the
                 said
                 Rain
                 had
                 been
                 ten
                 times
                 bigger
                 than
                 ours
                 at
                 Perugia
                 ,
                 the
                 rising
                 of
                 the
                 Waters
                 above
                 the
                 Terrestrial
                 Globe
                 would
                 reach
                 and
                 pass
                 a
                 mile
                 higher
                 than
                 the
                 tops
                 of
                 the
                 Hills
                 and
                 Mountains
                 that
                 are
                 upon
                 the
                 superficies
                 of
                 the
                 Earth
                 ;
                 and
                 they
                 also
                 would
                 concur
                 to
                 increase
                 the
                 rise
                 .
                 And
                 therefore
                 I
                 conclude
                 ,
                 that
                 the
                 rise
                 of
                 the
                 Waters
                 of
                 the
                 Deluge
                 have
                 a
                 rational
                 congruity
                 with
                 natural
                 Discourses
                 ,
                 of
                 which
                 I
                 know
                 very
                 well
                 that
                 the
                 eternal
                 truths
                 of
                 the
                 Divine
                 leaves
                 have
                 no
                 need
                 ;
                 but
                 however
                 I
                 think
                 so
                 clear
                 an
                 agreement
                 is
                 worthy
                 of
                 our
                 consideration
                 ,
                 which
                 gives
                 us
                 occasion
                 to
                 adore
                 and
                 admire
                 the
                 greatnesse
                 of
                 God
                 in
                 his
                 mighty
                 Works
                 ,
                 in
                 that
                 we
                 are
                 sometimes
                 able
                 ,
                 in
                 some
                 sort
                 ,
                 to
                 measure
                 them
                 by
                 the
                 short
                 Standard
                 of
                 our
                 Reason
                 .
              
               
                 Many
                 Lessons
                 also
                 may
                 be
                 deduced
                 from
                 the
                 same
                 Doctrine
                 ,
                 which
                 I
                 passe
                 by
                 ,
                 for
                 that
                 every
                 man
                 of
                 himself
                 may
                 easily
                 know
                 them
                 ,
                 having
                 once
                 stablished
                 this
                 Maxime
                 ;
                 That
                 it
                 is
                 not
                 possible
                 to
                 pronounce
                 any
                 thing
                 ,
                 of
                 a
                 certainty
                 ,
                 touching
                 the
                 quantity
                 of
                 Running
                 Waters
                 ,
                 by
                 considering
                 only
                 the
                 single
                 vulgar
                 measure
                 of
                 the
                 Water
                 without
                 the
                 velocity
                 ;
                 and
                 so
                 on
                 the
                 contrary
                 ,
                 he
                 that
                 computes
                 only
                 the
                 velocity
                 ,
                 without
                 the
                 measure
                 ,
                 shall
                 commit
                 very
                 great
                 errours
                 ;
                 for
                 treating
                 of
                 the
                 measure
                 of
                 Running
                 Waters
                 ,
                 it
                 is
                 necessary
                 ,
                 the
                 water
                 being
                 a
                 body
                 ,
                 in
                 handling
                 its
                 quantity
                 ,
                 to
                 consider
                 in
                 it
                 all
                 the
                 three
                 dimensions
                 of
                 breadth
                 ,
                 depth
                 ,
                 and
                 length
                 :
                 the
                 two
                 first
                 dimensions
                 are
                 observed
                 by
                 all
                 in
                 the
                 common
                 manner
                 ,
                 and
                 ordinary
                 way
                 of
                 measuring
                 Running
                 Waters
                 ;
                 but
                 the
                 third
                 dimension
                 of
                 length
                 is
                 omitted
                 ;
                 and
                 haply
                 such
                 an
                 oversight
                 is
                 committed
                 ,
                 by
                 reason
                 the
                 length
                 of
                 Running
                 
                 Water
                 is
                 reputed
                 in
                 some
                 sense
                 infinite
                 ,
                 in
                 that
                 it
                 never
                 ceaseth
                 to
                 move
                 away
                 ,
                 and
                 as
                 infinite
                 is
                 judged
                 incomprehensible
                 ;
                 and
                 such
                 as
                 that
                 there
                 is
                 no
                 exact
                 knowledge
                 to
                 be
                 had
                 thereof
                 ;
                 &
                 so
                 there
                 comes
                 to
                 be
                 no
                 account
                 made
                 thereof
                 ;
                 but
                 if
                 we
                 should
                 make
                 strict
                 reflection
                 upon
                 our
                 consideration
                 of
                 the
                 velocity
                 of
                 Water
                 ,
                 we
                 should
                 find
                 ,
                 that
                 keeping
                 account
                 of
                 the
                 same
                 ,
                 there
                 is
                 a
                 reckoning
                 also
                 made
                 of
                 the
                 length
                 ;
                 forasmuch
                 as
                 whilst
                 we
                 say
                 ,
                 the
                 Water
                 of
                 such
                 a
                 Spring
                 runs
                 with
                 the
                 velocity
                 of
                 passing
                 a
                 thousand
                 or
                 two
                 thousand
                 paces
                 an
                 hour
                 :
                 this
                 in
                 substance
                 is
                 no
                 other
                 than
                 if
                 we
                 had
                 said
                 ,
                 such
                 a
                 Fountain
                 dischargeth
                 in
                 an
                 hour
                 a
                 Water
                 of
                 a
                 thousand
                 or
                 two
                 thousand
                 paces
                 long
                 .
                 So
                 that
                 ,
                 albeit
                 the
                 total
                 length
                 of
                 Running
                 water
                 be
                 incomprehensible
                 ,
                 as
                 being
                 infinite
                 ,
                 yet
                 neverthelesse
                 it
                 s
                 rendered
                 intelligible
                 by
                 parts
                 in
                 its
                 velocity
                 .
                 And
                 so
                 much
                 sufficeth
                 to
                 have
                 hinted
                 about
                 this
                 matter
                 ,
                 hoping
                 to
                 impart
                 on
                 some
                 other
                 occasion
                 other
                 more
                 accurate
                 Observations
                 in
                 this
                 affair
                 .
              
               
                 LAVS
                 DEO
                 .
              
            
          
        
         
      
       
         
           
             
             
             
               GEOMETRICAL
               DEMONSTRATIONS
               OF
               THE
               MEASURE
               OF
               Running
               Waters
               .
            
             
               BY
               D.
               BENEDETTO
               CASTELLI
               ,
               Abbot
               of
               CASSINA
               ,
               and
               Mathematician
               to
               P.
               
                 VRBAN
                 .
                 VIII
              
               .
            
             
               DEDICATED
               To
               the
               most
               Illustrious
               ,
               and
               most
               Excellent
               Prince
               DON
               THADDEO
               BARBERINI
               ,
               PRINCE
               OF
               PALESTRINA
               ,
               AND
               GENERAL
               of
               the
               HOLY
               CHURCH
               .
            
             
               LONDON
               ,
               Printed
               
                 Anno
                 Domini
              
               ,
               MDCLXI
               .
            
          
        
         
           
             
             
             
               
                 OF
                 THE
                 MENSURATION
                 OF
                 Running
                 Waters
                 .
              
               
                 
                   SUPPOSITION
                   I.
                   
                
                 
                   LEt
                   it
                   be
                   supposed
                   ,
                   that
                   the
                   banks
                   of
                   the
                   Rivers
                   of
                   which
                   we
                   speak
                   be
                   erected
                   perpendicular
                   to
                   the
                   plane
                   of
                   the
                   upper
                   superficies
                   of
                   the
                   River
                   .
                
              
               
                 
                   SUPPOSITION
                   II.
                   
                
                 
                   WE
                   suppose
                   that
                   the
                   plane
                   of
                   the
                   bottome
                   of
                   the
                   River
                   ,
                   of
                   which
                   we
                   speak
                   is
                   at
                   right
                   angles
                   with
                   the
                   banks
                   .
                
              
               
                 
                   SUPPOSITION
                   III.
                   
                
                 
                   IT
                   is
                   to
                   be
                   supposed
                   ,
                   that
                   we
                   speak
                   of
                   Rivers
                   ,
                   when
                   they
                   are
                   at
                   ebbe
                   ,
                   in
                   that
                   state
                   of
                   shallownesse
                   ,
                   or
                   at
                   flowing
                   in
                   that
                   state
                   of
                   deepnesse
                   ,
                   and
                   not
                   in
                   their
                   transition
                   from
                   the
                   ebbe
                   to
                   the
                   flowing
                   ,
                   or
                   from
                   the
                   flowing
                   to
                   the
                   ebbe
                   .
                
              
               
                 
                   Declaration
                   of
                   Termes
                   .
                
                 
                   
                     FIRST
                     .
                  
                   
                     IF
                     a
                     River
                     shall
                     be
                     cut
                     by
                     a
                     Plane
                     at
                     right
                     angles
                     to
                     the
                     surface
                     of
                     the
                     water
                     of
                     the
                     River
                     ,
                     and
                     to
                     the
                     banks
                     of
                     the
                     River
                     ,
                     that
                     same
                     dividing
                     Plane
                     we
                     call
                     the
                     Section
                     of
                     the
                     River
                     ;
                     and
                     this
                     Section
                     ,
                     by
                     the
                     Suppositions
                     above
                     ,
                     shall
                     be
                     a
                     right
                     angled
                     Parallelogram
                     .
                  
                
                 
                   
                     SECOND
                     .
                  
                   
                     WE
                     call
                     those
                     Sections
                     equally
                     Swift
                     ,
                     by
                     which
                     the
                     water
                     runs
                     with
                     equal
                     velocity
                     ;
                     and
                     more
                     swift
                     and
                     less
                     swift
                     that
                     Section
                     of
                     another
                     ,
                     by
                     which
                     the
                     water
                     runs
                     with
                     greater
                     or
                     lesse
                     velocity
                     .
                  
                
              
               
                 
                 
                   AXIOME
                   I.
                   
                
                 
                   SEctions
                   equal
                   ,
                   and
                   equally
                   swift
                   ,
                   discharge
                   equal
                   quantities
                   of
                   Water
                   in
                   equal
                   times
                   .
                
              
               
                 
                   AXIOME
                   II.
                   
                
                 
                   SEctions
                   equally
                   swift
                   ,
                   and
                   that
                   discharge
                   equal
                   quantity
                   of
                   Water
                   ,
                   in
                   equal
                   time
                   ,
                   shall
                   be
                   equal
                   .
                
              
               
                 
                   AXIOME
                   III.
                   
                
                 
                   SEctions
                   equal
                   ,
                   and
                   that
                   discharge
                   equal
                   quantities
                   of
                   Water
                   in
                   equal
                   times
                   ,
                   shall
                   be
                   equally
                   swift
                   .
                
              
               
                 
                   AXIOME
                   IV.
                   
                
                 
                   WHen
                   Sections
                   are
                   unequal
                   ,
                   but
                   equally
                   swift
                   ,
                   the
                   quantity
                   of
                   the
                   Water
                   that
                   passeth
                   through
                   the
                   first
                   Section
                   ,
                   shall
                   have
                   the
                   same
                   proportion
                   to
                   the
                   quantity
                   that
                   passeth
                   through
                   the
                   Second
                   ,
                   that
                   the
                   first
                   Section
                   hath
                   to
                   the
                   second
                   Section
                   .
                   Which
                   is
                   manifest
                   ,
                   because
                   the
                   velocity
                   being
                   the
                   same
                   ,
                   the
                   difference
                   of
                   the
                   Water
                   that
                   passeth
                   shall
                   be
                   according
                   to
                   the
                   difference
                   of
                   the
                   Sections
                   .
                
              
               
                 
                   AXIOME
                   V.
                   
                
                 
                   IF
                   the
                   Sections
                   shall
                   be
                   equal
                   ,
                   and
                   of
                   unequal
                   velocity
                   ,
                   the
                   quantity
                   of
                   the
                   Water
                   that
                   passeth
                   through
                   the
                   first
                   ,
                   shall
                   have
                   the
                   same
                   proportion
                   to
                   that
                   which
                   passeth
                   through
                   the
                   second
                   ,
                   that
                   the
                   velocity
                   of
                   the
                   first
                   Section
                   ,
                   shall
                   have
                   to
                   the
                   velocity
                   of
                   the
                   second
                   Section
                   .
                   Which
                   also
                   is
                   manifest
                   ,
                   because
                   the
                   Sections
                   being
                   equal
                   ,
                   the
                   difference
                   of
                   the
                   Water
                   which
                   passeth
                   ,
                   dependeth
                   on
                   the
                   velocity
                   .
                
              
               
                 
                   PETITION
                   .
                
                 
                   A
                   Section
                   of
                   a
                   River
                   being
                   given
                   ,
                   we
                   may
                   suppose
                   another
                   equal
                   to
                   the
                   given
                   ,
                   of
                   different
                   breadth
                   ,
                   heigth
                   ,
                   and
                   velocity
                   .
                
              
               
                 
                 
                   PROPOSITION
                   I.
                   
                
                 
                   The
                   Sections
                   of
                   the
                   same
                   River
                   discharge
                   equal
                   quantities
                   of
                   Water
                   in
                   equal
                   times
                   ,
                   although
                   the
                   Sections
                   themselves
                   he
                   unequal
                   .
                
                 
                   LEt
                   the
                   two
                   Sections
                   be
                   A
                   and
                   B
                   ,
                   in
                   the
                   River
                   C
                   ,
                   running
                   from
                   A
                   ,
                   towards
                   B
                   ;
                   I
                   say
                   ,
                   that
                   they
                   discharge
                   equal
                   quantity
                   of
                   Water
                   in
                   equal
                   times
                   ;
                   for
                   if
                   greater
                   quantity
                   of
                   Water
                   should
                   pass
                   through
                   A
                   ,
                   than
                   passeth
                   through
                   B
                   ,
                   it
                   would
                   
                   follow
                   that
                   the
                   Water
                   in
                   the
                   intermediate
                   space
                   of
                   the
                   River
                   C
                   ,
                   would
                   increase
                   continually
                   ,
                   which
                   is
                   manifestly
                   false
                   ,
                   but
                   if
                   more
                   Water
                   should
                   issue
                   through
                   the
                   Section
                   B
                   ,
                   than
                   entreth
                   at
                   the
                   Section
                   A
                   ,
                   the
                   Water
                   in
                   the
                   intermediate
                   space
                   C
                   ,
                   would
                   grow
                   continually
                   less
                   ,
                   and
                   alwaies
                   ebb
                   ,
                   which
                   is
                   likewise
                   false
                   ;
                   therefore
                   the
                   quantity
                   of
                   Water
                   that
                   passeth
                   through
                   the
                   Section
                   B
                   ,
                   is
                   equal
                   to
                   the
                   quantity
                   of
                   Water
                   which
                   passeth
                   through
                   the
                   Section
                   A
                   ,
                   and
                   therefore
                   the
                   Sections
                   of
                   the
                   same
                   River
                   discharge
                   ,
                   &c.
                   
                   Which
                   was
                   to
                   be
                   demonstrated
                   .
                
              
               
                 
                   PROPOSITION
                   II.
                   
                
                 
                   In
                   two
                   Sections
                   of
                   Rivers
                   ,
                   the
                   quantity
                   of
                   the
                   Water
                   which
                   passeth
                   by
                   one
                   Section
                   ,
                   is
                   to
                   that
                   which
                   passeth
                   by
                   the
                   second
                   ,
                   in
                   a
                   Proportion
                   compounded
                   of
                   the
                   proportions
                   of
                   the
                   first
                   Section
                   to
                   the
                   second
                   ,
                   and
                   of
                   the
                   velocitie
                   through
                   the
                   first
                   ,
                   to
                   the
                   velocitie
                   of
                   the
                   second
                   .
                
                 
                   LEt
                   A
                   ,
                   and
                   B
                   be
                   two
                   Sections
                   of
                   a
                   River
                   ;
                   I
                   say
                   ,
                   that
                   the
                   quantity
                   of
                   Water
                   which
                   passeth
                   through
                   A
                   ,
                   is
                   to
                   that
                   which
                   passeth
                   through
                   B
                   ,
                   in
                   a
                   proportion
                   compounded
                   of
                   the
                   proportions
                   of
                   the
                   first
                   Section
                   A
                   ,
                   to
                   the
                   Section
                   B
                   ;
                   and
                   of
                   the
                   velocity
                   through
                   A
                   ,
                   to
                   the
                   velocity
                   through
                   B
                   :
                   Let
                   a
                   Section
                   be
                   
                   supposed
                   equal
                   to
                   the
                   Section
                   A
                   ,
                   in
                   magnitude
                   ;
                   but
                   of
                   velocity
                   equal
                   to
                   the
                   Section
                   B
                   ,
                   and
                   let
                   it
                   be
                   G
                   ;
                   and
                   as
                   the
                   Section
                   A
                   is
                   
                   to
                   the
                   Section
                   B
                   ,
                   so
                   let
                   the
                   line
                   F
                   be
                   to
                   the
                   line
                   D
                   ;
                   and
                   as
                   the
                   velocity
                   A
                   ,
                   is
                   to
                   the
                   velocity
                   by
                   B
                   ,
                   so
                   let
                   the
                   line
                   D
                   be
                   to
                   the
                   line
                   R
                   :
                   Therefore
                   the
                   Water
                   which
                   passeth
                   thorow
                   A
                   ,
                   shall
                   be
                   to
                   that
                   which
                   passeth
                   through
                   G
                   (
                   in
                   regard
                   the
                   Sections
                   A
                   and
                   G
                   are
                   of
                   equal
                   bigness
                   ,
                   but
                   of
                   〈◊〉
                   equal
                   velocity
                   )
                   as
                   the
                   velocity
                   through
                   A
                   ,
                   to
                   the
                   velocity
                   through
                   G
                   ;
                   But
                   as
                   the
                   velocity
                   through
                   A
                   ,
                   is
                   to
                   the
                   velocity
                   through
                   G
                   ,
                   so
                   is
                   the
                   velocity
                   through
                   A
                   ,
                   to
                   the
                   velocity
                   through
                   B
                   ;
                   namely
                   ,
                   as
                   the
                   line
                   D
                   to
                   the
                   line
                   R
                   :
                   therefore
                   the
                   quantity
                   of
                   the
                   Water
                   which
                   passe
                   the
                   through
                   A
                   ,
                   shall
                   be
                   to
                   the
                   quantity
                   which
                   passeth
                   through
                   G
                   ,
                   as
                   the
                   line
                   D
                   is
                   to
                   the
                   line
                   R
                   ;
                   but
                   the
                   quantity
                   which
                   passeth
                   through
                   G
                   ,
                   is
                   to
                   that
                   which
                   passeth
                   through
                   B
                   ,
                   (
                   in
                   regard
                   the
                   Sections
                   G
                   ,
                   and
                   B
                   ,
                   are
                   equally
                   swift
                   )
                   as
                   the
                   Section
                   G
                   to
                   the
                   Section
                   B
                   ,
                   that
                   is
                   ,
                   as
                   the
                   Section
                   A
                   ,
                   to
                   the
                   Section
                   B
                   ;
                   that
                   is
                   ,
                   as
                   the
                   line
                   F
                   to
                   the
                   line
                   D
                   :
                   Therefore
                   by
                   the
                   equal
                   and
                   perturbed
                   proportionality
                   ,
                   the
                   quantity
                   of
                   the
                   Water
                   which
                   passeth
                   through
                   A
                   ,
                   hath
                   the
                   same
                   proportion
                   to
                   that
                   which
                   passeth
                   through
                   B
                   ,
                   that
                   the
                   line
                   F
                   hath
                   to
                   the
                   line
                   R
                   ;
                   but
                   F
                   to
                   R
                   ,
                   hath
                   a
                   proportion
                   compounded
                   of
                   the
                   proportions
                   of
                   F
                   to
                   D
                   ,
                   and
                   of
                   D
                   to
                   R
                   ;
                   that
                   is
                   ,
                   of
                   the
                   Section
                   A
                   to
                   the
                   Section
                   B
                   ;
                   and
                   of
                   the
                   velocity
                   through
                   A
                   ,
                   to
                   the
                   velocity
                   through
                   B
                   ▪
                   Therefore
                   also
                   the
                   quantity
                   of
                   Water
                   which
                   passeth
                   through
                   the
                   Section
                   A
                   ,
                   shall
                   have
                   a
                   proportion
                   to
                   that
                   which
                   passeth
                   through
                   the
                   Section
                   B
                   ,
                   compounded
                   of
                   the
                   proportions
                   of
                   the
                   Section
                   A
                   ,
                   to
                   the
                   Section
                   B
                   ,
                   and
                   of
                   the
                   velocity
                   through
                   A
                   ,
                   to
                   the
                   velocity
                   through
                   B
                   :
                   And
                   therefore
                   in
                   two
                   Sections
                   of
                   Rivers
                   ,
                   the
                   quantity
                   of
                   Water
                   which
                   passeth
                   by
                   the
                   first
                   ,
                   &c.
                   which
                   was
                   to
                   be
                   demonstrated
                   .
                
              
               
                 
                   COROLLARIE
                   .
                
                 
                   THe
                   same
                   followeth
                   ,
                   though
                   the
                   quantity
                   of
                   the
                   Water
                   which
                   passeth
                   through
                   the
                   Section
                   A
                   ,
                   be
                   equal
                   to
                   the
                   quantity
                   of
                   Water
                   which
                   passeth
                   through
                   the
                   Section
                   B
                   ,
                   as
                   is
                   manifest
                   by
                   the
                   same
                   demonstration
                   .
                
              
               
                 
                 
                   PROPOSITION
                   III.
                   
                
                 
                   In
                   two
                   Sections
                   unequal
                   ,
                   through
                   which
                   pass
                   equal
                   quantities
                   of
                   Water
                   in
                   equal
                   times
                   ,
                   the
                   Sections
                   have
                   to
                   one
                   another
                   ,
                   reciprocal
                   proportion
                   to
                   their
                   velocitie
                   .
                
                 
                   LEt
                   the
                   two
                   unequal
                   Sections
                   ,
                   by
                   which
                   pass
                   equal
                   quantities
                   of
                   Water
                   in
                   equal
                   times
                   be
                   A
                   ,
                   the
                   greater
                   ;
                   and
                   B
                   ,
                   the
                   lesser
                   :
                   I
                   say
                   ,
                   that
                   the
                   Section
                   A
                   ,
                   shall
                   have
                   the
                   same
                   Proportion
                   to
                   the
                   Section
                   B
                   ,
                   that
                   reciprocally
                   the
                   velocity
                   through
                   B
                   ,
                   hath
                   to
                   the
                   velocity
                   through
                   A
                   ;
                   for
                   supposing
                   that
                   as
                   the
                   Water
                   that
                   passeth
                   through
                   A
                   ,
                   is
                   to
                   that
                   which
                   passeth
                   through
                   B
                   ,
                   so
                   is
                   the
                   
                   line
                   E
                   to
                   the
                   line
                   F
                   :
                   therefore
                   the
                   quantity
                   of
                   water
                   which
                   passeth
                   through
                   A
                   ,
                   being
                   equal
                   to
                   that
                   which
                   passeth
                   through
                   B
                   ,
                   the
                   line
                   E
                   shall
                   also
                   be
                   equal
                   to
                   the
                   line
                   F
                   :
                   Supposing
                   moreover
                   ,
                   That
                   as
                   the
                   Section
                   A
                   ,
                   is
                   to
                   the
                   Section
                   B
                   ,
                   so
                   is
                   the
                   line
                   F
                   ,
                   to
                   the
                   line
                   G
                   ;
                   and
                   because
                   the
                   quantity
                   of
                   water
                   which
                   passeth
                   through
                   the
                   Section
                   A
                   ,
                   is
                   to
                   that
                   which
                   passeth
                   through
                   the
                   Section
                   B
                   ,
                   in
                   a
                   proportion
                   composed
                   of
                   the
                   proportions
                   of
                   the
                   Section
                   A
                   ,
                   to
                   the
                   Section
                   B
                   ,
                   and
                   of
                   the
                   velocity
                   through
                   A
                   ,
                   to
                   the
                   velocity
                   through
                   B
                   ;
                   therefore
                   the
                   line
                   E
                   ,
                   shall
                   be
                   the
                   line
                   to
                   F
                   ,
                   in
                   a
                   proportion
                   compounded
                   of
                   the
                   same
                   proportions
                   ;
                   namely
                   ,
                   of
                   the
                   proportion
                   of
                   the
                   Section
                   A
                   ,
                   to
                   the
                   Section
                   B
                   ,
                   and
                   of
                   the
                   velocity
                   through
                   A
                   ,
                   to
                   the
                   velocity
                   through
                   B
                   ;
                   but
                   the
                   line
                   E
                   ,
                   hath
                   to
                   the
                   line
                   G
                   ,
                   the
                   proportion
                   of
                   the
                   Section
                   A
                   ,
                   to
                   the
                   Section
                   B
                   ,
                   therefore
                   the
                   proportion
                   remaining
                   of
                   the
                   line
                   G
                   ,
                   to
                   the
                   line
                   F
                   ,
                   shall
                   be
                   the
                   proportion
                   of
                   the
                   velocity
                   through
                   A
                   ,
                   to
                   the
                   velocity
                   through
                   B
                   ;
                   therefore
                   also
                   the
                   line
                   G
                   ,
                   shall
                   be
                   to
                   the
                   line
                   E
                   ,
                   as
                   the
                   velocity
                   by
                   A
                   ,
                   to
                   the
                   velocity
                   by
                   B
                   :
                   And
                   conversly
                   ,
                   the
                   velocity
                   through
                   B
                   ,
                   shall
                   be
                   to
                   the
                   velocity
                   through
                   A
                   ,
                   as
                   the
                   line
                   E
                   ,
                   to
                   the
                   line
                   G
                   ;
                   that
                   is
                   to
                   say
                   ,
                   as
                   the
                   Section
                   A
                   ,
                   to
                   the
                   Section
                   B
                   ,
                   and
                   therefore
                   in
                   two
                   Sections
                   ,
                   &c.
                   which
                   was
                   to
                   be
                   demonstrated
                   .
                
              
               
                 
                 
                   COROLLARIE
                   .
                
                 
                   HEnce
                   it
                   is
                   manifest
                   ,
                   that
                   Sections
                   of
                   the
                   same
                   River
                   (
                   which
                   are
                   no
                   other
                   than
                   the
                   vulgar
                   measures
                   of
                   the
                   River
                   )
                   have
                   betwixt
                   themselves
                   reciprocal
                   proportions
                   to
                   their
                   velocities
                   ;
                   for
                   in
                   the
                   first
                   Proposition
                   we
                   have
                   demonstrated
                   that
                   the
                   Sections
                   of
                   the
                   same
                   River
                   ,
                   discharge
                   equal
                   quantities
                   of
                   Water
                   in
                   equal
                   times
                   ;
                   therefore
                   ,
                   by
                   what
                   hath
                   now
                   been
                   demonstrated
                   the
                   Sections
                   of
                   the
                   same
                   River
                   shall
                   have
                   reciprocal
                   proportion
                   to
                   their
                   velocities
                   ;
                   And
                   therefore
                   the
                   same
                   running
                   water
                   changeth
                   measure
                   ,
                   when
                   it
                   changeth
                   velocity
                   ;
                   namely
                   ,
                   increaseth
                   the
                   measure
                   ,
                   when
                   it
                   decreaseth
                   the
                   velocity
                   ,
                   and
                   decreaseth
                   the
                   measure
                   ,
                   when
                   it
                   increaseth
                   the
                   velocity
                   .
                
                 
                   On
                   which
                   principally
                   depends
                   all
                   that
                   which
                   hath
                   been
                   said
                   above
                   in
                   the
                   Discourse
                   ,
                   and
                   observed
                   in
                   the
                   Corollaries
                   and
                   Appendixes
                   ;
                   and
                   therefore
                   is
                   worthy
                   to
                   be
                   well
                   understood
                   and
                   heeded
                   .
                
              
               
                 
                   PROPOSITION
                   IV.
                   
                
                 
                   If
                   a
                   River
                   fall
                   into
                   another
                   River
                   ,
                   the
                   height
                   of
                   the
                   first
                   in
                   its
                   own
                   Chanel
                   shall
                   be
                   to
                   the
                   height
                   that
                   it
                   shall
                   make
                   in
                   the
                   second
                   Chanel
                   ,
                   in
                   a
                   proportion
                   compounded
                   of
                   the
                   proportions
                   of
                   the
                   breadth
                   of
                   the
                   Chanel
                   of
                   the
                   second
                   ,
                   to
                   the
                   breadth
                   of
                   the
                   Chanel
                   of
                   the
                   first
                   ,
                   and
                   of
                   the
                   velocitie
                   acquired
                   in
                   the
                   Chanel
                   of
                   the
                   second
                   ,
                   to
                   that
                   which
                   it
                   had
                   in
                   its
                   proper
                   and
                   first
                   Chanel
                   .
                
                 
                   LEt
                   the
                   River
                   AB
                   ,
                   whose
                   height
                   is
                   AC
                   ,
                   and
                   breadth
                   CB
                   ,
                   that
                   is
                   ,
                   whose
                   Section
                   is
                   ACB
                   ;
                   let
                   it
                   enter
                   ,
                   I
                   say
                   ,
                   into
                   another
                   River
                   as
                   broad
                   as
                   the
                   line
                   EF
                   ,
                   and
                   let
                   it
                   therein
                   make
                   the
                   rise
                   or
                   height
                   DE
                   ,
                   that
                   is
                   to
                   say
                   ,
                   let
                   it
                   have
                   its
                   Section
                   in
                   the
                   River
                   whereinto
                   it
                   falls
                   DEF
                   ;
                   I
                   say
                   ,
                   that
                   the
                   height
                   AC
                   hath
                   to
                   the
                   height
                   DE
                   the
                   proportion
                   compounded
                   of
                   the
                   proportions
                   of
                   the
                   breadth
                   EF
                   ,
                   to
                   the
                   breadth
                   CB
                   ,
                   and
                   of
                   the
                   velocity
                   through
                   DF
                   ,
                   to
                   the
                   velocity
                   through
                   AB
                   .
                   Let
                   us
                   suppose
                   the
                   Section
                   G
                   ,
                   equal
                   in
                   velocity
                   to
                   the
                   Section
                   AB
                   ,
                   and
                   in
                   breadth
                   equal
                   to
                   EF
                   ,
                   which
                   carrieth
                   a
                   quantity
                   of
                   Water
                   equal
                   to
                   that
                   which
                   the
                   Section
                   AB
                   carrieth
                   ,
                   in
                   equal
                   times
                   ,
                   and
                   consequently
                   ,
                   equal
                   to
                   that
                   which
                   DF
                   carrieth
                   .
                   Moreover
                   ,
                   as
                   the
                   breadth
                   EF
                   is
                   to
                   the
                   breadth
                   CB
                   ,
                   so
                   let
                   the
                   line
                   H
                   be
                   to
                   
                   the
                   line
                   I
                   ;
                   and
                   as
                   the
                   velocity
                   of
                   DF
                   is
                   to
                   the
                   velocity
                   of
                   AB
                   ,
                   so
                   let
                   the
                   line
                   I
                   be
                   to
                   the
                   line
                   L
                   ;
                   because
                   therefore
                   the
                   two
                   Sections
                   AB
                   and
                   G
                   are
                   equally
                   swift
                   ,
                   and
                   discharge
                   equal
                   quantity
                   of
                   Water
                   in
                   equal
                   times
                   ,
                   they
                   shall
                   be
                   equal
                   Sections
                   ;
                   and
                   
                   therefore
                   the
                   height
                   of
                   AB
                   to
                   the
                   height
                   of
                   G
                   ,
                   shall
                   be
                   as
                   the
                   breadth
                   of
                   G
                   ,
                   to
                   the
                   breadth
                   of
                   AB
                   ,
                   that
                   is
                   ,
                   as
                   EF
                   to
                   CB
                   ,
                   that
                   is
                   ,
                   as
                   the
                   line
                   H
                   to
                   the
                   line
                   I
                   :
                   but
                   because
                   the
                   Water
                   which
                   passeth
                   through
                   G
                   ,
                   is
                   equal
                   to
                   that
                   which
                   passeth
                   through
                   DEF
                   ,
                   therefore
                   the
                   Section
                   G
                   ,
                   to
                   the
                   Section
                   DEF
                   ,
                   shall
                   have
                   the
                   reciprocal
                   proportion
                   of
                   the
                   velocity
                   through
                   DEF
                   ,
                   to
                   the
                   velocity
                   through
                   G
                   ;
                   but
                   also
                   the
                   height
                   of
                   G
                   ,
                   is
                   to
                   the
                   height
                   DE
                   ,
                   as
                   the
                   Section
                   G
                   ,
                   to
                   the
                   Section
                   DEF
                   :
                   Therefore
                   the
                   height
                   of
                   G
                   ,
                   is
                   to
                   the
                   height
                   DE
                   ,
                   as
                   the
                   velocity
                   through
                   DEF
                   ,
                   is
                   to
                   the
                   velocity
                   through
                   G
                   ;
                   that
                   is
                   ,
                   as
                   the
                   velocity
                   through
                   DEF
                   ,
                   is
                   to
                   the
                   velocity
                   through
                   AB
                   ;
                   That
                   is
                   ,
                   finally
                   ,
                   as
                   the
                   line
                   I
                   ,
                   to
                   the
                   line
                   L
                   ;
                   Therefore
                   ,
                   by
                   equal
                   proportion
                   ,
                   the
                   height
                   of
                   AB
                   ,
                   that
                   is
                   ,
                   AC
                   ,
                   shall
                   be
                   to
                   the
                   height
                   DE
                   ;
                   as
                   H
                   to
                   L
                   ,
                   that
                   is
                   ,
                   compounded
                   of
                   the
                   proportions
                   of
                   the
                   breadth
                   EF
                   ,
                   to
                   the
                   breadth
                   CB
                   ,
                   and
                   of
                   the
                   velocity
                   through
                   DF
                   ,
                   to
                   the
                   velocity
                   through
                   A
                   B
                   :
                   So
                   that
                   if
                   a
                   River
                   fall
                   into
                   another
                   River
                   ,
                   &c.
                   which
                   was
                   to
                   be
                   demonstrated
                   .
                
              
               
                 
                 
                   PROPOSITION
                   V.
                   
                
                 
                   If
                   a
                   River
                   discharge
                   a
                   certain
                   quantitie
                   of
                   Water
                   in
                   a
                   certain
                   time
                   ;
                   and
                   after
                   that
                   there
                   come
                   into
                   it
                   a
                   Flood
                   ,
                   the
                   quantity
                   of
                   Water
                   which
                   is
                   discharged
                   in
                   as
                   much
                   time
                   at
                   the
                   Flood
                   ,
                   is
                   to
                   that
                   which
                   was
                   discharged
                   before
                   ,
                   whilst
                   the
                   River
                   was
                   low
                   ,
                   in
                   a
                   proportion
                   compounded
                   of
                   the
                   proportions
                   of
                   the
                   velocity
                   of
                   the
                   Flood
                   ,
                   to
                   the
                   velocity
                   of
                   the
                   first
                   Water
                   ,
                   and
                   of
                   the
                   height
                   of
                   the
                   Flood
                   ,
                   to
                   the
                   height
                   of
                   the
                   first
                   Water
                   .
                
                 
                   SUppose
                   a
                   River
                   ,
                   which
                   whilst
                   it
                   is
                   low
                   ,
                   runs
                   by
                   the
                   Section
                   AF
                   ;
                   and
                   after
                   a
                   Flood
                   cometh
                   into
                   the
                   same
                   ,
                   and
                   runneth
                   through
                   the
                   Section
                   DF
                   ,
                   I
                   say
                   ,
                   that
                   the
                   quantity
                   of
                   the
                   Water
                   which
                   is
                   discharged
                   through
                   DF
                   ,
                   is
                   to
                   that
                   which
                   is
                   discharged
                   
                   through
                   AF
                   ,
                   in
                   a
                   proportion
                   compounded
                   of
                   the
                   proportions
                   of
                   the
                   velocity
                   through
                   DF
                   ,
                   to
                   the
                   velocity
                   through
                   AF
                   ,
                   and
                   of
                   the
                   height
                   DB
                   ,
                   to
                   the
                   height
                   AB
                   ;
                   As
                   the
                   velocity
                   through
                   DF
                   is
                   to
                   the
                   velocity
                   through
                   AF
                   ;
                   so
                   let
                   the
                   line
                   R
                   ,
                   to
                   the
                   line
                   S
                   ;
                   and
                   as
                   the
                   height
                   DB
                   is
                   to
                   the
                   height
                   AB
                   ,
                   so
                   let
                   the
                   line
                   S
                   ,
                   to
                   the
                   line
                   T
                   ;
                   and
                   let
                   us
                   suppose
                   a
                   Section
                   LMN
                   ,
                   equal
                   to
                   DF
                   in
                   height
                   and
                   breadth
                   ;
                   that
                   is
                   LM
                   equal
                   to
                   DB
                   ,
                   and
                   MN
                   equal
                   to
                   BF
                   ;
                   but
                   let
                   it
                   be
                   in
                   velocity
                   equal
                   to
                   the
                   Section
                   AF
                   ,
                   therefore
                   the
                   quantity
                   of
                   Water
                   which
                   runneth
                   through
                   DF
                   ,
                   shall
                   be
                   to
                   that
                   which
                   runneth
                   through
                   LN
                   ,
                   as
                   the
                   velocity
                   through
                   DF
                   ,
                   is
                   to
                   the
                   velocity
                   through
                   LN
                   ,
                   that
                   is
                   ,
                   to
                   the
                   velocity
                   through
                   AF
                   ;
                   and
                   the
                   line
                   R
                   being
                   to
                   the
                   line
                   S
                   ,
                   as
                   the
                   velocity
                   through
                   DF
                   ,
                   to
                   the
                   velocity
                   through
                   AF
                   ;
                   therefore
                   the
                   quantity
                   which
                   runneth
                   through
                   DF
                   ,
                   to
                   that
                   which
                   runneth
                   through
                   LN
                   ,
                   shall
                   have
                   the
                   proportion
                   of
                   R
                   to
                   S
                   ;
                   but
                   the
                   quantity
                   which
                   runneth
                   through
                   LN
                   ,
                   to
                   that
                   which
                   runneth
                   through
                   AF
                   ,
                   (
                   the
                   Sections
                   
                   being
                   equally
                   swift
                   )
                   shall
                   be
                   in
                   proportion
                   as
                   the
                   Section
                   LN
                   ,
                   to
                   the
                   Section
                   AF
                   ;
                   that
                   is
                   ,
                   as
                   DB
                   ,
                   to
                   AB
                   ;
                   that
                   is
                   as
                   the
                   line
                   S
                   ,
                   to
                   the
                   line
                   T
                   :
                   Therefore
                   by
                   equal
                   proportion
                   ,
                   the
                   quantity
                   of
                   the
                   water
                   which
                   runneth
                   through
                   DF
                   ,
                   shall
                   be
                   in
                   proportion
                   to
                   that
                   which
                   runneth
                   through
                   AF
                   ,
                   as
                   R
                   is
                   to
                   T
                   ;
                   that
                   is
                   ,
                   compounded
                   of
                   the
                   proportions
                   of
                   the
                   height
                   DB
                   ,
                   to
                   the
                   height
                   AB
                   ,
                   and
                   of
                   the
                   velocity
                   through
                   DF
                   ,
                   to
                   the
                   velocity
                   through
                   AF
                   ;
                   and
                   therefore
                   if
                   a
                   River
                   discharge
                   a
                   certain
                   quantity
                   ,
                   &c.
                   which
                   was
                   to
                   be
                   demonstrated
                   .
                
                 
                   
                     ANNOTATION
                     .
                  
                   
                     THe
                     same
                     might
                     have
                     been
                     demonstrated
                     by
                     the
                     second
                     Proposition
                     above
                     demonstrated
                     ,
                     as
                     is
                     manifest
                     .
                  
                
              
               
                 
                   PROPOSITION
                   VI.
                   
                
                 
                   If
                   two
                   equal
                   streams
                   of
                   the
                   same
                   Torrent
                   ,
                   fall
                   into
                   a
                   River
                   at
                   divers
                   times
                   ,
                   the
                   heights
                   made
                   in
                   the
                   River
                   by
                   the
                   Torrent
                   ,
                   shall
                   have
                   between
                   themselves
                   the
                   reciprocal
                   proportion
                   of
                   the
                   velocities
                   acquired
                   in
                   the
                   River
                   .
                
                 
                   LEt
                   A
                   and
                   B
                   ,
                   be
                   two
                   equal
                   streams
                   of
                   the
                   same
                   Torrent
                   ,
                   which
                   falling
                   into
                   a
                   River
                   at
                   divers
                   times
                   ,
                   make
                   the
                   heights
                   CD
                   ,
                   and
                   FG
                   ;
                   that
                   is
                   the
                   stream
                   A
                   ,
                   maketh
                   the
                   height
                   CD
                   ,
                   and
                   the
                   stream
                   B
                   ,
                   maketh
                   the
                   height
                   FG
                   ;
                   that
                   is
                   ,
                   Let
                   their
                   Sections
                   in
                   the
                   River
                   ,
                   into
                   which
                   they
                   are
                   fallen
                   ,
                   be
                   CE
                   ,
                   and
                   FH
                   ;
                   I
                   say
                   ,
                   that
                   the
                   height
                   CD
                   ,
                   shall
                   be
                   to
                   the
                   height
                   FG
                   ,
                   in
                   reciprocal
                   proportion
                   ,
                   as
                   the
                   velocity
                   through
                   FH
                   ,
                   to
                   the
                   velocity
                   through
                   CE
                   ;
                   for
                   the
                   quantity
                   of
                   water
                   which
                   passeth
                   through
                   A
                   ,
                   being
                   equal
                   to
                   the
                   quantity
                   which
                   passeth
                   through
                   B
                   ,
                   in
                   equal
                   times
                   ;
                   also
                   the
                   quantity
                   which
                   passeth
                   through
                   CE
                   ,
                   shall
                   
                   be
                   equal
                   to
                   that
                   which
                   passeth
                   through
                   F
                   H
                   :
                   And
                   therefore
                   the
                   proportion
                   that
                   the
                   Section
                   CE
                   ,
                   hath
                   to
                   the
                   Section
                   FH
                   ;
                   shall
                   be
                   the
                   same
                   that
                   the
                   velocity
                   through
                   FH
                   ,
                   hath
                   to
                   the
                   velocity
                   through
                   CE
                   ;
                   But
                   the
                   Section
                   CE
                   ,
                   is
                   to
                   the
                   Section
                   FH
                   ,
                   as
                   CD
                   ,
                   to
                   FG
                   ,
                   by
                   reason
                   they
                   are
                   of
                   the
                   same
                   breadth
                   :
                   Therefore
                   CD
                   ,
                   shall
                   be
                   to
                   FG
                   ,
                   in
                   reciprocal
                   proportion
                   ,
                   as
                   the
                   velocity
                   through
                   FH
                   ,
                   is
                   to
                   the
                   velocity
                   through
                   CE
                   ,
                   and
                   therefore
                   if
                   two
                   equal
                   streams
                   of
                   the
                   same
                   Torrent
                   ,
                   &c.
                   which
                   was
                   to
                   be
                   demonstrated
                   .
                
              
            
          
           
             
             
             
               
                 OF
                 THE
                 MENSURATION
                 OF
                 Running
                 Waters
                 .
              
               
                 Lib.
                 II.
                 
              
               
                 HAving
                 ,
                 in
                 the
                 close
                 of
                 my
                 Treatise
                 of
                 the
                 Mensuration
                 of
                 Running
                 Waters
                 promised
                 to
                 declare
                 upon
                 another
                 occasion
                 other
                 particulars
                 more
                 obscure
                 ,
                 and
                 of
                 very
                 great
                 concern
                 upon
                 the
                 same
                 argumement
                 :
                 I
                 now
                 do
                 perform
                 my
                 promise
                 on
                 the
                 occasion
                 that
                 I
                 had
                 the
                 past
                 year
                 1641.
                 to
                 propound
                 my
                 thoughts
                 touching
                 the
                 state
                 of
                 the
                 Lake
                 of
                 Venice
                 ,
                 a
                 business
                 certainly
                 most
                 important
                 ,
                 as
                 being
                 the
                 concernment
                 of
                 that
                 most
                 noble
                 and
                 most
                 admirable
                 City
                 ;
                 and
                 indeed
                 of
                 all
                 Italy
                 ,
                 yea
                 of
                 all
                 
                   Europe
                   ,
                   Asia
                
                 ,
                 &
                 Africa
                 ;
                 &
                 one
                 may
                 truly
                 say
                 of
                 all
                 the
                 whole
                 World.
                 And
                 being
                 to
                 proceed
                 according
                 to
                 the
                 method
                 necessary
                 in
                 Sciences
                 ,
                 I
                 wil
                 propose
                 ,
                 in
                 the
                 first
                 place
                 certain
                 Definitions
                 of
                 those
                 Terms
                 whereof
                 we
                 are
                 to
                 make
                 use
                 in
                 our
                 Discourse
                 :
                 and
                 then
                 ,
                 laying
                 down
                 certain
                 Principles
                 we
                 will
                 demonstrate
                 some
                 Problemes
                 and
                 Theoremes
                 necessary
                 for
                 the
                 understanding
                 of
                 those
                 things
                 which
                 we
                 are
                 to
                 deliver
                 ;
                 and
                 moreover
                 ,
                 recounting
                 sundry
                 cases
                 that
                 have
                 happened
                 ,
                 we
                 will
                 prove
                 by
                 practice
                 ,
                 of
                 what
                 utility
                 this
                 contemplation
                 of
                 the
                 Measure
                 of
                 Running
                 Waters
                 is
                 in
                 the
                 more
                 important
                 affairs
                 both
                 Publique
                 and
                 Private
                 .
              
               
                 
                   DEFINITION
                   I.
                   
                
                 
                   TWo
                   Rivers
                   are
                   said
                   to
                   move
                   with
                   equal
                   velocity
                   ,
                   when
                   in
                   equal
                   times
                   they
                   passe
                   spaces
                   of
                   equal
                   length
                   .
                
              
               
                 
                   DEFINITION
                   II.
                   
                
                 
                   RIvers
                   are
                   said
                   to
                   move
                   with
                   like
                   velocity
                   ,
                   when
                   their
                   proportional
                   parts
                   do
                   move
                   alike
                   ,
                   that
                   is
                   ,
                   the
                   upper
                   parts
                   alike
                   to
                   the
                   upper
                   ,
                   and
                   the
                   lower
                   to
                   the
                   lower
                   ;
                   so
                   that
                   if
                   the
                   upper
                   part
                   of
                   one
                   River
                   shall
                   be
                   more
                   swift
                   than
                   the
                   upper
                   part
                   of
                   another
                   ;
                   then
                   also
                   the
                   lower
                   part
                   of
                   the
                   former
                   shall
                   be
                   more
                   swift
                   than
                   the
                   part
                   correspondent
                   to
                   it
                   in
                   the
                   second
                   ,
                   proportionally
                   .
                
              
               
                 
                 
                   DEFINITION
                   III.
                   
                
                 
                   TO
                   measure
                   a
                   River
                   ,
                   or
                   running
                   Water
                   ,
                   is
                   in
                   our
                   sense
                   to
                   finde
                   out
                   how
                   many
                   determinate
                   measures
                   ,
                   or
                   weights
                   of
                   Water
                   in
                   a
                   given
                   time
                   passeth
                   through
                   the
                   River
                   ,
                   or
                   Channel
                   of
                   the
                   Water
                   that
                   is
                   to
                   be
                   measured
                   .
                
              
               
                 
                   DEFINITION
                   IV.
                   
                
                 
                   IF
                   a
                   Machine
                   be
                   made
                   either
                   of
                   Brick
                   ,
                   or
                   of
                   Stone
                   ,
                   or
                   of
                   Wood
                   ,
                   so
                   composed
                   that
                   two
                   sides
                   of
                   the
                   said
                   Machine
                   be
                   placed
                   at
                   right
                   angels
                   upon
                   the
                   ends
                   of
                   a
                   third
                   side
                   ,
                   that
                   is
                   supposed
                   to
                   be
                   placed
                   in
                   the
                   bottom
                   of
                   a
                   River
                   ,
                   parallel
                   to
                   the
                   Horizon
                   ,
                   in
                   such
                   a
                   manner
                   ,
                   that
                   all
                   the
                   water
                   which
                   runneth
                   through
                   the
                   said
                   River
                   ,
                   passeth
                   thorow
                   the
                   said
                   Machine
                   :
                   And
                   if
                   all
                   the
                   water
                   coming
                   to
                   be
                   diverted
                   
                   that
                   runneth
                   through
                   the
                   said
                   River
                   ,
                   the
                   upper
                   superficies
                   of
                   that
                   third
                   side
                   placed
                   in
                   the
                   bottom
                   do
                   remain
                   uncovered
                   and
                   dry
                   ,
                   and
                   that
                   the
                   dead
                   water
                   be
                   not
                   above
                   it
                   ;
                   This
                   same
                   Machine
                   shall
                   be
                   called
                   by
                   us
                   *
                   REGULATOR
                   :
                   And
                   that
                   third
                   side
                   of
                   the
                   Machine
                   which
                   standeth
                   Horizontally
                   is
                   called
                   the
                   bottom
                   of
                   the
                   Regulator
                   ;
                   and
                   the
                   other
                   two
                   sides
                   ,
                   are
                   called
                   the
                   banks
                   of
                   the
                   Regulator
                   ;
                   as
                   is
                   seen
                   in
                   this
                   first
                   Figure
                   :
                   ABCD
                   ,
                   shall
                   be
                   the
                   Regulator
                   ;
                   BC
                   the
                   bottom
                   ;
                   and
                   the
                   other
                   two
                   sides
                   AB
                   ,
                   and
                   CD
                   are
                   its
                   banks
                   .
                
              
               
                 
                   DEFINITION
                   V.
                   
                
                 
                   BY
                   the
                   quick
                   height
                   ,
                   we
                   mean
                   the
                   Perpendicular
                   from
                   the
                   upper
                   superficies
                   of
                   the
                   River
                   ,
                   unto
                   the
                   upper
                   superficies
                   of
                   the
                   bottom
                   of
                   the
                   Regulator
                   ;
                   as
                   in
                   the
                   foregoing
                   Figure
                   the
                   line
                   .
                   GH
                   .
                
              
               
                 
                   DEFINITION
                   VI.
                   
                
                 
                   IF
                   the
                   water
                   of
                   a
                   River
                   be
                   supposed
                   to
                   be
                   marked
                   by
                   three
                   sides
                   of
                   a
                   Regulator
                   ,
                   that
                   Rightangled
                   Parallelogram
                   comprehended
                   between
                   the
                   banks
                   of
                   the
                   Regulator
                   ,
                   and
                   the
                   bottom
                   ,
                   and
                   the
                   superficies
                   of
                   the
                   Water
                   is
                   called
                   a
                   Section
                   of
                   the
                   River
                   .
                
              
               
                 
                 
                   ANNOTATION
                   .
                
                 
                   HEre
                   it
                   is
                   to
                   be
                   noted
                   ,
                   that
                   the
                   River
                   it self
                   may
                   have
                   sundry
                   and
                   divers
                   heights
                   ,
                   in
                   several
                   parts
                   of
                   its
                   Chanel
                   ,
                   by
                   reason
                   of
                   the
                   various
                   velocities
                   of
                   the
                   water
                   ,
                   and
                   its
                   measures
                   ;
                   as
                   hath
                   been
                   demonstrated
                   in
                   the
                   first
                   book
                   .
                
              
               
                 
                   SUPPOSITION
                   I.
                   
                
                 
                   IT
                   is
                   supposed
                   ,
                   that
                   the
                   Rivers
                   equal
                   in
                   breadth
                   ,
                   and
                   quick
                   height
                   ,
                   that
                   have
                   the
                   same
                   inclination
                   of
                   bed
                   or
                   bottom
                   ,
                   ought
                   also
                   to
                   have
                   equal
                   velocities
                   ,
                   the
                   accidental
                   impediments
                   being
                   removed
                   that
                   are
                   dispersed
                   throughout
                   the
                   course
                   of
                   the
                   water
                   ,
                   and
                   abstracting
                   also
                   from
                   the
                   external
                   windes
                   ,
                   which
                   may
                   velocitate
                   ,
                   and
                   retard
                   the
                   course
                   of
                   the
                   water
                   of
                   the
                   River
                   .
                
              
               
                 
                   SUPPOSITION
                   II.
                   
                
                 
                   LEt
                   us
                   suppose
                   also
                   ,
                   that
                   if
                   there
                   be
                   two
                   Rivers
                   that
                   are
                   in
                   their
                   beds
                   of
                   equal
                   length
                   ,
                   and
                   of
                   the
                   same
                   inclination
                   ,
                   but
                   of
                   quick
                   heights
                   unequal
                   ,
                   they
                   ought
                   to
                   move
                   with
                   like
                   velocity
                   ,
                   according
                   to
                   the
                   sense
                   explained
                   in
                   the
                   second
                   definition
                   .
                
              
               
                 
                   SUPPOSITION
                   III.
                   
                
                 
                   BEcause
                   it
                   will
                   often
                   be
                   requisite
                   to
                   measure
                   the
                   time
                   exactly
                   in
                   the
                   following
                   Problems
                   ,
                   we
                   take
                   that
                   to
                   be
                   an
                   excellent
                   way
                   to
                   measure
                   the
                   time
                   ,
                   which
                   was
                   shewed
                   me
                   many
                   years
                   since
                   by
                   
                     Signore
                     Galilaeo
                     Galilaei
                  
                   ,
                   which
                   is
                   as
                   followeth
                   .
                
                 
                   A
                   string
                   is
                   to
                   be
                   taken
                   three
                   Roman
                   feet
                   long
                   ,
                   to
                   the
                   end
                   of
                   which
                   a
                   Bullet
                   of
                   Lead
                   is
                   to
                   be
                   hanged
                   ,
                   of
                   about
                   two
                   or
                   three
                   ounces
                   ;
                   and
                   holding
                   it
                   by
                   the
                   other
                   end
                   ,
                   the
                   Plummet
                   is
                   to
                   be
                   removed
                   from
                   its
                   perpendicularity
                   a
                   Palm
                   ,
                   more
                   or
                   less
                   ,
                   and
                   then
                   let
                   go
                   ,
                   which
                   will
                   make
                   many
                   swings
                   to
                   and
                   again
                   ,
                   passing
                   and
                   repassing
                   the
                   Perpendicular
                   ,
                   before
                   that
                   it
                   stay
                   in
                   the
                   same
                   :
                   Now
                   it
                   being
                   required
                   to
                   measure
                   the
                   time
                   that
                   is
                   spent
                   in
                   any
                   whatsoever
                   operation
                   ,
                   those
                   vibrations
                   are
                   to
                   be
                   numbred
                   ,
                   that
                   are
                   made
                   whilst
                   the
                   work
                   lasteth
                   ;
                   and
                   they
                   shall
                   be
                   so
                   many
                   second
                   minutes
                   of
                   an
                   hour
                   ,
                   if
                   so
                   be
                   ,
                   that
                   the
                   string
                   be
                   three
                   Roman
                   feet
                   long
                   ,
                   but
                   in
                   shorter
                   strings
                   ,
                   the
                   vibrations
                   are
                   more
                   frequent
                   ,
                   and
                   in
                   longer
                   ,
                   less
                   frequent
                   ;
                   and
                   all
                   this
                   still
                   followeth
                   ,
                   whether
                   the
                   Plummet
                   be
                   little
                   or
                   much
                   removed
                   from
                   its
                   Perpendicularity
                   ,
                   or
                   whether
                   the
                   weight
                   of
                   the
                   Lead
                   be
                   greater
                   or
                   lesser
                   .
                
                 
                   These
                   things
                   being
                   pre-supposed
                   ,
                   we
                   will
                   lay
                   down
                   some
                   familiar
                   
                   Problems
                   ,
                   from
                   which
                   we
                   shall
                   pass
                   to
                   the
                   Notions
                   and
                   questions
                   more
                   subtil
                   and
                   curious
                   ;
                   which
                   will
                   also
                   prove
                   profitable
                   ,
                   and
                   not
                   to
                   be
                   sleighted
                   in
                   this
                   business
                   of
                   Waters
                   .
                
              
               
                 
                   PROPOSITION
                   I.
                   PROBLEME
                   I.
                   
                
                 
                   A
                   Chanel
                   of
                   Running-Water
                   being
                   given
                   ,
                   the
                   breadth
                   of
                   which
                   passing
                   through
                   a
                   Regulator
                   ,
                   is
                   three
                   Palms
                   ;
                   and
                   the
                   height
                   one
                   Palm
                   ,
                   little
                   more
                   or
                   less
                   ,
                   to
                   measure
                   what
                   water
                   passeth
                   through
                   the
                   Regulator
                   in
                   a
                   time
                   given
                   .
                
                 
                   FIrst
                   ,
                   we
                   are
                   to
                   dam
                   up
                   the
                   Chanel
                   ;
                   so
                   that
                   there
                   pass
                   not
                   any
                   water
                   below
                   the
                   Dam
                   ;
                   then
                   we
                   must
                   place
                   in
                   the
                   side
                   of
                   the
                   Chanel
                   ,
                   in
                   the
                   parts
                   above
                   the
                   Regulator
                   three
                   ,
                   or
                   four
                   ,
                   or
                   five
                   Bent-pipes
                   ,
                   or
                   Syphons
                   ,
                   according
                   to
                   the
                   quantity
                   of
                   the
                   water
                   that
                   runneth
                   along
                   the
                   Chanel
                   ;
                   in
                   such
                   sort
                   ,
                   as
                   that
                   they
                   may
                   drink
                   up
                   ,
                   or
                   draw
                   out
                   of
                   the
                   Chanel
                   all
                   the
                   water
                   that
                   the
                   Chanel
                   beareth
                   (
                   and
                   then
                   shall
                   we
                   know
                   that
                   the
                   Syphons
                   drink
                   up
                   all
                   the
                   water
                   ,
                   when
                   we
                   see
                   that
                   the
                   water
                   at
                   the
                   Dam
                   doth
                   neither
                   rise
                   higher
                   ,
                   nor
                   abate
                   ,
                   but
                   alwaies
                   keepeth
                   in
                   the
                   same
                   Level
                   .
                   )
                   These
                   things
                   being
                   prepared
                   ,
                   taking
                   the
                   Instrument
                   to
                   measure
                   the
                   time
                   ,
                   we
                   will
                   examine
                   the
                   quantity
                   of
                   the
                   water
                   that
                   issueth
                   by
                   one
                   of
                   those
                   Syphons
                   in
                   the
                   space
                   of
                   twenty
                   vibrations
                   ,
                   and
                   the
                   like
                   will
                   we
                   do
                   one
                   by
                   one
                   with
                   the
                   other
                   Syphons
                   ;
                   and
                   then
                   collecting
                   the
                   whole
                   summe
                   ,
                   we
                   will
                   say
                   ,
                   that
                   so
                   much
                   is
                   the
                   water
                   that
                   passeth
                   and
                   runneth
                   thorow
                   the
                   Regulator
                   or
                   Chanel
                   (
                   the
                   Dam
                   being
                   taken
                   away
                   )
                   in
                   the
                   space
                   of
                   twenty
                   second
                   minutes
                   of
                   an
                   hour
                   ;
                   and
                   calculating
                   ,
                   we
                   may
                   easily
                   reduce
                   it
                   to
                   hours
                   ,
                   dayes
                   ,
                   months
                   ,
                   and
                   years
                   :
                   And
                   it
                   hath
                   fallen
                   to
                   my
                   turn
                   to
                   measure
                   this
                   way
                   the
                   waters
                   of
                   Mills
                   and
                   Fountains
                   ,
                   and
                   I
                   have
                   been
                   well
                   assured
                   of
                   its
                   exactness
                   ,
                   by
                   often
                   repeating
                   the
                   same
                   work
                   .
                
              
               
                 
                   CONSIDERATION
                   .
                
                 
                   ANd
                   this
                   method
                   must
                   be
                   made
                   use
                   of
                   in
                   measuring
                   the
                   waters
                   ,
                   that
                   we
                   are
                   to
                   bring
                   into
                   Conducts
                   ,
                   and
                   carry
                   into
                   Cities
                   and
                   Castles
                   ,
                   for
                   Fountains
                   ;
                   and
                   that
                   we
                   may
                   be
                   able
                   afterwards
                   to
                   divide
                   and
                   share
                   them
                   to
                   particular
                   persons
                   justly
                   ;
                   which
                   will
                   prevent
                   infinite
                   suits
                   and
                   controversies
                   that
                   every
                   day
                   happen
                   in
                   these
                   matters
                   .
                
              
               
                 
                 
                   PROPOSITION
                   II.
                   THEOREM
                   I.
                   
                
                 
                   If
                   a
                   River
                   moving
                   with
                   such
                   a
                   certain
                   velocitie
                   through
                   its
                   Regulator
                   ,
                   shall
                   have
                   a
                   given
                   quick
                   height
                   ,
                   and
                   afterwards
                   by
                   new
                   water
                   shall
                   increase
                   to
                   be
                   double
                   ,
                   it
                   shall
                   also
                   increase
                   double
                   in
                   velocitie
                   .
                
                 
                   LEt
                   the
                   quick
                   height
                   of
                   a
                   River
                   in
                   the
                   Regulator
                   ABCD
                   ,
                   be
                   the
                   perpendicular
                   FB
                   ,
                   and
                   afterwards
                   ,
                   by
                   new
                   water
                   that
                   is
                   added
                   to
                   the
                   River
                   ,
                   let
                   the
                   water
                   be
                   supposed
                   to
                   be
                   raised
                   to
                   G
                   ,
                   so
                   that
                   GB
                   may
                   be
                   double
                   to
                   EB
                   .
                   I
                   say
                   ,
                   that
                   all
                   the
                   water
                   GC
                   shall
                   be
                   double
                   in
                   velocity
                   to
                   
                   that
                   of
                   EC
                   :
                   For
                   the
                   water
                   GF
                   ,
                   having
                   for
                   its
                   bed
                   the
                   bottom
                   EF
                   ,
                   equally
                   inclined
                   as
                   the
                   bed
                   BC
                   ,
                   and
                   its
                   quick
                   height
                   GE
                   being
                   equal
                   to
                   the
                   quick
                   height
                   EC
                   ,
                   and
                   having
                   the
                   same
                   breadth
                   BC
                   ,
                   it
                   shall
                   have
                   of
                   it self
                   a
                   velocity
                   equal
                   to
                   the
                   velocity
                   of
                   the
                   first
                   water
                   FC
                   :
                   but
                   because
                   ,
                   besides
                   its
                   own
                   motion
                   ,
                   which
                   is
                   imparted
                   to
                   it
                   by
                   the
                   motion
                   of
                   the
                   water
                   EC
                   ,
                   it
                   hath
                   also
                   over
                   and
                   above
                   its
                   own
                   motion
                   ,
                   the
                   motion
                   of
                   EC
                   .
                   And
                   because
                   the
                   two
                   waters
                   GC
                   ,
                   and
                   EC
                   ,
                   are
                   alike
                   in
                   velocity
                   ,
                   by
                   the
                   third
                   Supposition
                   ;
                   therefore
                   the
                   whole
                   water
                   GC
                   shall
                   be
                   double
                   in
                   velocity
                   to
                   the
                   water
                   EC
                   ;
                   which
                   was
                   that
                   which
                   we
                   were
                   to
                   demonstrate
                   .
                
                 
                   This
                   demonstration
                   is
                   not
                   here
                   inserted
                   ,
                   as
                   perfect
                   ,
                   the
                   Authour
                   having
                   by
                   several
                   letters
                   to
                   his
                   friends
                   confessed
                   himself
                   unsatisfied
                   therewith
                   ;
                   and
                   that
                   he
                   intended
                   not
                   to
                   publish
                   the
                   Theorem
                   without
                   a
                   more
                   solid
                   demonstration
                   ,
                   which
                   he
                   was
                   in
                   hope
                   to
                   light
                   upon
                   .
                   But
                   being
                   overtaken
                   by
                   Death
                   ,
                   he
                   could
                   not
                   give
                   the
                   finishing
                   touch
                   either
                   to
                   this
                   ,
                   or
                   to
                   the
                   rest
                   of
                   the
                   second
                   Book
                   .
                   In
                   consideration
                   of
                   which
                   ,
                   it
                   seemed
                   good
                   to
                   the
                   Publisher
                   of
                   the
                   same
                   ,
                   rather
                   to
                   omit
                   it
                   ,
                   than
                   to
                   do
                   any
                   thing
                   contrary
                   to
                   the
                   mind
                   of
                   the
                   Authour
                   .
                   And
                   this
                   he
                   hints
                   ,
                   by
                   way
                   of
                   advertisement
                   ,
                   to
                   those
                   that
                   have
                   Manuscript
                   Copies
                   of
                   this
                   Book
                   ,
                   with
                   the
                   said
                   demonstration
                   .
                   For
                   this
                   time
                   let
                   the
                   Reader
                   content
                   himself
                   with
                   the
                   knowledge
                   of
                   so
                   ingenious
                   and
                   profitable
                   a
                   Conclusion
                   ;
                   of
                   the
                   truth
                   of
                   which
                   he
                   may
                   ,
                   with
                   small
                   expence
                   and
                   much
                   pleasure
                   ,
                   be
                   assured
                   by
                   means
                   of
                   the
                   experiment
                   to
                   be
                   made
                   in
                   the
                   same
                   manner
                   ,
                   with
                   that
                   which
                   is
                   laid
                   down
                   in
                   the
                   second
                   Corollary
                   of
                   
                   the
                   fourth
                   Theorem
                   of
                   this
                   ,
                   with
                   its
                   Table
                   ,
                   and
                   the
                   use
                   thereof
                   annexed
                   .
                
              
               
                 
                   COROLLARIE
                
                 
                   HEnce
                   it
                   followeth
                   ,
                   that
                   when
                   a
                   River
                   increaseth
                   in
                   quick
                   height
                   by
                   the
                   addition
                   of
                   new
                   water
                   ,
                   it
                   also
                   increaseth
                   in
                   velocity
                   ;
                   so
                   that
                   the
                   velocity
                   hath
                   the
                   same
                   proportion
                   to
                   the
                   velocity
                   that
                   the
                   quick
                   height
                   hath
                   to
                   the
                   quick
                   height
                   ;
                   as
                   may
                   be
                   demonstrated
                   in
                   the
                   same
                   manner
                   .
                
              
               
                 
                   PROPOS
                   .
                   III.
                   PROBLEME
                   II.
                   
                
                 
                   A
                   Chanel
                   of
                   Water
                   being
                   given
                   whose
                   breadth
                   exceeds
                   not
                   twenty
                   Palms
                   ,
                   or
                   thereabouts
                   ,
                   and
                   whose
                   quick
                   height
                   is
                   less
                   than
                   five
                   Palms
                   ,
                   to
                   measure
                   the
                   quantity
                   of
                   the
                   Water
                   that
                   runneth
                   thorow
                   the
                   Chanel
                   in
                   a
                   time
                   given
                   .
                
                 
                   PLace
                   in
                   the
                   Chanel
                   a
                   Regulator
                   ,
                   and
                   observe
                   the
                   quick
                   height
                   in
                   the
                   said
                   Regulator
                   ;
                   then
                   let
                   the
                   water
                   be
                   turned
                   away
                   from
                   the
                   Chanel
                   by
                   a
                   Chanellet
                   of
                   three
                   or
                   four
                   Palms
                   in
                   breadth
                   ,
                   or
                   thereabouts
                   :
                   And
                   that
                   being
                   done
                   ,
                   measure
                   the
                   quantity
                   of
                   the
                   water
                   which
                   passeth
                   thorow
                   the
                   said
                   Chanellet
                   ,
                   as
                   hath
                   been
                   taught
                   in
                   the
                   second
                   Proposition
                   ;
                   and
                   at
                   the
                   same
                   time
                   observe
                   exactly
                   how
                   much
                   the
                   quick
                   height
                   shall
                   be
                   abated
                   in
                   the
                   greater
                   Chanel
                   ,
                   by
                   means
                   of
                   the
                   diversion
                   of
                   the
                   Chanellet
                   ;
                   and
                   all
                   these
                   particulars
                   being
                   performed
                   ,
                   multiply
                   the
                   quick
                   height
                   of
                   the
                   greater
                   Chanel
                   into
                   it self
                   ,
                   and
                   likewise
                   multiply
                   into
                   it self
                   the
                   lesser
                   height
                   of
                   the
                   said
                   bigger
                   Chanel
                   ,
                   and
                   the
                   lesser
                   square
                   being
                   taken
                   ,
                   from
                   the
                   greater
                   ,
                   the
                   remainder
                   shall
                   have
                   the
                   same
                   proportion
                   to
                   the
                   whole
                   greater
                   square
                   ,
                   as
                   the
                   water
                   of
                   the
                   Chanellet
                   diverted
                   ,
                   hath
                   to
                   the
                   water
                   of
                   the
                   bigger
                   Chanel
                   :
                   And
                   because
                   the
                   water
                   of
                   the
                   Chanellet
                   is
                   known
                   by
                   the
                   Method
                   laid
                   down
                   in
                   the
                   first
                   Theorem
                   ,
                   and
                   the
                   terms
                   of
                   the
                   Theorem
                   being
                   also
                   known
                   ,
                   the
                   quantity
                   of
                   the
                   water
                   which
                   runneth
                   thorow
                   the
                   bigger
                   Chanel
                   ,
                   shall
                   be
                   also
                   known
                   by
                   the
                   Golden
                   Rule
                   ,
                   which
                   was
                   that
                   that
                   was
                   desired
                   to
                   be
                   known
                   .
                   We
                   will
                   explain
                   the
                   whole
                   business
                   by
                   an
                   example
                   .
                
                 
                   Let
                   a
                   Chanel
                   be
                   ,
                   for
                   example
                   ,
                   15
                   Palms
                   broad
                   ,
                   its
                   quick
                   height
                   before
                   its
                   diversion
                   by
                   the
                   Chanellet
                   shall
                   be
                   supposed
                   to
                   be
                   24
                   inches
                   ;
                   but
                   after
                   the
                   diversion
                   ,
                   let
                   the
                   quick
                   height
                   of
                   the
                   Chanel
                   be
                   onely
                   22
                   inches
                   .
                   Therefore
                   the
                   greater
                   height
                   to
                   the
                   lesser
                   ,
                   is
                   as
                   the
                   number
                   11.
                   to
                   12.
                   
                   But
                   the
                   square
                   of
                   11.
                   is
                   121
                   ,
                   and
                   the
                   square
                   of
                   12.
                   is
                   144
                   ,
                   the
                   difference
                   between
                   the
                   said
                   lesser
                   
                   square
                   and
                   the
                   greater
                   is
                   23.
                   
                   Therefore
                   the
                   diverted
                   water
                   ,
                   is
                   to
                   the
                   whole
                   water
                   ,
                   as
                   23.
                   to
                   144
                   :
                   which
                   is
                   well
                   near
                   as
                   1
                   to
                   6
                   6
                   /
                   23
                   :
                   and
                   that
                   is
                   the
                   proportion
                   that
                   the
                   quantity
                   of
                   the
                   water
                   which
                   runneth
                   through
                   the
                   Chanellet
                   shall
                   have
                   ,
                   to
                   all
                   the
                   water
                   that
                   runneth
                   thorow
                   the
                   great
                   Chanel
                   .
                   Now
                   if
                   we
                   should
                   finde
                   by
                   the
                   Rule
                   mentioned
                   above
                   in
                   the
                   first
                   Proposition
                   ,
                   that
                   the
                   quantity
                   of
                   the
                   water
                   that
                   runneth
                   through
                   the
                   Chanellet
                   ,
                   is
                   
                     v.
                     g.
                  
                   an
                   hundred
                   Barrels
                   ,
                   in
                   the
                   space
                   of
                   15
                   second
                   minutes
                   of
                   an
                   hour
                   ,
                   it
                   is
                   manifest
                   ,
                   that
                   the
                   water
                   which
                   runneth
                   through
                   the
                   great
                   Chanel
                   in
                   the
                   said
                   time
                   of
                   35
                   min.
                   sec
                   .
                   shall
                   be
                   about
                   600
                   Barrels
                   .
                
                 
                   
                     The
                     same
                     operation
                     performed
                     another
                     way
                     .
                  
                   
                     ANd
                     because
                     very
                     often
                     in
                     applying
                     the
                     Theory
                     to
                     Practice
                     it
                     happeneth
                     ,
                     that
                     all
                     the
                     necessary
                     particulars
                     in
                     the
                     Theory
                     cannot
                     so
                     easily
                     be
                     put
                     in
                     execution
                     ;
                     therefore
                     we
                     will
                     here
                     add
                     another
                     way
                     of
                     performing
                     the
                     same
                     Problem
                     ,
                     if
                     it
                     should
                     chance
                     to
                     happen
                     that
                     the
                     Chanellet
                     could
                     not
                     commodiously
                     be
                     diverted
                     from
                     the
                     great
                     Chanel
                     ,
                     but
                     that
                     it
                     were
                     easier
                     for
                     the
                     water
                     of
                     another
                     smaller
                     Chanel
                     to
                     be
                     brought
                     into
                     the
                     greater
                     Chanel
                     ;
                     which
                     water
                     of
                     the
                     smaller
                     Chanel
                     might
                     be
                     easily
                     measured
                     ,
                     as
                     hath
                     been
                     shewen
                     in
                     the
                     first
                     Probleme
                     ;
                     or
                     in
                     case
                     that
                     there
                     did
                     fall
                     into
                     a
                     greater
                     Chanel
                     ,
                     a
                     lesser
                     Chanel
                     that
                     might
                     be
                     diverted
                     and
                     measured
                     .
                     Therefore
                     I
                     say
                     in
                     the
                     first
                     case
                     ,
                     If
                     we
                     would
                     measure
                     the
                     quantity
                     of
                     the
                     water
                     that
                     runneth
                     in
                     a
                     certain
                     time
                     thorow
                     the
                     greater
                     Chanel
                     ,
                     into
                     which
                     another
                     lesser
                     Chanel
                     that
                     is
                     measurable
                     may
                     be
                     brought
                     ,
                     we
                     must
                     first
                     exactly
                     measure
                     the
                     Chanellet
                     ,
                     and
                     then
                     observe
                     the
                     quick
                     height
                     of
                     the
                     greater
                     Chanel
                     ,
                     before
                     the
                     introduction
                     of
                     the
                     lesser
                     ;
                     and
                     having
                     brought
                     in
                     the
                     said
                     Chanellet
                     ,
                     we
                     must
                     agnin
                     find
                     the
                     proportion
                     that
                     the
                     water
                     of
                     the
                     Chanellet
                     hath
                     to
                     all
                     the
                     water
                     of
                     the
                     great
                     Chanel
                     ;
                     for
                     these
                     terms
                     of
                     the
                     proportion
                     being
                     known
                     ,
                     as
                     also
                     the
                     quantity
                     of
                     the
                     water
                     of
                     the
                     Chanellet
                     ,
                     we
                     shall
                     also
                     come
                     to
                     know
                     the
                     quantity
                     of
                     the
                     water
                     that
                     runneth
                     thorow
                     the
                     great
                     Chanel
                     .
                     It
                     is
                     likewise
                     manifest
                     ,
                     that
                     we
                     shall
                     obtain
                     our
                     intent
                     ,
                     if
                     the
                     case
                     were
                     that
                     there
                     entered
                     into
                     the
                     great
                     Chanel
                     ,
                     another
                     lesser
                     Chanel
                     that
                     was
                     measurable
                     ,
                     and
                     that
                     might
                     be
                     diverted
                     .
                  
                
              
               
                 
                   CONSIDERATION
                   .
                
                 
                   IT
                   would
                   be
                   necessary
                   to
                   make
                   use
                   of
                   this
                   Doctrine
                   in
                   the
                   distribution
                   of
                   the
                   waters
                   that
                   are
                   imploy'd
                   to
                   overflow
                   the
                   fields
                   ,
                   as
                   is
                   used
                   in
                   the
                   
                     Brescian
                     ,
                     Cremonese
                     ,
                     Bergamase
                     ,
                     Lodigian
                     ,
                     Milanese
                  
                   
                   territories
                   ,
                   and
                   many
                   other
                   places
                   ,
                   where
                   very
                   great
                   suits
                   and
                   differences
                   arise
                   ,
                   which
                   not
                   being
                   to
                   be
                   determined
                   with
                   intelligible
                   reasons
                   ,
                   come
                   oftentimes
                   to
                   be
                   decided
                   ,
                   by
                   force
                   of
                   armes
                   ;
                   and
                   instead
                   of
                   flowing
                   their
                   Grounds
                   with
                   Waters
                   ,
                   they
                   cruelly
                   flow
                   them
                   with
                   the
                   shedding
                   of
                   humane
                   blood
                   ,
                   impiously
                   inverting
                   the
                   course
                   of
                   Peace
                   and
                   Justice
                   ,
                   sowing
                   such
                   disorders
                   and
                   feuds
                   ,
                   as
                   that
                   they
                   are
                   sometimes
                   accompanied
                   with
                   the
                   ruine
                   of
                   whole
                   Cities
                   ,
                   or
                   else
                   unprofitably
                   charge
                   them
                   with
                   vain
                   ,
                   and
                   sometimes
                   prejudicial
                   expences
                   .
                
              
               
                 
                   PROPOS
                   .
                   IV.
                   THEOR.
                   II.
                   
                
                 
                   If
                   a
                   River
                   increase
                   in
                   quick
                   height
                   ,
                   the
                   quantitie
                   of
                   Water
                   which
                   the
                   River
                   dischargeth
                   after
                   the
                   increase
                   ,
                   hath
                   the
                   Proportion
                   compounded
                   of
                   the
                   Proportions
                   of
                   the
                   Quick
                   height
                   to
                   the
                   Quick
                   height
                   ,
                   and
                   of
                   the
                   velocity
                   to
                   the
                   velocity
                   .
                
                 
                   LEt
                   there
                   be
                   a
                   River
                   ,
                   which
                   whilst
                   it
                   is
                   low
                   ,
                   runneth
                   thorow
                   the
                   Regulator
                   DF
                   ,
                   with
                   the
                   Quick
                   height
                   AB
                   ,
                   and
                   afterwards
                   let
                   a
                   Flood
                   come
                   ;
                   and
                   then
                   let
                   it
                   run
                   with
                   the
                   height
                   DB
                   ,
                   I
                   say
                   ,
                   that
                   the
                   quantity
                   of
                   the
                   Water
                   that
                   is
                   discharged
                   through
                   DF
                   ,
                   to
                   that
                   which
                   dischargeth
                   through
                   AF
                   ,
                   hath
                   the
                   proportion
                   compounded
                   of
                   the
                   proportions
                   of
                   the
                   velocity
                   through
                   DF
                   to
                   the
                   velocity
                   through
                   AF
                   ,
                   and
                   of
                   the
                   height
                   DB
                   to
                   the
                   height
                   AB
                   .
                   As
                   the
                   velocity
                   through
                   DF
                   is
                   to
                   the
                   velocity
                   through
                   AF
                   ,
                   so
                   let
                   the
                   line
                   R
                   be
                   to
                   the
                   line
                   S
                   ;
                   and
                   as
                   the
                   height
                   DB
                   is
                   to
                   the
                   height
                   AB
                   ;
                   so
                   let
                   the
                   line
                   S
                   be
                   to
                   the
                   
                   line
                   T.
                   And
                   let
                   a
                   Section
                   be
                   supposed
                   LMN
                   equal
                   to
                   the
                   Section
                   DF
                   in
                   height
                   and
                   length
                   ,
                   but
                   let
                   it
                   be
                   in
                   velocity
                   equal
                   to
                   the
                   Section
                   AF.
                   Therefore
                   the
                   quantity
                   of
                   the
                   Water
                   that
                   runneth
                   through
                   DF
                   to
                   that
                   which
                   runneth
                   through
                   LN
                   ,
                   shall
                   be
                   
                   as
                   the
                   velocity
                   through
                   DF
                   ,
                   to
                   the
                   velocity
                   of
                   LN
                   ,
                   that
                   is
                   ,
                   to
                   the
                   velocity
                   through
                   LN
                   ,
                   that
                   is
                   ,
                   to
                   the
                   velocity
                   through
                   AF.
                   therefore
                   the
                   quantity
                   of
                   Water
                   which
                   runneth
                   through
                   DF
                   ,
                   to
                   that
                   which
                   passeth
                   through
                   LN
                   ,
                   shall
                   have
                   the
                   proportion
                   that
                   R
                   hath
                   to
                   S
                   ;
                   but
                   the
                   quantity
                   of
                   the
                   Water
                   that
                   runneth
                   through
                   LN
                   ,
                   to
                   that
                   which
                   runneth
                   through
                   AF
                   ;
                   (
                   the
                   Sections
                   being
                   equally
                   swift
                   )
                   shall
                   have
                   the
                   proportion
                   that
                   the
                   Section
                   LN
                   hath
                   to
                   the
                   Section
                   AF
                   ,
                   that
                   is
                   ,
                   that
                   the
                   height
                   BD
                   hath
                   to
                   the
                   height
                   BA
                   ,
                   that
                   is
                   ,
                   that
                   S
                   hath
                   to
                   T.
                   Therefore
                   ,
                   by
                   equal
                   proportion
                   ,
                   the
                   quantity
                   of
                   the
                   Water
                   which
                   runneth
                   by
                   DF
                   ,
                   to
                   that
                   which
                   runneth
                   by
                   AF
                   ,
                   shall
                   have
                   the
                   proportion
                   of
                   R
                   to
                   T
                   ,
                   that
                   is
                   ,
                   shall
                   be
                   compounded
                   of
                   the
                   proportions
                   of
                   the
                   height
                   DB
                   ,
                   to
                   the
                   height
                   AB
                   ;
                   and
                   of
                   the
                   velocity
                   through
                   DF
                   ,
                   to
                   the
                   velocity
                   through
                   AF.
                   And
                   therefore
                   if
                   a
                   River
                   increase
                   in
                   quick
                   height
                   ,
                   the
                   quantity
                   of
                   the
                   Water
                   that
                   runneth
                   after
                   the
                   increase
                   ,
                   to
                   that
                   which
                   runneth
                   before
                   the
                   increase
                   ,
                   hath
                   the
                   proportion
                   compounded
                   ,
                   &c.
                   
                   Which
                   was
                   to
                   be
                   demonstrated
                   .
                
              
               
                 
                   COROLLARIE
                   I.
                   
                
                 
                   HEnce
                   it
                   followeth
                   ,
                   that
                   we
                   having
                   shewn
                   ,
                   that
                   the
                   quantity
                   of
                   the
                   Water
                   which
                   runneth
                   ,
                   whilst
                   the
                   River
                   is
                   high
                   ,
                   to
                   that
                   which
                   ran
                   ,
                   whilst
                   it
                   was
                   low
                   ,
                   hath
                   the
                   proportion
                   compounded
                   of
                   the
                   velocity
                   to
                   the
                   velocity
                   ,
                   and
                   of
                   the
                   height
                   to
                   the
                   height
                   .
                   And
                   it
                   having
                   been
                   demonstrated
                   ,
                   that
                   the
                   velocity
                   to
                   the
                   velocity
                   is
                   as
                   the
                   height
                   to
                   the
                   height
                   ;
                   it
                   followeth
                   ,
                   I
                   say
                   ,
                   that
                   the
                   quantity
                   of
                   the
                   Water
                   that
                   runneth
                   ,
                   whilst
                   the
                   River
                   is
                   high
                   ,
                   to
                   that
                   which
                   runneth
                   ,
                   whilst
                   it
                   is
                   low
                   ,
                   hath
                   duplicate
                   proportion
                   of
                   the
                   height
                   to
                   the
                   height
                   ,
                   that
                   is
                   ,
                   the
                   proportion
                   that
                   the
                   squares
                   of
                   the
                   heights
                   have
                   .
                
              
               
                 
                   COROLLARIE
                   II.
                   
                
                 
                   VPon
                   which
                   things
                   dependeth
                   the
                   reason
                   of
                   that
                   which
                   I
                   have
                   said
                   ,
                   in
                   my
                   second
                   Consideration
                   ,
                   that
                   if
                   by
                   the
                   diversion
                   of
                   5
                   /
                   9
                   of
                   the
                   Water
                   that
                   entereth
                   by
                   the
                   Rivers
                   into
                   the
                   Moor
                   or
                   Fen
                   ,
                   the
                   Water
                   be
                   abated
                   such
                   a
                   measure
                   ,
                   that
                   same
                   shall
                   be
                   only
                   one
                   third
                   of
                   its
                   whole
                   height
                   ;
                   but
                   moreover
                   diverting
                   the
                   4
                   /
                   9
                   ,
                   it
                   shall
                   abate
                   two
                   other
                   thirds
                   ,
                   a
                   most
                   principal
                   point
                   ;
                   and
                   such
                   ,
                   that
                   it
                   s
                   not
                   having
                   been
                   well
                   understood
                   ,
                   hath
                   caused
                   very
                   great
                   disorders
                   ,
                   and
                   there
                   would
                   now
                   ,
                   more
                   than
                   ever
                   ,
                   follow
                   extream
                   dammage
                   ,
                   if
                   one
                   should
                   put
                   in
                   execution
                   the
                   diversion
                   of
                   the
                   Sile
                   and
                   other
                   Rivers
                   ;
                   and
                   it
                   is
                   manifest
                   ,
                   that
                   in
                   the
                   same
                   manner
                   ,
                   wherewith
                   it
                   hath
                   been
                   demonstrated
                   ,
                   that
                   the
                   quantity
                   of
                   the
                   Water
                   increasing
                   quadruple
                   ,
                   the
                   height
                   would
                   increase
                   onely
                   
                   double
                   ,
                   and
                   the
                   quantity
                   increasing
                   nonuple
                   ,
                   the
                   height
                   increaseth
                   triple
                   ;
                   so
                   that
                   ,
                   by
                   adding
                   to
                   units
                   all
                   the
                   odde
                   numbers
                   ,
                   according
                   to
                   their
                   Series
                   ,
                   the
                   heights
                   increase
                   according
                   to
                   the
                   natural
                   progression
                   of
                   all
                   the
                   numbers
                   ,
                   from
                   units
                   .
                   As
                   for
                   example
                   ,
                   there
                   passing
                   thorow
                   a
                   Regulator
                   such
                   a
                   certain
                   quantity
                   of
                   Water
                   in
                   one
                   time
                   ;
                   adding
                   three
                   of
                   those
                   measures
                   ,
                   the
                   quick
                   height
                   is
                   two
                   of
                   those
                   parts
                   ,
                   which
                   at
                   first
                   was
                   one
                   ;
                   and
                   continuing
                   to
                   adde
                   five
                   of
                   those
                   said
                   measures
                   ,
                   the
                   height
                   is
                   three
                   of
                   those
                   parts
                   which
                   at
                   first
                   were
                   one
                   ;
                   and
                   thus
                   adding
                   seven
                   ,
                   and
                   then
                   nine
                   ,
                   and
                   then
                   11.
                   and
                   then
                   13
                   ,
                   &c.
                   the
                   heights
                   shall
                   be
                   4.
                   then
                   5
                   ,
                   then
                   6.
                   then
                   7
                   ,
                   &c.
                   
                   And
                   for
                   the
                   greater
                   facility
                   of
                   the
                   Work
                   ,
                   we
                   have
                   described
                   the
                   following
                   Table
                   ,
                   of
                   which
                   we
                   will
                   declare
                   the
                   use
                   :
                   The
                   Table
                   is
                   divided
                   into
                   three
                   Series
                   or
                   Progressions
                   of
                   Numbers
                   :
                   the
                   first
                   Series
                   containeth
                   all
                   the
                   Numbers
                   in
                   the
                   Natural
                   Progression
                   ,
                   beginning
                   at
                   a
                   Unit
                   ,
                   and
                   is
                   called
                   the
                   Series
                   of
                   the
                   Heights
                   ;
                   the
                   second
                   containeth
                   all
                   the
                   odde
                   numbers
                   ,
                   beginning
                   at
                   an
                   unit
                   ,
                   and
                   is
                   called
                   the
                   Series
                   of
                   the
                   Additions
                   :
                   the
                   third
                   containeth
                   all
                   the
                   square
                   numbers
                   ,
                   beginning
                   at
                   an
                   unit
                   ,
                   and
                   is
                   called
                   the
                   Series
                   of
                   Quantity
                   .
                
                 
                   
                     
                       
                         Heights
                         .
                      
                       
                         1
                      
                       
                         2
                      
                       
                         3
                      
                       
                         4
                      
                       
                         5
                      
                       
                         6
                      
                       
                         7
                      
                       
                         8
                      
                       
                         9
                      
                       
                         10
                      
                       
                         11
                      
                    
                     
                       
                         Additions
                         .
                      
                       
                         1
                      
                       
                         3
                      
                       
                         5
                      
                       
                         7
                      
                       
                         9
                      
                       
                         11
                      
                       
                         13
                      
                       
                         15
                      
                       
                         17
                      
                       
                         19
                      
                       
                         21
                      
                    
                     
                       
                         Quantities
                         .
                      
                       
                         1
                      
                       
                         4
                      
                       
                         9
                      
                       
                         16
                      
                       
                         25
                      
                       
                         36
                      
                       
                         49
                      
                       
                         64
                      
                       
                         81
                      
                       
                         100
                      
                       
                         121
                      
                    
                  
                
                 
                   
                     The
                     use
                     of
                     the
                     afore-mentioned
                     Table
                     .
                  
                   
                     FIrst
                     ,
                     if
                     we
                     suppose
                     the
                     whole
                     quick
                     height
                     of
                     a
                     River
                     of
                     Running
                     Water
                     to
                     be
                     divided
                     into
                     any
                     number
                     of
                     equal
                     parts
                     ,
                     at
                     pleasure
                     ,
                     and
                     would
                     abate
                     the
                     same
                     one
                     fift
                     ,
                     by
                     means
                     of
                     a
                     division
                     ;
                     let
                     there
                     be
                     found
                     in
                     the
                     Table
                     in
                     the
                     Series
                     of
                     heights
                     the
                     number
                     5.
                     the
                     denominator
                     of
                     the
                     part
                     which
                     the
                     River
                     is
                     to
                     abate
                     ,
                     and
                     take
                     the
                     number
                     that
                     is
                     immediately
                     under
                     it
                     in
                     the
                     row
                     of
                     Additions
                     ,
                     which
                     is
                     9.
                     which
                     let
                     be
                     substracted
                     from
                     the
                     number
                     25.
                     placed
                     underneath
                     the
                     same
                     in
                     the
                     row
                     of
                     Quantities
                     ,
                     the
                     remainder
                     16.
                     signifieth
                     that
                     of
                     the
                     25.
                     parts
                     of
                     Water
                     that
                     ran
                     in
                     the
                     River
                     ,
                     whilst
                     it
                     was
                     5
                     measures
                     high
                     ,
                     there
                     do
                     onely
                     run
                     16.
                     parts
                     ;
                     so
                     that
                     to
                     make
                     it
                     abate
                     1
                     /
                     5
                     it
                     is
                     necessary
                     to
                     take
                     9
                     /
                     25
                     from
                     the
                     Water
                     that
                     the
                     whole
                     River
                     did
                     carry
                     ;
                     so
                     that
                     with
                     substracting
                     somewhat
                     more
                     than
                     one
                     third
                     of
                     the
                     Water
                     of
                     the
                     River
                     ,
                     it
                     is
                     abated
                     but
                     only
                     one
                     fift
                     .
                  
                   
                     2.
                     
                     And
                     thus
                     ,
                     in
                     the
                     second
                     place
                     ,
                     if
                     one
                     the
                     contrary
                     ,
                     one
                     would
                     know
                     how
                     much
                     water
                     is
                     to
                     be
                     added
                     to
                     the
                     said
                     River
                     to
                     make
                     it
                     increase
                     one
                     fift
                     more
                     in
                     height
                     ,
                     so
                     as
                     that
                     it
                     may
                     run
                     in
                     the
                     
                     Regulator
                     6.
                     of
                     those
                     parts
                     high
                     ;
                     of
                     which
                     it
                     ran
                     before
                     but
                     5.
                     let
                     6
                     be
                     found
                     in
                     the
                     row
                     of
                     heights
                     ,
                     and
                     let
                     the
                     number
                     11.
                     standing
                     under
                     the
                     same
                     be
                     taken
                     and
                     added
                     to
                     the
                     number
                     25.
                     that
                     is
                     placed
                     under
                     the
                     number
                     9.
                     in
                     the
                     Additions
                     ,
                     and
                     5.
                     in
                     the
                     heights
                     ,
                     and
                     you
                     shall
                     have
                     36
                     ;
                     which
                     is
                     the
                     quantity
                     of
                     the
                     water
                     that
                     runneth
                     with
                     the
                     height
                     of
                     the
                     River
                     ,
                     when
                     it
                     is
                     high
                     6
                     of
                     those
                     parts
                     ,
                     whereof
                     it
                     was
                     before
                     but
                     5.
                     
                  
                   
                     3.
                     
                     But
                     if
                     it
                     should
                     be
                     desired
                     ,
                     to
                     know
                     how
                     much
                     water
                     it
                     is
                     requisite
                     to
                     add
                     to
                     make
                     the
                     River
                     rise
                     so
                     ,
                     as
                     that
                     it
                     may
                     run
                     in
                     height
                     8.
                     of
                     those
                     parts
                     of
                     which
                     before
                     it
                     ran
                     but
                     5
                     ;
                     one
                     ought
                     to
                     take
                     the
                     sum
                     of
                     the
                     number
                     of
                     the
                     Series
                     of
                     Additions
                     standing
                     under
                     8.
                     7.
                     and
                     6
                     ,
                     which
                     are
                     15.
                     13.
                     and
                     11.
                     that
                     is
                     ,
                     39.
                     and
                     this
                     shall
                     be
                     the
                     summe
                     that
                     must
                     be
                     added
                     to
                     25
                     :
                     So
                     that
                     to
                     make
                     the
                     River
                     to
                     run
                     8.
                     of
                     those
                     parts
                     in
                     height
                     ,
                     of
                     which
                     it
                     before
                     did
                     run
                     5
                     ,
                     it
                     will
                     be
                     necessary
                     to
                     add
                     39.
                     of
                     those
                     parts
                     ,
                     of
                     which
                     the
                     River
                     before
                     was
                     25.
                     
                  
                   
                     4.
                     
                     Likewise
                     the
                     same
                     Table
                     giveth
                     the
                     quantity
                     of
                     water
                     that
                     runneth
                     from
                     time
                     to
                     time
                     through
                     a
                     River
                     ,
                     that
                     increaseth
                     by
                     the
                     addition
                     of
                     new
                     water
                     to
                     the
                     same
                     in
                     one
                     of
                     its
                     heights
                     ,
                     the
                     quantity
                     of
                     its
                     water
                     be
                     known
                     .
                     As
                     for
                     example
                     :
                     If
                     we
                     knew
                     that
                     the
                     River
                     in
                     one
                     minute
                     of
                     an
                     hour
                     dischargeth
                     2500.
                     of
                     those
                     measures
                     of
                     water
                     ,
                     and
                     runneth
                     in
                     height
                     5.
                     parts
                     in
                     the
                     Regulator
                     ,
                     and
                     afterwards
                     should
                     see
                     that
                     it
                     runneth
                     8
                     Palms
                     high
                     ,
                     finding
                     in
                     the
                     row
                     of
                     quantity
                     the
                     number
                     placed
                     under
                     8.
                     which
                     is
                     64.
                     we
                     would
                     say
                     that
                     the
                     River
                     heightned
                     ,
                     carrieth
                     of
                     water
                     64.
                     of
                     those
                     parts
                     whereof
                     it
                     carried
                     before
                     but
                     25
                     ;
                     and
                     because
                     before
                     it
                     carried
                     2500.
                     measures
                     ,
                     by
                     the
                     Golden
                     Rule
                     we
                     will
                     say
                     ,
                     that
                     the
                     River
                     carrieth
                     6400.
                     of
                     those
                     measures
                     ,
                     of
                     which
                     before
                     it
                     carried
                     2500.
                     
                  
                   
                     In
                     this
                     progress
                     of
                     Nature
                     ,
                     is
                     one
                     thing
                     really
                     curious
                     ,
                     and
                     that
                     at
                     first
                     sight
                     seemeth
                     to
                     be
                     somewhat
                     Paradoxal
                     ,
                     that
                     we
                     proceeding
                     ordinately
                     in
                     the
                     diversions
                     and
                     additions
                     ,
                     with
                     additions
                     and
                     diversions
                     so
                     unequal
                     ,
                     the
                     abatings
                     do
                     notwithstanding
                     alwaies
                     prove
                     equal
                     ,
                     and
                     so
                     do
                     the
                     risings
                     :
                     And
                     who
                     would
                     ever
                     think
                     that
                     a
                     River
                     in
                     height
                     ,
                     
                       v.
                       g.
                    
                     10.
                     
                     Palms
                     ,
                     running
                     and
                     carrying
                     an
                     hundred
                     measures
                     in
                     a
                     minute
                     of
                     an
                     hour
                     ,
                     is
                     to
                     abate
                     but
                     one
                     Palm
                     ,
                     onely
                     by
                     the
                     diversion
                     of
                     19.
                     of
                     those
                     measures
                     ;
                     and
                     then
                     again
                     ,
                     that
                     the
                     buisiness
                     cometh
                     to
                     that
                     pass
                     ,
                     that
                     it
                     abateth
                     likewise
                     a
                     Palm
                     by
                     the
                     diversion
                     of
                     three
                     onely
                     of
                     those
                     measures
                     ,
                     nay
                     ,
                     by
                     the
                     diversion
                     of
                     but
                     one
                     measure
                     ?
                     and
                     yet
                     it
                     is
                     most
                     certain
                     :
                     And
                     this
                     truth
                     meets
                     with
                     so
                     manifest
                     proofs
                     in
                     experience
                     ,
                     that
                     it
                     is
                     very
                     admirable
                     !
                     And
                     for
                     the
                     full
                     satisfaction
                     of
                     those
                     ,
                     who
                     not
                     being
                     able
                     to
                     comprehend
                     subtil
                     demonstrations
                     ,
                     desire
                     to
                     be
                     clearly
                     inform'd
                     by
                     the
                     matters
                     of
                     fact
                     ,
                     and
                     to
                     see
                     with
                     their
                     bodily
                     eyes
                     ,
                     and
                     touch
                     with
                     their
                     hands
                     ,
                     what
                     their
                     understanding
                     and
                     reason
                     cannot
                     reach
                     unto
                     :
                     I
                     will
                     hear
                     add
                     another
                     very
                     easie
                     way
                     to
                     reduce
                     all
                     to
                     an
                     experiment
                     ,
                     the
                     
                     which
                     may
                     be
                     made
                     in
                     little
                     ,
                     in
                     great
                     ,
                     or
                     in
                     very
                     great
                     ;
                     of
                     which
                     I
                     make
                     use
                     frequently
                     ,
                     to
                     the
                     admiration
                     of
                     such
                     as
                     see
                     it
                     .
                  
                   
                     I
                     prepared
                     an
                     hundred
                     Siphons
                     ,
                     or
                     ,
                     if
                     you
                     will
                     ,
                     bowed
                     Pipes
                     ,
                     all
                     equal
                     ;
                     and
                     placed
                     them
                     at
                     the
                     brim
                     of
                     a
                     Vessel
                     ,
                     wherein
                     the
                     water
                     is
                     kept
                     at
                     one
                     and
                     the
                     same
                     level
                     (
                     whether
                     all
                     the
                     Syphons
                     work
                     ,
                     or
                     but
                     a
                     certain
                     number
                     of
                     them
                     )
                     the
                     mouths
                     by
                     which
                     the
                     water
                     issueth
                     being
                     all
                     placed
                     in
                     the
                     same
                     level
                     ,
                     parallel
                     to
                     the
                     Horizon
                     ;
                     but
                     lower
                     in
                     level
                     than
                     the
                     water
                     in
                     the
                     Vessel
                     ;
                     and
                     gathered
                     all
                     the
                     water
                     falling
                     from
                     the
                     Syphons
                     into
                     another
                     Vessel
                     standing
                     lower
                     than
                     the
                     former
                     ,
                     I
                     made
                     it
                     to
                     run
                     away
                     thorow
                     a
                     Chanel
                     ,
                     in
                     such
                     manner
                     inclined
                     ,
                     that
                     wanting
                     water
                     from
                     the
                     Syphons
                     ,
                     the
                     said
                     Chanel
                     remained
                     quite
                     dry
                     .
                  
                   
                     And
                     this
                     done
                     ,
                     I
                     measured
                     the
                     quick
                     height
                     of
                     the
                     Chanel
                     with
                     care
                     ,
                     and
                     afterwards
                     divided
                     it
                     exactly
                     into
                     10
                     equal
                     parts
                     ,
                     and
                     causing
                     19.
                     of
                     those
                     Syphons
                     to
                     be
                     taken
                     away
                     ,
                     so
                     that
                     the
                     Chanel
                     did
                     not
                     run
                     water
                     ,
                     save
                     onely
                     with
                     81
                     of
                     those
                     Syphons
                     ,
                     I
                     again
                     observed
                     the
                     quick
                     height
                     of
                     the
                     water
                     in
                     the
                     same
                     site
                     observed
                     before
                     ,
                     and
                     found
                     that
                     its
                     height
                     was
                     diminished
                     precisely
                     the
                     tenth
                     part
                     of
                     all
                     its
                     first
                     height
                     ;
                     and
                     thus
                     continuing
                     to
                     take
                     away
                     17.
                     other
                     Syphons
                     ,
                     the
                     height
                     was
                     likewise
                     diminished
                     1
                     /
                     10
                     of
                     all
                     its
                     first
                     quick
                     height
                     ;
                     and
                     trying
                     to
                     take
                     away
                     15.
                     
                     Syphons
                     ,
                     then
                     13
                     ,
                     then
                     11
                     ,
                     then
                     9
                     ,
                     then
                     7
                     ,
                     then
                     5
                     ,
                     and
                     then
                     3.
                     alwaies
                     in
                     these
                     diversions
                     ,
                     made
                     in
                     order
                     as
                     hath
                     been
                     said
                     ,
                     there
                     ensued
                     still
                     an
                     abatement
                     of
                     1
                     /
                     10
                     of
                     the
                     whole
                     height
                     .
                  
                   
                     And
                     here
                     was
                     one
                     thing
                     worthy
                     of
                     observation
                     ,
                     that
                     the
                     water
                     encreasing
                     in
                     [
                     
                       or
                       through
                    
                     ]
                     the
                     Chanel
                     ,
                     its
                     quick
                     height
                     was
                     different
                     in
                     different
                     sites
                     of
                     the
                     Chanel
                     ,
                     that
                     is
                     still
                     lesser
                     ,
                     the
                     more
                     one
                     approached
                     to
                     the
                     Out-let
                     ;
                     notwithstanding
                     which
                     the
                     abatement
                     followed
                     in
                     all
                     places
                     proportionably
                     ,
                     that
                     is
                     in
                     all
                     its
                     sites
                     the
                     first
                     part
                     of
                     the
                     height
                     of
                     that
                     site
                     diminished
                     :
                     And
                     moreover
                     the
                     water
                     issued
                     from
                     the
                     Chanel
                     ,
                     and
                     dilated
                     into
                     a
                     broader
                     course
                     ,
                     from
                     which
                     likewise
                     having
                     divers
                     Out-lets
                     and
                     Mouths
                     ;
                     yet
                     nevertheless
                     in
                     that
                     breadth
                     also
                     the
                     quick
                     heights
                     successively
                     varied
                     and
                     altered
                     in
                     the
                     same
                     proportions
                     .
                     Nor
                     did
                     I
                     here
                     desist
                     my
                     observation
                     ,
                     but
                     the
                     water
                     being
                     diminished
                     ,
                     that
                     issued
                     from
                     the
                     Syphons
                     ,
                     and
                     there
                     being
                     but
                     one
                     of
                     them
                     left
                     that
                     discharged
                     water
                     ;
                     I
                     observed
                     the
                     quick
                     height
                     that
                     it
                     made
                     in
                     the
                     above-said
                     sites
                     ,
                     (
                     the
                     which
                     was
                     likewise
                     1
                     /
                     10
                     of
                     all
                     the
                     first
                     height
                     )
                     there
                     being
                     added
                     to
                     the
                     water
                     of
                     that
                     Syphon
                     ,
                     the
                     water
                     of
                     three
                     other
                     Syphons
                     ;
                     so
                     that
                     all
                     the
                     water
                     was
                     of
                     4
                     Syphons
                     ,
                     and
                     consequently
                     quadruple
                     to
                     the
                     first
                     Syphon
                     ;
                     but
                     the
                     quick
                     height
                     was
                     onely
                     double
                     ,
                     and
                     adding
                     five
                     Siphons
                     ,
                     the
                     quick
                     height
                     became
                     triple
                     ,
                     and
                     with
                     adding
                     seven
                     Syphons
                     ,
                     the
                     height
                     increased
                     quadruple
                     ;
                     and
                     so
                     by
                     adding
                     of
                     9.
                     it
                     increased
                     quintuple
                     ,
                     and
                     by
                     adding
                     of
                     11.
                     it
                     increased
                     sextuple
                     ,
                     and
                     by
                     adding
                     
                     of
                     13.
                     it
                     increased
                     septuple
                     ,
                     and
                     by
                     adding
                     of
                     15.
                     octuple
                     ,
                     and
                     by
                     adding
                     of
                     17.
                     nonuple
                     ,
                     and
                     lastly
                     by
                     adding
                     19.
                     
                     Syphons
                     ;
                     so
                     that
                     all
                     the
                     water
                     was
                     centuple
                     to
                     the
                     water
                     of
                     one
                     Syphon
                     ,
                     yet
                     nevertheless
                     the
                     quick
                     height
                     of
                     all
                     this
                     water
                     was
                     onely
                     decuple
                     to
                     the
                     first
                     height
                     conjoyned
                     by
                     the
                     water
                     that
                     issued
                     from
                     one
                     onely
                     Syphon
                     .
                  
                   
                     For
                     the
                     more
                     clear
                     understanding
                     of
                     all
                     which
                     ,
                     I
                     have
                     made
                     the
                     following
                     Figure
                     ;
                     in
                     which
                     we
                     have
                     the
                     mouth
                     A
                     ,
                     that
                     maintaineth
                     the
                     water
                     of
                     the
                     Vessel
                     BC
                     in
                     the
                     same
                     level
                     ;
                     though
                     it
                     continually
                     run
                     ;
                     to
                     the
                     brim
                     of
                     the
                     Vessel
                     are
                     put
                     25.
                     
                     Syphons
                     (
                     and
                     there
                     may
                     be
                     many
                     more
                     )
                     divided
                     into
                     5
                     Classes
                     ,
                     DEFGH
                     ,
                     and
                     the
                     first
                     D
                     ,
                     are
                     of
                     one
                     onely
                     Syphon
                     ;
                     the
                     second
                     E
                     ,
                     of
                     three
                     Syphons
                     ;
                     the
                     third
                     F
                     ,
                     of
                     five
                     ;
                     the
                     fourth
                     G
                     ,
                     of
                     7
                     ;
                     the
                     fifth
                     H
                     ,
                     of
                     9
                     ;
                     and
                     one
                     may
                     suppose
                     the
                     sixth
                     of
                     11
                     ,
                     the
                     seventh
                     of
                     13
                     Syphons
                     ,
                     and
                     so
                     of
                     the
                     other
                     Classes
                     ,
                     all
                     containing
                     in
                     consequent
                     odd
                     numbers
                     successively
                     (
                     we
                     are
                     content
                     to
                     represent
                     in
                     the
                     Figure
                     no
                     more
                     but
                     the
                     five
                     forenamed
                     Classes
                     to
                     avoid
                     confusion
                     )
                     the
                     gathered
                     water
                     DEFGH
                     ,
                     which
                     runneth
                     thorow
                     the
                     Chanel
                     IKL
                     ,
                     and
                     falleth
                     into
                     the
                     out-let
                     MNOP
                     ;
                     and
                     so
                     much
                     sufficeth
                     for
                     the
                     explanation
                     of
                     this
                     experiment
                     .
                  
                   
                
              
               
                 
                 
                   PROPOS
                   .
                   V.
                   PROB.
                   III.
                   
                
                 
                   Any
                   River
                   of
                   any
                   bigness
                   ,
                   if
                   being
                   given
                   to
                   examine
                   the
                   quantity
                   of
                   the
                   Water
                   that
                   runneth
                   thorow
                   the
                   River
                   in
                   a
                   time
                   assigned
                   .
                
                 
                   BY
                   what
                   we
                   have
                   said
                   already
                   in
                   the
                   two
                   preceding
                   Problems
                   ,
                   we
                   may
                   also
                   resolve
                   this
                   that
                   we
                   have
                   now
                   before
                   us
                   ;
                   and
                   it
                   is
                   done
                   ,
                   by
                   diverting
                   in
                   the
                   first
                   place
                   from
                   the
                   great
                   River
                   a
                   good
                   big
                   measurable
                   Chanel
                   ,
                   as
                   is
                   taught
                   in
                   the
                   second
                   Probleme
                   ,
                   and
                   observing
                   the
                   abatement
                   of
                   the
                   River
                   ,
                   caused
                   by
                   the
                   diversion
                   of
                   the
                   Chanel
                   ;
                   and
                   finding
                   the
                   proportion
                   that
                   the
                   Water
                   of
                   the
                   Chanel
                   hath
                   to
                   that
                   of
                   the
                   River
                   ,
                   then
                   let
                   the
                   Water
                   of
                   the
                   Chanel
                   be
                   measured
                   by
                   the
                   second
                   Probleme
                   ,
                   and
                   work
                   as
                   above
                   ,
                   and
                   you
                   shall
                   have
                   your
                   desire
                   .
                
              
               
                 
                   CONSIDERATION
                   .
                   I.
                   
                
                 
                   ANd
                   although
                   it
                   seemeth
                   as
                   if
                   it
                   might
                   prove
                   difficult
                   ,
                   and
                   almost
                   impossible
                   to
                   make
                   use
                   of
                   the
                   Regulator
                   number
                   ,
                   if
                   one
                   be
                   about
                   to
                   measure
                   the
                   water
                   of
                   some
                   great
                   River
                   ,
                   and
                   consequently
                   would
                   be
                   impossible
                   ,
                   or
                   at
                   least
                   very
                   difficult
                   to
                   reduce
                   the
                   Theory
                   of
                   the
                   first
                   Probleme
                   into
                   practice
                   :
                   Yet
                   nevertheless
                   ,
                   I
                   could
                   say
                   that
                   such
                   great
                   conceits
                   of
                   measuring
                   the
                   water
                   of
                   a
                   great
                   River
                   ,
                   are
                   not
                   to
                   come
                   into
                   the
                   minds
                   of
                   any
                   but
                   great
                   Personages
                   ,
                   and
                   potent
                   Princes
                   ;
                   of
                   whom
                   it
                   is
                   expected
                   for
                   their
                   extraordinary
                   concerns
                   ,
                   that
                   they
                   will
                   make
                   these
                   kinde
                   of
                   enquiries
                   ;
                   as
                   if
                   here
                   in
                   Italy
                   it
                   should
                   be
                   of
                   the
                   Rivers
                   
                     Tyber
                     ,
                     Velino
                     ,
                     Chiana
                     ,
                     Arno
                     ,
                     Serchio
                     ,
                     Adice
                     ,
                  
                   in
                   which
                   it
                   seemeth
                   really
                   difficult
                   to
                   apply
                   the
                   Regulator
                   ,
                   to
                   finde
                   exactly
                   the
                   quick
                   height
                   of
                   the
                   River
                   :
                   But
                   because
                   in
                   such
                   like
                   cases
                   sometimes
                   it
                   would
                   turn
                   to
                   account
                   to
                   be
                   at
                   some
                   charge
                   ,
                   to
                   come
                   to
                   the
                   exact
                   and
                   true
                   knowledge
                   of
                   the
                   quantity
                   of
                   water
                   which
                   that
                   River
                   carrieth
                   ,
                   by
                   knowledge
                   whereof
                   ,
                   other
                   greater
                   disbursments
                   might
                   afterwards
                   be
                   avoided
                   ,
                   that
                   would
                   oft
                   times
                   be
                   made
                   in
                   vain
                   ;
                   and
                   prevent
                   the
                   disgusts
                   ,
                   which
                   sometimes
                   happen
                   amongst
                   Princes
                   :
                   Upon
                   this
                   ground
                   I
                   think
                   it
                   will
                   be
                   well
                   to
                   shew
                   also
                   the
                   way
                   how
                   to
                   make
                   use
                   of
                   the
                   Regulator
                   in
                   these
                   great
                   Rivers
                   ;
                   in
                   which
                   if
                   we
                   will
                   but
                   open
                   our
                   eyes
                   ,
                   we
                   shall
                   meet
                   with
                   good
                   ones
                   ,
                   and
                   those
                   made
                   without
                   great
                   cost
                   or
                   labour
                   ,
                   which
                   will
                   serve
                   our
                   turn
                   .
                
                 
                   For
                   upon
                   such
                   like
                   Rivers
                   there
                   are
                   Wears
                   ,
                   or
                   Lockes
                   made
                   ,
                   
                   to
                   cause
                   the
                   Waters
                   to
                   rise
                   ,
                   and
                   to
                   turn
                   them
                   for
                   the
                   service
                   of
                   Mills
                   ,
                   or
                   the
                   like
                   .
                   Now
                   in
                   these
                   Cases
                   it
                   is
                   sufficient
                   ,
                   that
                   one
                   erect
                   upon
                   the
                   two
                   extreames
                   of
                   the
                   Weare
                   two
                   Pilasters
                   either
                   of
                   Wood
                   or
                   Brick
                   ,
                   which
                   with
                   the
                   bottome
                   of
                   the
                   Weare
                   do
                   compose
                   our
                   Regulator
                   ,
                   wherewith
                   we
                   may
                   make
                   our
                   desired
                   operation
                   ,
                   yea
                   the
                   Chanel
                   it self
                   diverted
                   shall
                   serve
                   ,
                   without
                   making
                   any
                   other
                   diversion
                   or
                   union
                   .
                   And
                   in
                   brief
                   ,
                   if
                   the
                   businesses
                   be
                   but
                   managed
                   by
                   a
                   judicious
                   person
                   ,
                   there
                   may
                   wayes
                   and
                   helps
                   be
                   made
                   use
                   of
                   ,
                   according
                   to
                   occasion
                   ,
                   of
                   which
                   it
                   would
                   be
                   too
                   tedious
                   to
                   speak
                   ,
                   and
                   therefore
                   this
                   little
                   that
                   hath
                   been
                   hinted
                   shall
                   suffice
                   .
                
              
               
                 
                   CONSIDERATION
                   II.
                   
                
                 
                   FRom
                   what
                   hath
                   been
                   declared
                   ,
                   if
                   it
                   shall
                   be
                   well
                   understood
                   ,
                   may
                   be
                   deduced
                   many
                   benefits
                   and
                   conveniences
                   ,
                   not
                   onely
                   in
                   dividing
                   of
                   Running
                   Waters
                   for
                   infinite
                   uses
                   that
                   they
                   are
                   put
                   to
                   in
                   turning
                   of
                   Corne-Mills
                   ,
                   Paper-Mills
                   ,
                   Gins
                   ,
                   Powder-Mills
                   ,
                   Rice-Mills
                   ,
                   Iron-Mills
                   ,
                   Oil-Mills
                   ,
                   Sawing-Mills
                   ,
                   Mirtle-Mills
                   ,
                   Felling-Mills
                   ,
                   Fulling-Mills
                   ,
                   Silk-Mills
                   ,
                   and
                   such
                   other
                   Machines
                   ;
                   but
                   also
                   in
                   ordering
                   Navigable
                   Chanels
                   ,
                   diverting
                   Rivers
                   and
                   Chanels
                   of
                   Waters
                   ,
                   or
                   terminating
                   and
                   limiting
                   the
                   sizes
                   of
                   Pipes
                   for
                   Fountains
                   :
                   In
                   all
                   which
                   affairs
                   there
                   are
                   great
                   errours
                   com●●●ed
                   ,
                   to
                   the
                   losse
                   of
                   much
                   expence
                   ,
                   the
                   Chanels
                   and
                   Pipes
                   that
                   are
                   made
                   ,
                   sometimes
                   not
                   being
                   sufficient
                   to
                   carry
                   the
                   designed
                   Waters
                   ,
                   and
                   sometimes
                   they
                   are
                   made
                   bigger
                   than
                   is
                   necessary
                   ;
                   which
                   disorders
                   shall
                   be
                   avoided
                   ,
                   if
                   the
                   Engineer
                   be
                   advised
                   of
                   the
                   things
                   abovesaid
                   :
                   and
                   in
                   case
                   that
                   to
                   these
                   Notions
                   there
                   be
                   added
                   the
                   knowledge
                   of
                   Philosophy
                   and
                   Mathematicks
                   ,
                   agreeable
                   to
                   the
                   sublime
                   Discoveries
                   of
                   
                     Signore
                     Galilaeo
                  
                   ,
                   and
                   the
                   further
                   improvement
                   thereof
                   by
                   
                     Signore
                     Evangelista
                     Torricelli
                  
                   ,
                   Mathematician
                   to
                   the
                   Grand
                   
                     Duke
                     of
                     Tuscany
                  
                   ,
                   who
                   hath
                   subtilly
                   and
                   admirably
                   handled
                   this
                   whole
                   businesse
                   of
                   Motion
                   ,
                   one
                   shall
                   then
                   come
                   to
                   the
                   knowledge
                   of
                   particular
                   notions
                   of
                   great
                   curiosity
                   in
                   the
                   Theoricks
                   ,
                   and
                   of
                   extraordinary
                   benefit
                   in
                   the
                   Practicks
                   that
                   daily
                   occur
                   in
                   these
                   businesses
                   .
                
                 
                   And
                   to
                   shew
                   ,
                   in
                   effect
                   ,
                   of
                   what
                   utility
                   these
                   Notions
                   are
                   ,
                   I
                   have
                   thought
                   fit
                   to
                   insert
                   ,
                   in
                   this
                   place
                   ,
                   the
                   Considerations
                   by
                   me
                   made
                   upon
                   the
                   Lake
                   of
                   Venice
                   ,
                   and
                   to
                   represent
                   ,
                   at
                   large
                   ,
                   by
                   the
                   experience
                   of
                   the
                   last
                   year
                   1641.
                   the
                   most
                   Serene
                   Erizzo
                   ,
                   then
                   Duke
                   of
                   the
                   said
                   Republique
                   .
                   Being
                   therefore
                   at
                   Venice
                   ,
                   in
                   the
                   year
                   aforesaid
                   ,
                   I
                   was
                   requested
                   by
                   the
                   most
                   Illustrious
                   and
                   most
                   Excellent
                   
                     Signore
                     Giovanni
                     Basadonna
                  
                   ,
                   
                   a
                   Senatour
                   of
                   great
                   worth
                   and
                   merit
                   ,
                   that
                   I
                   would
                   ingenously
                   deliver
                   my
                   opinion
                   touching
                   the
                   state
                   of
                   the
                   Lake
                   of
                   Venice
                   ;
                   and
                   after
                   I
                   had
                   discoursed
                   with
                   his
                   Honour
                   several
                   times
                   ,
                   in
                   the
                   end
                   I
                   had
                   order
                   to
                   set
                   down
                   the
                   whole
                   businesse
                   in
                   writing
                   ,
                   who
                   having
                   afterwards
                   read
                   it
                   privately
                   ,
                   the
                   said
                   Signore
                   imparted
                   the
                   same
                   ,
                   with
                   like
                   privacy
                   ,
                   to
                   the
                   most
                   Serene
                   PRINCE
                   ,
                   and
                   I
                   received
                   order
                   to
                   represent
                   the
                   same
                   to
                   the
                   full
                   Colledge
                   ,
                   as
                   accordingly
                   I
                   did
                   in
                   the
                   Moneth
                   of
                   May
                   ,
                   the
                   same
                   year
                   ,
                   and
                   it
                   was
                   as
                   followeth
                   .
                
              
            
             
               
               
                 CONSIDERATIONS
                 Concerning
                 the
                 LAKE
                 OF
                 VENICE
                 .
                 BY
                 D.
                 BENEDETTO
                 CASTELLI
                 ,
                 Abbot
                 of
                 S.
                 Benedetto
                 Aloysio
                 ,
                 Mathematician
                 to
                 Pope
                 VRBAN
                 VIII
                 .
                 and
                 Professor
                 in
                 ROME
                 .
              
               
                 
                   CONSIDERATION
                   I.
                   
                
                 
                   THough
                   the
                   principal
                   cause
                   be
                   but
                   one
                   onely
                   ,
                   that
                   in
                   my
                   judgment
                   threatneth
                   irreparable
                   ruine
                   to
                   the
                   Lake
                   of
                   Venice
                   ,
                   in
                   the
                   present
                   state
                   in
                   which
                   it
                   now
                   stands
                   ;
                   Yet
                   neverthelesse
                   ,
                   I
                   think
                   that
                   two
                   Heads
                   may
                   be
                   considered
                   .
                   And
                   this
                   Consideration
                   may
                   peradventure
                   serve
                   us
                   for
                   to
                   facilitate
                   and
                   explain
                   the
                   opportune
                   remedies
                   ,
                   though
                   not
                   to
                   render
                   the
                   state
                   of
                   things
                   absolutely
                   unchangeable
                   and
                   eternal
                   :
                   an
                   enterprize
                   impossible
                   ,
                   and
                   especially
                   in
                   that
                   which
                   having
                   had
                   some
                   beginning
                   ,
                   ought
                   likewise
                   necessarily
                   to
                   have
                   its
                   end
                   ;
                   or
                   at
                   least
                   to
                   prevent
                   the
                   danger
                   for
                   many
                   hundreds
                   of
                   years
                   ;
                   and
                   possibly
                   it
                   may
                   ,
                   in
                   the
                   mean
                   time
                   ,
                   by
                   the
                   mutation
                   it self
                   be
                   brought
                   into
                   a
                   better
                   condition
                   .
                
                 
                   I
                   say
                   therefore
                   ,
                   that
                   the
                   present
                   disorder
                   may
                   be
                   considered
                   under
                   two
                   Heads
                   ;
                   One
                   is
                   the
                   very
                   notable
                   discovery
                   of
                   Land
                   that
                   is
                   observed
                   at
                   the
                   time
                   of
                   low
                   Water
                   ,
                   the
                   which
                   ,
                   besides
                   the
                   obstructing
                   of
                   Navigation
                   in
                   the
                   Lake
                   and
                   also
                   in
                   the
                   Chanels
                   ,
                   doth
                   likewise
                   threaten
                   another
                   mischief
                   and
                   disorder
                   
                   worthy
                   of
                   very
                   particular
                   consideration
                   ,
                   which
                   is
                   ,
                   That
                   the
                   Sun
                   drying
                   up
                   that
                   mudde
                   ,
                   especially
                   in
                   the
                   times
                   of
                   hot
                   Summers
                   ,
                   doth
                   raise
                   thence
                   the
                   putrified
                   and
                   pernicious
                   vapours
                   ,
                   fogs
                   ,
                   and
                   exhalations
                   that
                   infect
                   the
                   Air
                   ,
                   and
                   may
                   render
                   the
                   City
                   unhabitable
                   .
                
                 
                   The
                   second
                   Head
                   is
                   the
                   great
                   Stoppage
                   that
                   daily
                   is
                   growing
                   in
                   the
                   Ports
                   ,
                   especially
                   of
                   Venice
                   ,
                   at
                   Malamoco
                   ;
                   concerning
                   which
                   matters
                   I
                   will
                   hint
                   certain
                   general
                   points
                   ,
                   and
                   then
                   will
                   proceed
                   to
                   the
                   more
                   particular
                   and
                   important
                   affairs
                   .
                
                 
                   And
                   first
                   ,
                   I
                   say
                   ,
                   that
                   I
                   hold
                   it
                   altogether
                   impossible
                   to
                   effect
                   any
                   thing
                   ,
                   though
                   never
                   so
                   profitable
                   ,
                   which
                   doth
                   not
                   bring
                   with
                   it
                   some
                   mischief
                   ;
                   and
                   therefore
                   the
                   good
                   and
                   the
                   hurt
                   ought
                   to
                   be
                   very
                   well
                   weighed
                   ,
                   and
                   then
                   the
                   lesse
                   harmful
                   part
                   to
                   be
                   imbraced
                   .
                
                 
                   Secondly
                   ,
                   I
                   propose
                   to
                   consideration
                   ,
                   that
                   the
                   so
                   notable
                   discovery
                   of
                   Earth
                   &
                   Mud
                   ,
                   hath
                   not
                   been
                   long
                   observed
                   ,
                   as
                   I
                   understand
                   ,
                   from
                   old
                   persons
                   that
                   can
                   remember
                   passages
                   for
                   fifty
                   years
                   past
                   ;
                   which
                   thing
                   being
                   true
                   ,
                   as
                   to
                   me
                   it
                   seemeth
                   most
                   true
                   ,
                   it
                   should
                   appear
                   that
                   it
                   could
                   not
                   but
                   be
                   good
                   to
                   reduce
                   matters
                   to
                   that
                   passe
                   that
                   they
                   were
                   at
                   formerly
                   ,
                   (
                   laying
                   aside
                   all
                   affection
                   or
                   passion
                   that
                   self-flattering
                   minds
                   have
                   entertained
                   for
                   their
                   own
                   conceits
                   )
                   or
                   at
                   least
                   it
                   shall
                   be
                   necessary
                   speedily
                   to
                   consult
                   the
                   whole
                   .
                
                 
                   Thirdly
                   ,
                   I
                   hold
                   that
                   it
                   is
                   necessary
                   to
                   weigh
                   ,
                   whether
                   from
                   the
                   foresaid
                   discovery
                   of
                   Land
                   ,
                   it
                   followeth
                   ,
                   that
                   onely
                   the
                   Earth
                   riseth
                   ,
                   as
                   it
                   is
                   commonly
                   thought
                   by
                   all
                   ,
                   without
                   dispute
                   ;
                   or
                   whether
                   the
                   Waters
                   are
                   abated
                   and
                   faln
                   away
                   ;
                   or
                   else
                   whether
                   it
                   proceedeth
                   from
                   both
                   the
                   one
                   and
                   other
                   cause
                   .
                   And
                   here
                   it
                   would
                   be
                   seasonable
                   to
                   enquire
                   ,
                   what
                   share
                   the
                   said
                   causes
                   may
                   have
                   ,
                   each
                   considered
                   apart
                   in
                   the
                   foresaid
                   effect
                   .
                   For
                   ,
                   in
                   the
                   first
                   case
                   ,
                   if
                   the
                   Earth
                   have
                   been
                   raised
                   ,
                   it
                   would
                   be
                   necessary
                   to
                   consider
                   of
                   taking
                   it
                   down
                   ,
                   and
                   removing
                   it
                   :
                   But
                   if
                   the
                   Waters
                   have
                   failed
                   or
                   abated
                   ,
                   I
                   believe
                   that
                   it
                   would
                   be
                   extreamly
                   necessary
                   to
                   restore
                   and
                   raise
                   them
                   :
                   And
                   if
                   both
                   these
                   reasons
                   have
                   conspired
                   in
                   this
                   effect
                   ,
                   it
                   will
                   be
                   necessary
                   to
                   remedy
                   them
                   each
                   apart
                   .
                   And
                   I
                   do
                   ,
                   for
                   my
                   part
                   ,
                   think
                   ,
                   that
                   the
                   so
                   notable
                   appearance
                   of
                   Shelves
                   at
                   the
                   time
                   of
                   low
                   Water
                   ,
                   proceeds
                   principally
                   from
                   the
                   decrease
                   and
                   abatement
                   of
                   the
                   Waters
                   ,
                   which
                   may
                   confidently
                   be
                   affirmed
                   to
                   need
                   no
                   other
                   proof
                   ,
                   in
                   regard
                   that
                   the
                   Brent
                   hath
                   been
                   actually
                   diverted
                   which
                   did
                   formerly
                   discharge
                   its
                   Water
                   into
                   the
                   Lake
                   .
                
                 
                   As
                   to
                   the
                   other
                   point
                   of
                   the
                   great
                   Stoppage
                   of
                   Ports
                   ,
                   I
                   hold
                   ,
                   that
                   all
                   proceedeth
                   from
                   the
                   violence
                   of
                   the
                   Sea
                   ,
                   which
                   being
                   sometimes
                   disturbed
                   by
                   windes
                   ,
                   especially
                   at
                   the
                   time
                   of
                   the
                   waters
                   flowing
                   ,
                   doth
                   continually
                   raise
                   from
                   its
                   bottome
                   immense
                   
                   heaps
                   of
                   sand
                   ,
                   carrying
                   them
                   by
                   the
                   tide
                   ;
                   and
                   force
                   of
                   the
                   waves
                   into
                   the
                   Lake
                   ;
                   it
                   not
                   having
                   on
                   its
                   part
                   any
                   sttength
                   of
                   current
                   that
                   may
                   raise
                   and
                   carry
                   them
                   away
                   ,
                   they
                   sink
                   to
                   the
                   bottom
                   ,
                   and
                   so
                   they
                   choke
                   up
                   the
                   Ports
                   .
                   And
                   that
                   this
                   effect
                   happeneth
                   in
                   this
                   manner
                   ,
                   we
                   have
                   most
                   frequent
                   experiences
                   thereof
                   along
                   the
                   Sea-coasts
                   :
                   And
                   I
                   have
                   observed
                   in
                   Tuscany
                   on
                   the
                   Roman-shores
                   ,
                   and
                   in
                   the
                   Kingdom
                   of
                   of
                   Naples
                   ,
                   that
                   when
                   a
                   river
                   falleth
                   into
                   the
                   Sea
                   ,
                   there
                   is
                   alwaies
                   seen
                   in
                   the
                   Sea
                   it self
                   ,
                   at
                   the
                   place
                   of
                   the
                   rivers
                   out-let
                   ,
                   the
                   resemblance
                   ,
                   as
                   it
                   were
                   ,
                   of
                   an
                   half-Moon
                   ,
                   or
                   a
                   great
                   shelf
                   of
                   settled
                   sand
                   under
                   water
                   ,
                   much
                   higher
                   then
                   the
                   rest
                   of
                   the
                   shore
                   ,
                   and
                   it
                   is
                   called
                   in
                   
                     Tuscany
                     ,
                     il
                     Cavallo
                  
                   ;
                   and
                   here
                   in
                   
                     Venice
                     ,
                     lo
                     S●anto
                  
                   :
                   the
                   which
                   cometh
                   to
                   be
                   cut
                   by
                   the
                   current
                   of
                   the
                   river
                   ,
                   one
                   while
                   on
                   the
                   right
                   side
                   ;
                   another
                   while
                   on
                   the
                   left
                   ,
                   and
                   sometimes
                   in
                   the
                   midst
                   ,
                   according
                   as
                   the
                   Wind
                   sits
                   .
                   And
                   a
                   like
                   effect
                   I
                   have
                   observed
                   in
                   certain
                   little
                   Rillets
                   of
                   water
                   ,
                   along
                   the
                   Lake
                   of
                   Bolsena
                   ;
                   with
                   no
                   other
                   difference
                   ,
                   save
                   that
                   of
                   small
                   and
                   great
                   .
                
                 
                   Now
                   whoso
                   well
                   considereth
                   this
                   effect
                   ,
                   plainly
                   seeth
                   that
                   it
                   proceeds
                   from
                   no
                   other
                   ,
                   than
                   from
                   the
                   contrariety
                   of
                   the
                   stream
                   of
                   the
                   River
                   ,
                   to
                   the
                   impetus
                   of
                   the
                   Sea-waves
                   ;
                   seeing
                   that
                   great
                   abundance
                   of
                   sand
                   which
                   the
                   Sea
                   continually
                   throws
                   upon
                   the
                   shore
                   ,
                   cometh
                   to
                   be
                   driven
                   into
                   the
                   Sea
                   by
                   the
                   stream
                   of
                   the
                   river
                   ;
                   and
                   in
                   that
                   place
                   where
                   those
                   two
                   impediments
                   meet
                   with
                   equal
                   force
                   ,
                   the
                   sand
                   setleth
                   under
                   water
                   ,
                   and
                   thereupon
                   is
                   made
                   that
                   same
                   Shelf
                   for
                   Cavallo
                   ;
                   the
                   which
                   if
                   the
                   river
                   carry
                   water
                   ,
                   and
                   that
                   any
                   considerable
                   store
                   ,
                   it
                   shall
                   be
                   thereby
                   cut
                   and
                   broken
                   ;
                   one
                   while
                   in
                   one
                   place
                   ,
                   and
                   another
                   while
                   in
                   another
                   ;
                   as
                   hath
                   been
                   said
                   ,
                   according
                   as
                   the
                   Wind
                   blows
                   :
                   And
                   through
                   that
                   Chanel
                   it
                   is
                   that
                   Vessels
                   fall
                   down
                   into
                   the
                   Sea
                   ,
                   and
                   again
                   make
                   to
                   the
                   river
                   ,
                   as
                   into
                   a
                   Port.
                   But
                   if
                   the
                   Water
                   of
                   the
                   river
                   shall
                   not
                   be
                   continual
                   or
                   shall
                   be
                   weak
                   ,
                   in
                   that
                   case
                   the
                   force
                   of
                   the
                   Sea-Wind
                   shall
                   drive
                   such
                   a
                   quantity
                   of
                   sand
                   into
                   the
                   mouth
                   of
                   the
                   Port
                   ,
                   and
                   of
                   the
                   river
                   ,
                   as
                   shall
                   wholly
                   choak
                   it
                   up
                   .
                   And
                   hereupon
                   there
                   are
                   seen
                   along
                   the
                   Sea-side
                   ,
                   very
                   many
                   Lakes
                   and
                   Meers
                   ,
                   which
                   at
                   certain
                   times
                   of
                   the
                   year
                   abound
                   with
                   waters
                   ,
                   and
                   the
                   Lakes
                   bear
                   down
                   that
                   enclosure
                   ,
                   and
                   run
                   into
                   the
                   Sea.
                   
                
                 
                   Now
                   it
                   is
                   necessary
                   to
                   make
                   the
                   like
                   reflections
                   on
                   our
                   Ports
                   of
                   
                     Venice
                     ,
                     Malamocco
                     ,
                     Bondolo
                  
                   ,
                   and
                   Chiozza
                   ;
                   which
                   in
                   a
                   certain
                   sense
                   are
                   no
                   other
                   than
                   Creeks
                   ,
                   mouths
                   ,
                   and
                   openings
                   of
                   the
                   shore
                   that
                   parts
                   the
                   Lake
                   from
                   the
                   main
                   Sea
                   ;
                   and
                   therefore
                   I
                   hold
                   that
                   if
                   the
                   Waters
                   in
                   the
                   Lake
                   were
                   plentiful
                   ,
                   they
                   would
                   have
                   strength
                   to
                   scowr
                   the
                   mouths
                   of
                   the
                   Ports
                   thorowly
                   ,
                   &
                   with
                   great
                   force
                   ;
                   but
                   the
                   Water
                   in
                   the
                   Lake
                   failing
                   ,
                   the
                   Sea
                   will
                   without
                   any
                   opposal
                   ,
                   bring
                   such
                   a
                   drift
                   of
                   sand
                   into
                   the
                   Ports
                   ;
                   that
                   if
                   
                   it
                   doth
                   not
                   wholly
                   choke
                   them
                   up
                   ,
                   it
                   shall
                   render
                   them
                   at
                   least
                   unprofitable
                   ,
                   and
                   impossible
                   for
                   Barks
                   and
                   great
                   Vessels
                   .
                
                 
                   Many
                   other
                   considerations
                   might
                   be
                   propounded
                   concerning
                   these
                   two
                   heads
                   of
                   the
                   stoppage
                   of
                   the
                   Ports
                   ,
                   and
                   of
                   the
                   appearance
                   of
                   the
                   Ouze
                   and
                   Mud
                   in
                   the
                   Lakes
                   ,
                   but
                   so
                   much
                   shall
                   suffice
                   us
                   to
                   have
                   hinted
                   ,
                   to
                   make
                   way
                   for
                   discoursing
                   of
                   the
                   operations
                   about
                   the
                   oportune
                   remedies
                   .
                
                 
                   Yet
                   before
                   that
                   I
                   propound
                   my
                   opinion
                   ,
                   I
                   say
                   ,
                   That
                   I
                   know
                   very
                   well
                   that
                   my
                   proposal
                   ,
                   at
                   first
                   sight
                   ,
                   will
                   seem
                   absurd
                   and
                   inconvenient
                   ;
                   and
                   therefore
                   ,
                   as
                   such
                   ,
                   will
                   perhaps
                   be
                   rejected
                   by
                   the
                   most
                   :
                   and
                   so
                   much
                   the
                   rather
                   ,
                   for
                   that
                   it
                   will
                   prove
                   directly
                   contrary
                   to
                   what
                   hath
                   hitherto
                   been
                   ,
                   and
                   as
                   I
                   hear
                   ,
                   is
                   intended
                   to
                   be
                   done
                   :
                   And
                   I
                   am
                   not
                   so
                   wedded
                   to
                   my
                   opinions
                   ,
                   but
                   that
                   I
                   do
                   consider
                   what
                   others
                   may
                   judge
                   thereof
                   :
                   But
                   be
                   it
                   as
                   it
                   will
                   ,
                   I
                   am
                   obliged
                   to
                   speak
                   my
                   thoughts
                   freely
                   ,
                   and
                   that
                   being
                   done
                   ,
                   I
                   will
                   leave
                   it
                   to
                   wiser
                   men
                   than
                   my self
                   ;
                   when
                   they
                   shall
                   have
                   well
                   considered
                   my
                   reasons
                   ,
                   to
                   judge
                   and
                   deliberate
                   of
                   the
                   
                     quid
                     agendum
                  
                   :
                   And
                   if
                   the
                   sentence
                   shall
                   go
                   against
                   me
                   ,
                   I
                   appeal
                   to
                   the
                   most
                   equitable
                   and
                   inexorable
                   Tribunal
                   of
                   Nature
                   ,
                   who
                   not
                   caring
                   in
                   the
                   least
                   to
                   please
                   either
                   one
                   party
                   or
                   another
                   ,
                   will
                   be
                   alwaies
                   a
                   punctual
                   and
                   inviolable
                   executrix
                   of
                   her
                   eternal
                   Decrees
                   ,
                   against
                   which
                   neither
                   humane
                   deliberations
                   ,
                   nor
                   our
                   vain
                   desires
                   ,
                   shall
                   ever
                   have
                   power
                   to
                   rebell
                   .
                   I
                   added
                   by
                   word
                   of
                   mouth
                   that
                   which
                   followeth
                   .
                
                 
                   Though
                   your
                   Highness
                   interest
                   your self
                   in
                   this
                   Noble
                   Colledge
                   ,
                   and
                   cause
                   it
                   to
                   be
                   confirmed
                   in
                   the
                   *
                   Senate
                   by
                   universal
                   Vote
                   ,
                   that
                   the
                   Winds
                   do
                   not
                   blow
                   ,
                   that
                   the
                   Sea
                   doth
                   not
                   fluctuate
                   ,
                   that
                   the
                   Rivers
                   do
                   not
                   run
                   ;
                   yet
                   shall
                   the
                   Winds
                   be
                   alwaies
                   deaf
                   ,
                   the
                   Sea
                   shall
                   be
                   constant
                   in
                   its
                   inconstancy
                   ,
                   and
                   the
                   Rivers
                   most
                   obstinate
                   :
                   And
                   these
                   shall
                   be
                   my
                   Judges
                   ,
                   and
                   to
                   their
                   determination
                   I
                   refer
                   my self
                   .
                
                 
                   By
                   what
                   hath
                   been
                   said
                   ,
                   in
                   my
                   opinion
                   ,
                   that
                   is
                   made
                   very
                   clear
                   and
                   manifest
                   ,
                   which
                   in
                   the
                   beginning
                   of
                   this
                   discourse
                   I
                   glanced
                   at
                   ;
                   namely
                   ,
                   That
                   the
                   whole
                   disorder
                   ,
                   although
                   it
                   be
                   divided
                   into
                   two
                   heads
                   ,
                   into
                   the
                   discovery
                   of
                   the
                   Mud
                   ,
                   and
                   of
                   the
                   stoppage
                   Ports
                   ,
                   yet
                   nevertheless
                   ,
                   by
                   the
                   application
                   of
                   one
                   onely
                   remedy
                   ,
                   and
                   that
                   in
                   my
                   esteem
                   very
                   easie
                   ,
                   the
                   whole
                   shall
                   be
                   removed
                   :
                   And
                   this
                   it
                   is
                   ;
                   That
                   there
                   be
                   restored
                   into
                   the
                   Lake
                   as
                   much
                   Water
                   as
                   can
                   be
                   possible
                   ,
                   and
                   in
                   particular
                   from
                   the
                   upper
                   parts
                   of
                   Venice
                   ,
                   taking
                   care
                   that
                   the
                   Water
                   be
                   as
                   free
                   from
                   Mud
                   as
                   is
                   possible
                   .
                   And
                   that
                   this
                   is
                   the
                   true
                   and
                   real
                   remedy
                   of
                   the
                   precedent
                   disorders
                   ,
                   is
                   manifest
                   :
                   For
                   in
                   the
                   passage
                   that
                   this
                   Water
                   shall
                   make
                   thorow
                   the
                   Lakes
                   ,
                   it
                   shall
                   of
                   it self
                   by
                   degrees
                   clear
                   the
                   Chanels
                   in
                   sundry
                   parts
                   of
                   them
                   ,
                   according
                   to
                   the
                   currents
                   that
                   it
                   shall
                   successively
                   acquire
                   ,
                   and
                   in
                   this
                   manner
                   being
                   dispersed
                   
                   thorow
                   the
                   Lake
                   ,
                   it
                   shall
                   maintain
                   the
                   waters
                   in
                   the
                   same
                   ,
                   and
                   in
                   the
                   Chanels
                   much
                   higher
                   ,
                   as
                   I
                   shall
                   prove
                   hereafter
                   ;
                   a
                   thing
                   that
                   will
                   make
                   Navigation
                   commodious
                   ;
                   and
                   that
                   ,
                   which
                   moreover
                   is
                   of
                   great
                   moment
                   in
                   our
                   businesse
                   ;
                   those
                   Shelves
                   of
                   Mud
                   which
                   now
                   discover
                   themselves
                   at
                   the
                   time
                   of
                   Low-Waters
                   shall
                   be
                   alwayes
                   covered
                   ,
                   so
                   that
                   the
                   putrefaction
                   of
                   the
                   Air
                   shall
                   also
                   be
                   remedied
                   .
                
                 
                   And
                   lastly
                   ,
                   this
                   abundance
                   of
                   Water
                   being
                   alwayes
                   of
                   discharge
                   it self
                   into
                   the
                   Sea
                   by
                   the
                   Ports
                   ,
                   I
                   do
                   not
                   doubt
                   ,
                   but
                   that
                   their
                   bottomes
                   will
                   be
                   scoured
                   .
                   And
                   that
                   these
                   effects
                   must
                   follow
                   ,
                   Nature
                   her self
                   seemeth
                   to
                   perswade
                   ,
                   there
                   remaining
                   onely
                   one
                   great
                   doubt
                   ,
                   whether
                   that
                   abundance
                   of
                   Water
                   that
                   shall
                   be
                   brought
                   into
                   the
                   Lake
                   may
                   be
                   really
                   sufficient
                   to
                   make
                   the
                   Waters
                   rise
                   so
                   much
                   as
                   to
                   keep
                   the
                   Shelves
                   covered
                   ,
                   and
                   to
                   facilitate
                   Navigation
                   ,
                   which
                   ought
                   to
                   be
                   at
                   least
                   half
                   a
                   *
                   Brace
                   ,
                   or
                   thereabouts
                   .
                   And
                   indeed
                   it
                   seemeth
                   at
                   first
                   sight
                   to
                   be
                   impossible
                   ,
                   that
                   the
                   sole
                   Water
                   of
                   the
                   *
                   Brent
                   let
                   into
                   the
                   Lake
                   ,
                   and
                   dispersed
                   over
                   the
                   same
                   ,
                   can
                   occasion
                   so
                   notable
                   an
                   height
                   of
                   water
                   ;
                   and
                   the
                   more
                   to
                   confirm
                   the
                   difficulties
                   ,
                   one
                   might
                   say
                   ,
                   reducing
                   the
                   reason
                   to
                   calculation
                   ,
                   that
                   in
                   case
                   the
                   Brent
                   were
                   40.
                   
                   Braces
                   broad
                   ,
                   and
                   two
                   and
                   an
                   half
                   high
                   ,
                   and
                   the
                   breadth
                   of
                   the
                   Lake
                   were
                   20000.
                   
                   Braces
                   ,
                   it
                   would
                   seem
                   necessary
                   that
                   the
                   height
                   of
                   the
                   water
                   of
                   the
                   Brent
                   dilated
                   and
                   distended
                   thorow
                   the
                   Lake
                   would
                   be
                   but
                   onely
                   1
                   /
                   200
                   of
                   a
                   Brace
                   in
                   height
                   ,
                   which
                   is
                   imperceptible
                   ,
                   and
                   would
                   be
                   of
                   no
                   avail
                   to
                   our
                   purpose
                   ;
                   nay
                   more
                   ,
                   it
                   being
                   very
                   certain
                   that
                   the
                   brent
                   runneth
                   very
                   muddy
                   and
                   foul
                   ,
                   this
                   would
                   occasion
                   very
                   great
                   mischief
                   ,
                   filling
                   and
                   contracting
                   the
                   Lake
                   ,
                   and
                   for
                   that
                   reason
                   this
                   remedy
                   ought
                   ,
                   as
                   pernicious
                   ,
                   to
                   be
                   totally
                   excluded
                   and
                   condemned
                   .
                
                 
                   I
                   here
                   confesse
                   that
                   I
                   am
                   surprized
                   at
                   the
                   forme
                   of
                   the
                   Argument
                   ,
                   as
                   if
                   I
                   were
                   in
                   a
                   certain
                   manner
                   convinced
                   ,
                   that
                   I
                   dare
                   not
                   adventure
                   to
                   say
                   more
                   ,
                   or
                   open
                   my
                   mouth
                   in
                   this
                   matter
                   ;
                   but
                   the
                   strength
                   it self
                   of
                   the
                   Argument
                   ,
                   as
                   being
                   founded
                   upon
                   the
                   means
                   of
                   Gemoetrical
                   and
                   Arithmetical
                   Calculation
                   ,
                   hath
                   opened
                   me
                   the
                   way
                   to
                   discover
                   a
                   very
                   crafty
                   fraud
                   that
                   is
                   couched
                   in
                   the
                   same
                   Argument
                   ,
                   which
                   fraud
                   I
                   will
                   make
                   out
                   to
                   any
                   one
                   that
                   hath
                   but
                   any
                   insight
                   in
                   Geometry
                   and
                   Arithmetick
                   .
                   And
                   as
                   it
                   is
                   impossible
                   ,
                   that
                   such
                   an
                   argument
                   should
                   be
                   produced
                   by
                   any
                   but
                   such
                   as
                   have
                   tasted
                   of
                   these
                   ,
                   in
                   such
                   affairs
                   ,
                   most
                   profitable
                   ,
                   and
                   most
                   necessary
                   Sciences
                   ;
                   so
                   do
                   not
                   I
                   pretend
                   to
                   make
                   my self
                   understood
                   ,
                   save
                   onely
                   by
                   such
                   ,
                   to
                   whom
                   I
                   will
                   evince
                   so
                   clearly
                   ,
                   as
                   that
                   more
                   it
                   cannot
                   be
                   desired
                   ,
                   the
                   errour
                   and
                   fraud
                   wherein
                   those
                   Ancients
                   and
                   Moderns
                   have
                   been
                   ,
                   and
                   alwayes
                   are
                   intangled
                   ,
                   that
                   have
                   in
                   any
                   way
                   yet
                   handled
                   this
                   matter
                   of
                   considering
                   the
                   Measure
                   and
                   Quantity
                   of
                   the
                   Waters
                   that
                   move
                   .
                
                 
                 
                   And
                   so
                   great
                   is
                   the
                   esteem
                   that
                   I
                   have
                   for
                   that
                   which
                   I
                   am
                   now
                   about
                   to
                   say
                   touching
                   this
                   particular
                   ,
                   that
                   I
                   am
                   content
                   that
                   all
                   the
                   rest
                   of
                   my
                   Discourse
                   be
                   rejected
                   ;
                   provided
                   ,
                   that
                   that
                   be
                   perfectly
                   understood
                   ,
                   which
                   I
                   am
                   hereafter
                   to
                   propose
                   ,
                   I
                   holding
                   and
                   knowing
                   it
                   to
                   be
                   a
                   main
                   Principle
                   ,
                   upon
                   which
                   all
                   that
                   is
                   founded
                   that
                   can
                   be
                   said
                   either
                   well
                   or
                   handsomely
                   on
                   this
                   particular
                   .
                   The
                   other
                   Discourses
                   may
                   have
                   an
                   appearance
                   of
                   being
                   probable
                   ,
                   but
                   this
                   hits
                   the
                   mark
                   as
                   full
                   as
                   can
                   be
                   desired
                   ,
                   arriving
                   at
                   the
                   highest
                   degree
                   of
                   certainty
                   .
                
                 
                   I
                   have
                   ,
                   seventeen
                   years
                   since
                   ,
                   as
                   I
                   represented
                   to
                   the
                   most
                   Serene
                   Prince
                   ,
                   and
                   to
                   the
                   Right
                   Honourable
                   the
                   President
                   of
                   the
                   Lords
                   the
                   Commissioners
                   of
                   the
                   *
                   Sewers
                   ,
                   written
                   a
                   Treatise
                   of
                   the
                   Measure
                   of
                   the
                   waters
                   that
                   move
                   ,
                   in
                   which
                   I
                   Geometrically
                   demonstrate
                   and
                   declare
                   this
                   businesse
                   ,
                   and
                   they
                   who
                   shall
                   have
                   well
                   understood
                   the
                   ground
                   of
                   my
                   Discourse
                   ,
                   will
                   rest
                   fully
                   satisfied
                   with
                   that
                   which
                   I
                   am
                   now
                   about
                   to
                   propose
                   :
                   But
                   that
                   all
                   may
                   become
                   rhe
                   more
                   easie
                   ,
                   I
                   will
                   more
                   briefly
                   explicate
                   and
                   declare
                   so
                   much
                   thereof
                   as
                   I
                   have
                   demonstrated
                   in
                   the
                   Discourse
                   ,
                   which
                   will
                   suffice
                   for
                   our
                   purpose
                   :
                   And
                   if
                   that
                   should
                   not
                   be
                   enough
                   ,
                   we
                   have
                   alwayes
                   the
                   experiment
                   of
                   a
                   very
                   easie
                   and
                   cheap
                   way
                   to
                   clear
                   up
                   the
                   whole
                   businesse
                   .
                   And
                   moreover
                   I
                   will
                   take
                   the
                   boldnesse
                   to
                   affirm
                   ,
                   that
                   in
                   case
                   there
                   should
                   not
                   for
                   the
                   present
                   any
                   deliberation
                   be
                   made
                   concerning
                   this
                   affair
                   ,
                   according
                   to
                   my
                   opinion
                   ;
                   yet
                   neverthelesse
                   it
                   will
                   be
                   ,
                   at
                   some
                   time
                   or
                   other
                   ;
                   or
                   if
                   it
                   be
                   not
                   ,
                   things
                   will
                   grow
                   worse
                   and
                   worse
                   .
                
                 
                   For
                   more
                   clear
                   understanding
                   ,
                   therefore
                   ,
                   it
                   ought
                   to
                   be
                   known
                   ,
                   that
                   it
                   being
                   required
                   ,
                   as
                   it
                   is
                   generally
                   used
                   ,
                   to
                   measure
                   the
                   waters
                   of
                   a
                   River
                   ,
                   its
                   breadth
                   and
                   its
                   depth
                   is
                   taken
                   ,
                   and
                   these
                   two
                   dimensions
                   being
                   multiplied
                   together
                   ,
                   the
                   product
                   is
                   affirmed
                   to
                   be
                   the
                   quantity
                   of
                   that
                   River
                   :
                   As
                   for
                   example
                   ,
                   if
                   a
                   River
                   shall
                   be
                   100.
                   feet
                   broad
                   ,
                   and
                   20.
                   feet
                   high
                   ,
                   it
                   will
                   be
                   said
                   ,
                   that
                   that
                   River
                   is
                   2000
                   feet
                   of
                   Water
                   ,
                   and
                   so
                   if
                   a
                   Ditch
                   shall
                   be
                   15.
                   feet
                   broad
                   ,
                   and
                   5.
                   feet
                   high
                   ,
                   this
                   same
                   Ditch
                   will
                   be
                   affirmed
                   to
                   be
                   75.
                   feet
                   of
                   Water
                   :
                   And
                   this
                   manner
                   of
                   measuring
                   Running
                   Water
                   hath
                   been
                   used
                   by
                   the
                   Ancients
                   ,
                   and
                   by
                   Moderns
                   ,
                   with
                   no
                   other
                   difference
                   ,
                   save
                   onely
                   that
                   some
                   have
                   made
                   use
                   of
                   the
                   Foot
                   ,
                   others
                   of
                   the
                   Palme
                   ,
                   others
                   of
                   the
                   Brace
                   ,
                   and
                   others
                   of
                   other
                   measures
                   .
                
                 
                   Now
                   because
                   that
                   in
                   observing
                   these
                   Waters
                   that
                   move
                   ,
                   I
                   frequently
                   found
                   ,
                   that
                   the
                   same
                   Water
                   of
                   the
                   same
                   River
                   was
                   in
                   some
                   sites
                   of
                   its
                   Chanel
                   pretty
                   big
                   ,
                   and
                   in
                   others
                   much
                   lesse
                   ,
                   not
                   arriving
                   in
                   some
                   places
                   to
                   the
                   twentieth
                   ,
                   nor
                   to
                   the
                   hundreth
                   part
                   of
                   that
                   which
                   it
                   is
                   seen
                   to
                   be
                   in
                   other
                   places
                   ;
                   therefore
                   this
                   vulgar
                   way
                   of
                   measuring
                   the
                   Waters
                   that
                   move
                   ,
                   for
                   that
                   they
                   did
                   
                   not
                   give
                   me
                   a
                   certain
                   and
                   stable
                   measure
                   and
                   quantity
                   of
                   Water
                   ,
                   began
                   deservedly
                   to
                   be
                   suspected
                   by
                   me
                   ,
                   as
                   difficult
                   and
                   defective
                   ,
                   being
                   alwayes
                   various
                   ,
                   and
                   the
                   measure
                   ,
                   on
                   the
                   contrary
                   ,
                   being
                   to
                   be
                   alwayes
                   determinate
                   ,
                   and
                   the
                   same
                   ;
                   it
                   is
                   therefore
                   written
                   ,
                   that
                   
                     Pondus
                     &
                     Pondus
                     ,
                     Mensura
                     &
                     Mensura
                     ,
                     utrumque
                     abominabile
                     est
                     apud
                     Deum
                     ,
                  
                   Exod.
                   I
                   considered
                   that
                   in
                   the
                   Territory
                   of
                   Brescia
                   ,
                   my
                   native
                   Countrey
                   ,
                   and
                   in
                   other
                   places
                   ,
                   where
                   Waters
                   are
                   divided
                   to
                   overflow
                   the
                   Grounds
                   ,
                   by
                   the
                   like
                   way
                   of
                   measuring
                   them
                   ,
                   there
                   were
                   committed
                   grievous
                   and
                   most
                   important
                   errours
                   ,
                   to
                   the
                   great
                   prejudice
                   of
                   the
                   Publique
                   and
                   of
                   Private
                   persons
                   ,
                   neither
                   they
                   that
                   sell
                   ,
                   nor
                   they
                   that
                   buy
                   understanding
                   the
                   true
                   quantity
                   of
                   that
                   which
                   is
                   sold
                   and
                   bought
                   :
                   In
                   regard
                   that
                   the
                   same
                   square
                   measure
                   ,
                   as
                   is
                   accustomed
                   in
                   those
                   parts
                   ,
                   assigned
                   one
                   particular
                   person
                   ,
                   carried
                   to
                   sometimes
                   above
                   twice
                   or
                   thrice
                   as
                   much
                   water
                   ,
                   as
                   did
                   the
                   same
                   square
                   measure
                   assigned
                   to
                   another
                   .
                   Which
                   thing
                   proveth
                   to
                   be
                   the
                   same
                   inconvenience
                   ,
                   as
                   if
                   the
                   measure
                   wherewith
                   Wine
                   and
                   Oil
                   is
                   bought
                   and
                   sold
                   ,
                   should
                   hold
                   twice
                   or
                   thrice
                   as
                   much
                   Wine
                   or
                   Oil
                   at
                   one
                   time
                   as
                   at
                   another
                   .
                   Now
                   this
                   Consideration
                   invited
                   my
                   minde
                   and
                   curiosity
                   to
                   the
                   finding
                   out
                   of
                   the
                   true
                   measure
                   of
                   Running
                   Waters
                   .
                   And
                   in
                   the
                   end
                   ,
                   by
                   occasion
                   of
                   a
                   most
                   important
                   businesse
                   that
                   I
                   was
                   imployed
                   in
                   some
                   years
                   since
                   ,
                   with
                   great
                   intensenesse
                   of
                   minde
                   ,
                   and
                   with
                   the
                   sure
                   direction
                   of
                   Geometry
                   ,
                   I
                   have
                   discovered
                   the
                   mistake
                   ,
                   which
                   was
                   ,
                   that
                   we
                   being
                   upon
                   the
                   businesse
                   of
                   taking
                   the
                   measure
                   of
                   the
                   Waters
                   that
                   move
                   ,
                   do
                   make
                   use
                   of
                   two
                   dimensions
                   onely
                   ,
                   namely
                   ,
                   breadth
                   and
                   depth
                   ,
                   keeping
                   no
                   account
                   of
                   the
                   length
                   .
                   And
                   yet
                   the
                   Water
                   being
                   ,
                   though
                   running
                   ,
                   a
                   Body
                   ,
                   it
                   is
                   necessary
                   in
                   forming
                   a
                   conceit
                   of
                   its
                   quantity
                   ,
                   in
                   relation
                   to
                   another
                   ,
                   to
                   keep
                   account
                   of
                   all
                   the
                   three
                   Dimensions
                   ,
                   that
                   is
                   of
                   length
                   ,
                   breadth
                   ,
                   and
                   depth
                   .
                
                 
                   Here
                   an
                   objection
                   hath
                   been
                   put
                   to
                   me
                   ,
                   in
                   behalf
                   of
                   the
                   ordinary
                   way
                   of
                   measuring
                   Running
                   Waters
                   ,
                   in
                   opposition
                   to
                   what
                   I
                   have
                   above
                   considered
                   and
                   proposed
                   :
                   and
                   I
                   was
                   told
                   ,
                   It
                   s
                   true
                   ,
                   that
                   in
                   measuring
                   a
                   Body
                   that
                   stands
                   still
                   ,
                   one
                   ought
                   to
                   take
                   all
                   the
                   three
                   Dimensions
                   ;
                   but
                   in
                   measuring
                   a
                   Body
                   that
                   continually
                   moveth
                   ,
                   as
                   the
                   Water
                   ,
                   the
                   case
                   is
                   not
                   the
                   same
                   :
                   For
                   the
                   length
                   is
                   not
                   to
                   be
                   had
                   ,
                   the
                   length
                   of
                   the
                   water
                   that
                   moveth
                   being
                   infinite
                   ,
                   as
                   never
                   finishing
                   its
                   running
                   ;
                   and
                   consequently
                   is
                   incomprehensible
                   by
                   humane
                   understanding
                   ,
                   and
                   therefore
                   with
                   reason
                   ,
                   nay
                   upon
                   necessity
                   it
                   cometh
                   to
                   be
                   omitted
                   .
                
                 
                   In
                   answer
                   to
                   this
                   ,
                   I
                   say
                   ,
                   that
                   in
                   the
                   abovesaid
                   Discourse
                   ,
                   two
                   things
                   are
                   to
                   be
                   considered
                   distinctly
                   ;
                   First
                   ,
                   whether
                   it
                   be
                   possible
                   to
                   frame
                   any
                   conceit
                   of
                   the
                   quantity
                   of
                   the
                   Body
                   of
                   the
                   Water
                   with
                   two
                   Dimensions
                   onely
                   .
                   And
                   secondly
                   ,
                   whether
                   this
                   length
                   be
                   to
                   be
                   found
                   .
                   As
                   to
                   the
                   first
                   ,
                   I
                   am
                   very
                   certain
                   that
                   no
                   man
                   ,
                   let
                   
                   him
                   be
                   never
                   so
                   great
                   a
                   Wit
                   ,
                   can
                   never
                   promise
                   to
                   frame
                   a
                   conceit
                   of
                   the
                   quantity
                   of
                   the
                   Body
                   of
                   Water
                   ,
                   without
                   the
                   third
                   Dimension
                   of
                   length
                   :
                   and
                   hereupon
                   I
                   return
                   to
                   affirm
                   ,
                   that
                   the
                   vulgar
                   Rule
                   of
                   measuring
                   Running
                   water
                   is
                   vain
                   and
                   erroneous
                   .
                   This
                   point
                   being
                   agreed
                   on
                   ,
                   I
                   come
                   to
                   the
                   second
                   ,
                   which
                   is
                   ,
                   Whether
                   the
                   third
                   Dimension
                   of
                   length
                   may
                   be
                   measured
                   .
                   And
                   I
                   say
                   ,
                   that
                   if
                   one
                   would
                   know
                   the
                   whole
                   length
                   of
                   the
                   water
                   of
                   a
                   Fountain
                   or
                   River
                   ,
                   thereby
                   to
                   come
                   to
                   know
                   the
                   quantity
                   of
                   all
                   the
                   Water
                   ,
                   it
                   would
                   prove
                   an
                   impossible
                   enterprize
                   ,
                   nay
                   the
                   knowing
                   of
                   it
                   would
                   not
                   be
                   useful
                   .
                   But
                   if
                   one
                   would
                   know
                   how
                   much
                   water
                   a
                   Fountain
                   ,
                   or
                   a
                   River
                   carrieth
                   in
                   a
                   determinate
                   time
                   of
                   an
                   hour
                   ,
                   of
                   a
                   day
                   ,
                   or
                   of
                   a
                   moneth
                   ,
                   &c.
                   
                   I
                   say
                   ,
                   that
                   it
                   is
                   a
                   very
                   possible
                   and
                   profitable
                   enquiry
                   ,
                   by
                   reason
                   of
                   the
                   innumerable
                   benefits
                   that
                   may
                   be
                   derived
                   thence
                   ,
                   it
                   much
                   importing
                   to
                   know
                   how
                   much
                   Water
                   a
                   Chanel
                   carrieth
                   in
                   a
                   time
                   given
                   ;
                   and
                   I
                   have
                   demonstrated
                   the
                   same
                   above
                   in
                   the
                   beginning
                   of
                   this
                   Book
                   ;
                   and
                   of
                   this
                   we
                   stand
                   in
                   need
                   in
                   the
                   businesse
                   of
                   the
                   Lake
                   ,
                   that
                   so
                   we
                   may
                   be
                   able
                   to
                   determine
                   how
                   much
                   shall
                   be
                   the
                   height
                   of
                   the
                   Brent
                   ,
                   when
                   it
                   is
                   spread
                   all
                   over
                   the
                   Lake
                   :
                   For
                   the
                   three
                   dimensions
                   of
                   a
                   Body
                   being
                   given
                   ,
                   the
                   Body
                   is
                   known
                   ;
                   and
                   the
                   quantity
                   of
                   a
                   Body
                   being
                   given
                   ,
                   if
                   you
                   have
                   but
                   two
                   dimensions
                   ,
                   the
                   third
                   shall
                   be
                   known
                   .
                   And
                   thus
                   diving
                   farther
                   and
                   farther
                   into
                   this
                   Consideration
                   ,
                   I
                   found
                   that
                   the
                   Velocity
                   of
                   the
                   course
                   of
                   the
                   water
                   may
                   be
                   an
                   hundred
                   times
                   greater
                   or
                   lesser
                   in
                   one
                   part
                   of
                   its
                   Chanel
                   than
                   in
                   another
                   .
                   And
                   therefore
                   although
                   there
                   should
                   be
                   two
                   mouths
                   of
                   Waters
                   equal
                   in
                   bignesse
                   ;
                   yet
                   nevertheless
                   it
                   might
                   come
                   to
                   passe
                   ,
                   that
                   one
                   might
                   discharge
                   an
                   hundred
                   or
                   a
                   thousand-times
                   more
                   water
                   than
                   another
                   :
                   and
                   this
                   would
                   be
                   ,
                   if
                   the
                   water
                   in
                   one
                   of
                   the
                   mouths
                   should
                   run
                   with
                   an
                   hundred
                   or
                   a
                   thousand
                   times
                   greater
                   velocity
                   ,
                   than
                   the
                   other
                   ;
                   for
                   that
                   it
                   would
                   be
                   the
                   same
                   as
                   to
                   say
                   ,
                   that
                   the
                   swifter
                   was
                   an
                   hundred
                   or
                   a
                   thousand
                   times
                   longer
                   ,
                   than
                   the
                   slower
                   :
                   and
                   in
                   this
                   manner
                   I
                   discovered
                   that
                   to
                   keep
                   account
                   of
                   the
                   velocity
                   ,
                   was
                   the
                   keeping
                   account
                   of
                   the
                   Length
                   .
                
                 
                   And
                   therefore
                   it
                   is
                   manifest
                   ,
                   that
                   when
                   two
                   Mouths
                   discharge
                   the
                   same
                   quantity
                   of
                   Water
                   in
                   an
                   equal
                   velocity
                   ,
                   it
                   is
                   necessary
                   that
                   the
                   less
                   swift
                   Mouth
                   be
                   so
                   much
                   bigger
                   than
                   the
                   more
                   swift
                   ;
                   as
                   the
                   more
                   swift
                   exceedeth
                   in
                   velocity
                   the
                   less
                   swift
                   ;
                   as
                   for
                   example
                   .
                
                 
                   In
                   case
                   two
                   Rivers
                   should
                   carry
                   equal
                   quantity
                   of
                   water
                   in
                   equal
                   times
                   ,
                   but
                   that
                   one
                   of
                   them
                   should
                   be
                   four
                   times
                   more
                   swift
                   than
                   the
                   other
                   ,
                   the
                   more
                   slow
                   should
                   of
                   necessity
                   be
                   four
                   times
                   more
                   large
                   .
                   And
                   because
                   the
                   same
                   River
                   in
                   any
                   part
                   thereof
                   alwaies
                   dischargeth
                   the
                   same
                   quantity
                   of
                   Water
                   in
                   equal
                   times
                   (
                   as
                   is
                   demonstrated
                   in
                   the
                   first
                   Proposition
                   of
                   the
                   first
                   
                   Book
                   *
                   of
                   the
                   measure
                   of
                   Running
                   Waters
                   ;
                   )
                   but
                   yet
                   doth
                   not
                   run
                   thorowout
                   with
                   the
                   same
                   velocity
                   :
                   Hence
                   it
                   is
                   ,
                   that
                   the
                   vulgar
                   measures
                   of
                   the
                   said
                   River
                   ,
                   in
                   divers
                   parts
                   of
                   its
                   Chanel
                   ,
                   are
                   alwaies
                   divers
                   ;
                   insomuch
                   ,
                   that
                   if
                   a
                   River
                   passing
                   through
                   its
                   chanel
                   had
                   such
                   velocity
                   ,
                   that
                   it
                   ran
                   100
                   Braces
                   in
                   the
                   1
                   /
                   60
                   of
                   an
                   hour-and
                   afterwards
                   the
                   said
                   River
                   should
                   be
                   reduced
                   to
                   so
                   much
                   tardi
                   ,
                   ty
                   of
                   motion
                   ,
                   as
                   that
                   in
                   the
                   same
                   time
                   it
                   should
                   not
                   run
                   more
                   than
                   one
                   Brace
                   ,
                   it
                   would
                   be
                   necessary
                   that
                   that
                   same
                   River
                   should
                   become
                   100.
                   times
                   bigger
                   in
                   that
                   place
                   where
                   it
                   was
                   retarded
                   ;
                   I
                   mean
                   ,
                   100.
                   times
                   bigger
                   than
                   it
                   was
                   in
                   the
                   place
                   where
                   it
                   was
                   swifter
                   .
                   And
                   let
                   it
                   be
                   kept
                   well
                   in
                   mind
                   ,
                   that
                   this
                   point
                   rightly
                   understood
                   ,
                   will
                   clear
                   the
                   understanding
                   to
                   discover
                   very
                   many
                   accidents
                   worthy
                   to
                   be
                   known
                   .
                   But
                   for
                   this
                   time
                   let
                   it
                   suffice
                   ,
                   that
                   we
                   have
                   onely
                   declared
                   that
                   which
                   makes
                   for
                   our
                   purpose
                   ,
                   referring
                   apprehensive
                   and
                   studious
                   Wits
                   to
                   the
                   perusal
                   of
                   my
                   aforenamed
                   Treatise
                   ;
                   for
                   therein
                   he
                   shall
                   finde
                   profit
                   and
                   delight
                   both
                   together
                   .
                
                 
                   Now
                   applying
                   all
                   to
                   our
                   principal
                   intent
                   ,
                   I
                   say
                   ,
                   That
                   by
                   what
                   hath
                   been
                   declared
                   it
                   is
                   manifest
                   ,
                   that
                   if
                   the
                   Brent
                   were
                   48.
                   
                   Braces
                   broad
                   ,
                   and
                   2
                   ½
                   high
                   ,
                   in
                   some
                   one
                   part
                   of
                   its
                   Chanel
                   ,
                   that
                   afterwards
                   the
                   same
                   Water
                   of
                   the
                   Brent
                   falling
                   into
                   the
                   Lake
                   ,
                   and
                   passing
                   thorow
                   the
                   same
                   to
                   the
                   Sea
                   ,
                   it
                   should
                   lose
                   so
                   much
                   of
                   its
                   velocity
                   ,
                   that
                   it
                   should
                   run
                   but
                   one
                   Brace
                   ,
                   in
                   the
                   time
                   wherein
                   whilst
                   it
                   was
                   in
                   its
                   Chanel
                   at
                   the
                   place
                   aforesaid
                   ,
                   it
                   ran
                   100.
                   
                   Braces
                   .
                   It
                   would
                   be
                   absolutely
                   necessary
                   ,
                   that
                   increasing
                   in
                   measure
                   ,
                   it
                   should
                   become
                   an
                   hundred
                   times
                   *
                   thicker
                   ;
                   and
                   therefore
                   if
                   we
                   should
                   suppose
                   that
                   the
                   Lake
                   were
                   20000.
                   
                   Braces
                   ,
                   the
                   Brent
                   that
                   already
                   hath
                   been
                   supposed
                   in
                   its
                   Chanel
                   100.
                   
                   Braces
                   ,
                   being
                   brought
                   into
                   the
                   Lake
                   ,
                   should
                   be
                   100.
                   times
                   100.
                   
                   Brates
                   ;
                   that
                   is
                   ,
                   shall
                   be
                   10000.
                   
                   Braces
                   in
                   thickness
                   ,
                   and
                   consequently
                   shall
                   be
                   in
                   height
                   half
                   a
                   Brace
                   ;
                   that
                   is
                   ,
                   100
                   /
                   200
                   of
                   a
                   Brace
                   ,
                   and
                   not
                   1
                   /
                   200
                   of
                   a
                   Brace
                   ,
                   as
                   was
                   concluded
                   in
                   the
                   Argument
                   .
                
                 
                   Now
                   one
                   may
                   see
                   into
                   what
                   a
                   gross
                   errour
                   of
                   99.
                   in
                   100.
                   one
                   may
                   fall
                   through
                   the
                   not
                   well
                   understanding
                   the
                   true
                   quantity
                   of
                   Running
                   Water
                   ,
                   which
                   being
                   well
                   understood
                   ,
                   doth
                   open
                   a
                   direct
                   way
                   to
                   our
                   judging
                   aright
                   in
                   this
                   most
                   considerable
                   affair
                   .
                
                 
                   And
                   therefore
                   admitting
                   that
                   wich
                   hath
                   been
                   demonstrated
                   ,
                   I
                   say
                   ,
                   that
                   I
                   would
                   (
                   if
                   it
                   did
                   concern
                   me
                   )
                   greatly
                   encline
                   to
                   consult
                   upon
                   the
                   returning
                   of
                   the
                   Brent
                   again
                   into
                   the
                   Lake
                   :
                   For
                   it
                   being
                   most
                   evident
                   ,
                   that
                   the
                   Brent
                   in
                   the
                   Chanel
                   of
                   its
                   mouth
                   ,
                   is
                   much
                   swifter
                   than
                   the
                   Brent
                   being
                   brought
                   into
                   the
                   Lake
                   ,
                   it
                   will
                   certainly
                   follow
                   thereupon
                   ,
                   that
                   the
                   thickness
                   of
                   the
                   Water
                   of
                   Brent
                   in
                   the
                   Lake
                   ,
                   shall
                   be
                   so
                   much
                   greater
                   than
                   that
                   of
                   Brent
                   in
                   Brent
                   ,
                   by
                   how
                   much
                   the
                   Bront
                   in
                   Brent
                   is
                   swifter
                   than
                   thh
                   Brent
                   in
                   the
                   Lake
                   .
                
                 
                 
                   1.
                   
                   From
                   which
                   operation
                   doth
                   follow
                   in
                   the
                   first
                   place
                   ,
                   that
                   the
                   Lake
                   being
                   filled
                   and
                   increased
                   by
                   these
                   Waters
                   ,
                   shall
                   be
                   more
                   Navigable
                   ,
                   and
                   passible
                   ,
                   than
                   at
                   present
                   we
                   see
                   it
                   to
                   be
                   .
                
                 
                   2.
                   
                   By
                   the
                   current
                   of
                   these
                   Waters
                   ,
                   the
                   Chanels
                   will
                   be
                   scoured
                   ,
                   and
                   will
                   be
                   kept
                   clean
                   from
                   time
                   to
                   time
                   .
                
                 
                   3.
                   
                   There
                   will
                   not
                   appear
                   at
                   the
                   times
                   of
                   low-waters
                   so
                   many
                   Shelves
                   ,
                   and
                   such
                   heaps
                   of
                   Mud
                   ,
                   as
                   do
                   now
                   appear
                   .
                
                 
                   4.
                   
                   The
                   Ayr
                   will
                   become
                   more
                   wholesom
                   ,
                   for
                   that
                   it
                   shall
                   not
                   be
                   so
                   infected
                   by
                   putrid
                   vapours
                   exhaled
                   by
                   the
                   Sun
                   ,
                   so
                   long
                   as
                   the
                   Miery
                   Ouze
                   shall
                   be
                   covered
                   by
                   the
                   Waters
                   .
                
                 
                   5.
                   
                   Lastly
                   ,
                   in
                   the
                   current
                   of
                   these
                   advantagious
                   Waters
                   ,
                   ,
                   which
                   must
                   issue
                   out
                   of
                   the
                   Lake
                   into
                   the
                   Sea
                   ,
                   besides
                   those
                   of
                   the
                   Tyde
                   ,
                   the
                   Ports
                   will
                   be
                   kept
                   scoured
                   ,
                   and
                   clear
                   :
                   And
                   this
                   is
                   as
                   much
                   as
                   I
                   shall
                   offer
                   for
                   the
                   present
                   ,
                   touching
                   this
                   weighty
                   business
                   ;
                   alwaies
                   submitting
                   my self
                   to
                   sounder
                   judgements
                   .
                
                 
                   Of
                   the
                   above-said
                   Writing
                   I
                   presented
                   a
                   Copy
                   at
                   Venice
                   ,
                   at
                   a
                   full
                   Colledge
                   ,
                   in
                   which
                   I
                   read
                   it
                   all
                   ,
                   and
                   it
                   was
                   hearkned
                   to
                   with
                   very
                   great
                   attention
                   ;
                   and
                   at
                   last
                   I
                   presented
                   it
                   to
                   the
                   Duke
                   ,
                   and
                   left
                   some
                   Copies
                   thereof
                   with
                   sundry
                   Senators
                   ,
                   and
                   went
                   my
                   way
                   ,
                   promising
                   with
                   all
                   intenseness
                   to
                   apply
                   my
                   pains
                   with
                   reiterated
                   studies
                   in
                   the
                   publick
                   service
                   ;
                   and
                   if
                   any
                   other
                   things
                   should
                   come
                   into
                   my
                   minde
                   ,
                   I
                   promised
                   to
                   declare
                   them
                   sincerely
                   ,
                   and
                   so
                   took
                   leave
                   of
                   
                     His
                     serenity
                  
                   ,
                   and
                   that
                   Noble
                   Council
                   .
                   When
                   I
                   was
                   returned
                   to
                   Rome
                   ,
                   this
                   business
                   night
                   and
                   day
                   continually
                   running
                   in
                   my
                   mind
                   ,
                   I
                   hapned
                   to
                   think
                   of
                   another
                   admirable
                   and
                   most
                   important
                   conceit
                   ,
                   which
                   with
                   effectual
                   reasons
                   ,
                   confirmed
                   by
                   exact
                   operations
                   ,
                   I
                   with
                   the
                   Divine
                   assistance
                   ,
                   made
                   clear
                   and
                   manifest
                   ;
                   and
                   though
                   the
                   thing
                   at
                   first
                   sight
                   seemed
                   to
                   me
                   a
                   most
                   extravagant
                   Paradox
                   ,
                   yet
                   notwithstanding
                   ,
                   having
                   satisfied
                   my self
                   of
                   the
                   whole
                   business
                   ,
                   I
                   sent
                   it
                   in
                   writing
                   to
                   the
                   most
                   Illustrious
                   and
                   most
                   Noble
                   
                     Signore
                     Gio.
                     Basadonna
                  
                   ;
                   who
                   after
                   he
                   had
                   well
                   considered
                   my
                   Paper
                   ,
                   carried
                   it
                   to
                   the
                   Council
                   ;
                   and
                   after
                   that
                   those
                   Lords
                   had
                   for
                   many
                   months
                   maturely
                   considered
                   thereon
                   ,
                   they
                   in
                   the
                   end
                   resolved
                   to
                   suspend
                   the
                   execution
                   of
                   the
                   diversion
                   which
                   they
                   had
                   before
                   consulted
                   to
                   make
                   of
                   the
                   River
                   Sile
                   ,
                   and
                   of
                   four
                   other
                   Rivers
                   ,
                   which
                   also
                   fall
                   into
                   the
                   Lake
                   ;
                   a
                   thing
                   by
                   me
                   blamed
                   in
                   this
                   second
                   Paper
                   ,
                   as
                   most
                   prejudicial
                   ,
                   and
                   harmful
                   .
                   The
                   writing
                   spake
                   as
                   followeth
                   .
                
              
               
                 
                 
                   CONSIDERATIONS
                   Concerning
                   the
                   LAKE
                   OF
                   VENICE
                   .
                
                 
                   PART
                   II.
                   
                
                 
                   IF
                   the
                   discoursing
                   well
                   about
                   the
                   truth
                   of
                   things
                   ,
                   Most
                   Serene
                   Prince
                   ,
                   were
                   as
                   the
                   carrying
                   of
                   Burdens
                   ,
                   in
                   which
                   we
                   see
                   that
                   an
                   hundred
                   Horses
                   carry
                   a
                   greater
                   weight
                   than
                   one
                   Horse
                   onely
                   ;
                   it
                   would
                   seem
                   that
                   one
                   might
                   make
                   more
                   account
                   of
                   the
                   opinion
                   of
                   many
                   men
                   ,
                   than
                   of
                   one
                   alone
                   ;
                   But
                   because
                   that
                   discoursing
                   more
                   resembleth
                   running
                   ,
                   than
                   carrying
                   Burdens
                   ,
                   in
                   which
                   we
                   see
                   that
                   one
                   Barb
                   alone
                   runneth
                   faster
                   than
                   an
                   hundred
                   heavy-heel'd
                   Jades
                   ;
                   therefore
                   I
                   have
                   ever
                   more
                   esteemed
                   one
                   Conclusion
                   well
                   managed
                   ,
                   and
                   well
                   considered
                   by
                   one
                   understanding
                   man
                   ,
                   although
                   alone
                   ,
                   than
                   the
                   common
                   and
                   Vulgar
                   opinions
                   ;
                   especially
                   ,
                   when
                   they
                   concern
                   abstruce
                   and
                   arduous
                   points
                   :
                   Nay
                   in
                   such
                   cases
                   the
                   opinions
                   moulded
                   and
                   framed
                   by
                   the
                   most
                   ignorant
                   and
                   stupid
                   Vulgar
                   ,
                   have
                   been
                   ever
                   suspected
                   by
                   me
                   as
                   false
                   ,
                   for
                   that
                   it
                   would
                   be
                   a
                   great
                   wonder
                   if
                   in
                   difficult
                   matters
                   a
                   common
                   capacity
                   should
                   hit
                   upon
                   that
                   which
                   is
                   handsom
                   ,
                   good
                   ,
                   and
                   true
                   .
                   Hence
                   I
                   have
                   ,
                   and
                   do
                   hold
                   in
                   very
                   great
                   veneration
                   the
                   summe
                   of
                   the
                   Government
                   of
                   the
                   most
                   Serene
                   ,
                   and
                   eternal
                   Republick
                   of
                   Venice
                   ;
                   which
                   although
                   ,
                   as
                   being
                   in
                   nature
                   a
                   Common-wealth
                   ,
                   it
                   ought
                   to
                   be
                   governed
                   by
                   the
                   greater
                   part
                   ;
                   yet
                   nevertheless
                   ,
                   in
                   arduous
                   affairs
                   ,
                   it
                   is
                   alwaies
                   directed
                   by
                   the
                   Grave
                   Judgement
                   of
                   few
                   ,
                   and
                   not
                   judged
                   blindly
                   
                   by
                   the
                   Plebeian
                   Rout.
                   T
                   is
                   true
                   ,
                   that
                   he
                   that
                   propoundeth
                   Propositions
                   far
                   above
                   the
                   reach
                   of
                   common
                   capacity
                   ,
                   runneth
                   a
                   great
                   hazard
                   of
                   being
                   very
                   often
                   condemned
                   without
                   further
                   Process
                   ,
                   or
                   knowledge
                   of
                   the
                   Cause
                   ;
                   but
                   yet
                   for
                   all
                   that
                   ,
                   the
                   truth
                   is
                   not
                   to
                   be
                   deserted
                   in
                   most
                   weighty
                   affairs
                   ,
                   but
                   ought
                   rather
                   to
                   be
                   explained
                   in
                   due
                   place
                   and
                   time
                   with
                   all
                   possible
                   perspicuity
                   ;
                   that
                   so
                   being
                   well
                   understood
                   ,
                   and
                   considered
                   ,
                   it
                   may
                   come
                   afterwards
                   for
                   the
                   Common
                   good
                   to
                   be
                   embraced
                   .
                
                 
                   This
                   which
                   I
                   speak
                   in
                   general
                   ,
                   hath
                   often
                   been
                   my
                   fortune
                   in
                   very
                   many
                   particulars
                   ,
                   not
                   onely
                   when
                   I
                   have
                   kept
                   within
                   the
                   bounds
                   of
                   meer
                   speculation
                   ,
                   but
                   also
                   when
                   I
                   have
                   chanced
                   to
                   descend
                   to
                   Practice
                   ,
                   and
                   to
                   Operations
                   :
                   and
                   your
                   Highness
                   knoweth
                   very
                   well
                   what
                   befel
                   me
                   the
                   last
                   Summer
                   1641.
                   when
                   in
                   obedience
                   to
                   your
                   Soveraign
                   Command
                   ,
                   I
                   did
                   in
                   full
                   Colledge
                   represent
                   my
                   thoughts
                   touching
                   the
                   state
                   of
                   the
                   Lake
                   of
                   Venice
                   ;
                   for
                   there
                   not
                   being
                   such
                   wanting
                   ,
                   who
                   without
                   so
                   much
                   as
                   vouchsafing
                   to
                   understand
                   me
                   ,
                   but
                   having
                   onely
                   had
                   an
                   inkling
                   ,
                   and
                   bad
                   apprehension
                   of
                   my
                   opinion
                   ,
                   fell
                   furiously
                   upon
                   me
                   ,
                   and
                   by
                   violent
                   means
                   both
                   with
                   the
                   Pen
                   and
                   Press
                   ,
                   full
                   of
                   Gall
                   ,
                   did
                   abuse
                   me
                   in
                   reward
                   of
                   the
                   readiness
                   that
                   I
                   had
                   exprest
                   to
                   obey
                   and
                   serve
                   them
                   :
                   But
                   I
                   was
                   above
                   measure
                   encouraged
                   and
                   pleased
                   ,
                   to
                   see
                   that
                   those
                   few
                   who
                   vouchsafed
                   to
                   hear
                   me
                   ,
                   were
                   all
                   either
                   thorowly
                   perswaded
                   that
                   my
                   opinion
                   was
                   well
                   grounded
                   ,
                   or
                   at
                   least
                   suspended
                   their
                   prudent
                   verdict
                   to
                   more
                   mature
                   deliberation
                   .
                   And
                   though
                   at
                   the
                   first
                   bout
                   I
                   chanced
                   to
                   propose
                   a
                   thing
                   that
                   was
                   totally
                   contrary
                   to
                   the
                   most
                   received
                   and
                   antiquated
                   opinion
                   ,
                   and
                   to
                   the
                   resolutions
                   and
                   consultations
                   taken
                   above
                   an
                   hundred
                   years
                   ago
                   :
                   Moved
                   by
                   these
                   things
                   ,
                   and
                   to
                   satisfie
                   also
                   to
                   the
                   promise
                   that
                   I
                   had
                   made
                   of
                   tendering
                   unto
                   them
                   what
                   should
                   farther
                   offer
                   it self
                   unto
                   me
                   touching
                   the
                   same
                   business
                   ;
                   I
                   have
                   resolved
                   to
                   present
                   to
                   the
                   Throne
                   of
                   your
                   Highness
                   ,
                   another
                   Consideration
                   of
                   no
                   less
                   importance
                   ,
                   which
                   perhaps
                   at
                   first
                   sight
                   will
                   appear
                   a
                   stranger
                   Paradox
                   ;
                   but
                   yet
                   brought
                   to
                   the
                   Test
                   and
                   Touch-stone
                   of
                   experience
                   ,
                   it
                   shall
                   prove
                   most
                   clear
                   and
                   evident
                   .
                   If
                   it
                   shall
                   be
                   accounted
                   of
                   ,
                   so
                   that
                   it
                   succeedeth
                   to
                   the
                   benefit
                   of
                   your
                   Highness
                   ,
                   I
                   shall
                   have
                   obtained
                   my
                   desire
                   and
                   intent
                   :
                   And
                   if
                   not
                   ,
                   I
                   shall
                   have
                   satisfied
                   my self
                   ,
                   and
                   shall
                   not
                   have
                   been
                   wanting
                   to
                   the
                   Obligation
                   of
                   your
                   most
                   faithful
                   Servant
                   ,
                   and
                   native
                   subject
                   .
                
                 
                   That
                   which
                   I
                   propounded
                   in
                   the
                   Mouths
                   pass
                   ,
                   touching
                   the
                   most
                   important
                   business
                   of
                   the
                   Lake
                   ,
                   though
                   it
                   did
                   onely
                   expresly
                   concern
                   the
                   point
                   of
                   the
                   diversion
                   of
                   the
                   Mouth
                   of
                   the
                   Lake
                   ,
                   already
                   made
                   and
                   put
                   in
                   execution
                   ;
                   yet
                   it
                   may
                   be
                   understood
                   and
                   applyed
                   also
                   to
                   the
                   diversion
                   under
                   debate
                   ,
                   to
                   be
                   made
                   of
                   the
                   other
                   five
                   Rivers
                   ,
                   and
                   of
                   the
                   Sile
                   in
                   particular
                   .
                
                 
                 
                   Now
                   touching
                   this
                   ,
                   I
                   had
                   the
                   fortune
                   to
                   offer
                   an
                   admirable
                   accident
                   that
                   we
                   meet
                   with
                   when
                   we
                   come
                   to
                   the
                   effect
                   ,
                   which
                   I
                   verily
                   believe
                   will
                   be
                   an
                   utter
                   ruine
                   to
                   the
                   Lake
                   of
                   Venice
                   .
                
                 
                   I
                   say
                   therefore
                   ,
                   that
                   by
                   diverting
                   these
                   five
                   Rivers
                   that
                   remain
                   ,
                   although
                   their
                   water
                   that
                   they
                   discharge
                   for
                   the
                   present
                   into
                   the
                   Lake
                   is
                   not
                   all
                   taken
                   together
                   4
                   /
                   5
                   parts
                   of
                   what
                   the
                   Brent
                   alone
                   did
                   carry
                   ,
                   yet
                   neverthelesse
                   the
                   abatement
                   of
                   the
                   water
                   of
                   the
                   Lake
                   which
                   shall
                   ensue
                   upon
                   this
                   last
                   diversion
                   of
                   four
                   parts
                   ,
                   which
                   was
                   the
                   whole
                   water
                   ,
                   shall
                   prove
                   double
                   to
                   that
                   which
                   hath
                   happened
                   by
                   the
                   diversion
                   of
                   Brent
                   onely
                   ,
                   although
                   that
                   the
                   Brent
                   alone
                   carried
                   five
                   parts
                   of
                   that
                   water
                   ,
                   of
                   which
                   the
                   Rivers
                   that
                   are
                   to
                   be
                   diverted
                   carry
                   four
                   :
                   A
                   wonder
                   really
                   great
                   ,
                   and
                   altogether
                   unlikely
                   ;
                   for
                   the
                   reducing
                   all
                   this
                   Proposition
                   to
                   be
                   understood
                   ,
                   is
                   as
                   if
                   we
                   should
                   say
                   ,
                   that
                   there
                   being
                   given
                   us
                   three
                   Rivers
                   ,
                   of
                   which
                   the
                   first
                   dischargeth
                   five
                   parts
                   ,
                   the
                   second
                   three
                   ,
                   and
                   the
                   third
                   one
                   ,
                   and
                   that
                   from
                   the
                   diversion
                   of
                   the
                   first
                   ,
                   there
                   did
                   follow
                   such
                   a
                   certain
                   abatement
                   or
                   fall
                   ;
                   from
                   the
                   taking
                   away
                   of
                   the
                   second
                   there
                   ought
                   to
                   follow
                   also
                   so
                   much
                   more
                   abatement
                   ;
                   And
                   lastly
                   ,
                   from
                   the
                   withdrawing
                   of
                   the
                   third
                   the
                   water
                   ought
                   to
                   fall
                   so
                   much
                   more
                   ,
                   which
                   is
                   wholly
                   impossible
                   :
                   And
                   yet
                   it
                   is
                   most
                   certain
                   ,
                   and
                   besides
                   the
                   demonstration
                   that
                   perswades
                   me
                   to
                   it
                   ,
                   which
                   I
                   shall
                   explain
                   in
                   due
                   time
                   ,
                   I
                   can
                   set
                   before
                   your
                   eyes
                   such
                   an
                   experiment
                   as
                   is
                   not
                   to
                   be
                   denied
                   by
                   any
                   one
                   ,
                   although
                   obstinate
                   :
                   and
                   I
                   will
                   make
                   it
                   plainly
                   seen
                   and
                   felt
                   ,
                   that
                   by
                   taking
                   away
                   only
                   four
                   parts
                   of
                   the
                   five
                   ,
                   which
                   shall
                   have
                   been
                   taken
                   away
                   ,
                   the
                   abatement
                   proveth
                   double
                   to
                   the
                   abatement
                   ensuing
                   upon
                   the
                   diverting
                   first
                   of
                   the
                   five
                   onely
                   ;
                   which
                   thing
                   being
                   true
                   ,
                   as
                   most
                   certainly
                   it
                   is
                   ,
                   it
                   will
                   give
                   us
                   to
                   understand
                   how
                   pernicious
                   this
                   diversion
                   of
                   five
                   Rivers
                   is
                   like
                   to
                   prove
                   ,
                   if
                   it
                   shall
                   be
                   put
                   in
                   execution
                   .
                
                 
                   By
                   this
                   little
                   that
                   I
                   have
                   hinted
                   ,
                   and
                   the
                   much
                   that
                   I
                   could
                   say
                   ,
                   let
                   your
                   Highnesse
                   gather
                   with
                   what
                   circumspection
                   this
                   businesse
                   ought
                   to
                   be
                   managed
                   ,
                   and
                   with
                   how
                   great
                   skill
                   he
                   ought
                   to
                   be
                   furnished
                   who
                   would
                   behave
                   himself
                   well
                   in
                   these
                   difficult
                   affairs
                   .
                
                 
                   I
                   have
                   not
                   at
                   this
                   time
                   explained
                   the
                   demonstration
                   ,
                   nor
                   have
                   I
                   so
                   much
                   as
                   propounded
                   the
                   way
                   to
                   make
                   the
                   Experiment
                   ,
                   that
                   I
                   am
                   able
                   to
                   make
                   in
                   confirmation
                   of
                   what
                   I
                   have
                   said
                   ,
                   that
                   so
                   by
                   some
                   one
                   or
                   others
                   mis-apprehending
                   the
                   Demonstration
                   ,
                   and
                   maiming
                   the
                   Experiment
                   ,
                   the
                   truth
                   may
                   not
                   happen
                   to
                   shine
                   with
                   lesse
                   clarity
                   than
                   it
                   doth
                   ,
                   when
                   all
                   mists
                   of
                   difficulty
                   are
                   removed
                   :
                   and
                   if
                   so
                   be
                   ,
                   no
                   account
                   should
                   be
                   made
                   of
                   the
                   Reasons
                   by
                   me
                   alledged
                   ,
                   and
                   that
                   men
                   should
                   shut
                   their
                   eyes
                   against
                   the
                   Experiments
                   that
                   without
                   cost
                   or
                   charge
                   may
                   be
                   made
                   ,
                   I
                   do
                   declare
                   
                   and
                   protest
                   that
                   there
                   shall
                   follow
                   very
                   great
                   dammages
                   to
                   the
                   Fields
                   of
                   the
                   main
                   Land
                   ,
                   and
                   extraordinary
                   summes
                   shall
                   be
                   expended
                   to
                   no
                   purpose
                   .
                   The
                   Lake
                   undoubtedly
                   will
                   become
                   almost
                   dry
                   ,
                   and
                   will
                   prove
                   impassible
                   for
                   Navigation
                   ,
                   with
                   a
                   manifest
                   danger
                   of
                   corrupting
                   the
                   Air
                   :
                   And
                   in
                   the
                   last
                   place
                   there
                   will
                   unavoidably
                   ensue
                   the
                   choaking
                   and
                   stoppage
                   of
                   the
                   Ports
                   of
                   Venice
                   .
                
                 
                   Upon
                   the
                   20th
                   .
                   of
                   December
                   ,
                   1641.
                   
                   I
                   imparted
                   this
                   my
                   second
                   Consideration
                   to
                   the
                   most
                   Excellent
                   
                     Signore
                     Basadonna
                  
                   ,
                   presenting
                   him
                   with
                   a
                   Copy
                   thereof
                   amongst
                   other
                   Writings
                   ,
                   which
                   I
                   have
                   thought
                   good
                   to
                   insert
                   ,
                   although
                   they
                   seem
                   not
                   to
                   belong
                   directly
                   to
                   our
                   businesse
                   of
                   the
                   Lake
                   .
                
              
               
                 
                   The
                   way
                   to
                   examine
                   the
                   MUD
                   and
                   SAND
                   that
                   entereth
                   and
                   remaineth
                   in
                   the
                   LAKE
                   OF
                   VENICE
                   .
                
                 
                   
                     To
                     the
                     most
                     Excellent
                     SIGNORE
                     GIO.
                     BASADONNA
                     .
                  
                
                 
                   TWo
                   very
                   considerable
                   Objections
                   have
                   been
                   made
                   against
                   my
                   opinion
                   concerning
                   the
                   Lake
                   of
                   Venice
                   :
                   One
                   was
                   that
                   ,
                   of
                   which
                   I
                   have
                   spoken
                   at
                   large
                   in
                   my
                   first
                   Consideration
                   ,
                   namely
                   ,
                   that
                   the
                   Brents
                   having
                   been
                   taken
                   out
                   of
                   the
                   Lake
                   ,
                   cannot
                   have
                   been
                   the
                   occasion
                   of
                   the
                   notable
                   fall
                   of
                   the
                   Waters
                   in
                   the
                   Lake
                   ,
                   as
                   I
                   pretend
                   ,
                   and
                   consequently
                   ,
                   that
                   the
                   turning
                   Brent
                   into
                   the
                   Lake
                   would
                   be
                   no
                   considerable
                   remedy
                   ,
                   in
                   regard
                   that
                   the
                   water
                   of
                   Brent
                   ,
                   and
                   the
                   great
                   expansion
                   of
                   the
                   Lake
                   over
                   which
                   the
                   water
                   of
                   Brent
                   is
                   to
                   diffuse
                   and
                   spread
                   being
                   considered
                   ,
                   it
                   is
                   found
                   that
                   the
                   rise
                   proveth
                   insensible
                   .
                
                 
                   The
                   second
                   Objection
                   was
                   ,
                   that
                   the
                   Brent
                   is
                   very
                   muddy
                   ,
                   and
                   therefore
                   if
                   it
                   should
                   fall
                   muddy
                   into
                   the
                   Lake
                   ,
                   the
                   Sand
                   would
                   sink
                   and
                   fill
                   up
                   the
                   same
                   .
                
                 
                   Touching
                   the
                   first
                   Query
                   ,
                   enough
                   hath
                   been
                   said
                   in
                   my
                   first
                   Consideration
                   ,
                   where
                   I
                   have
                   plainly
                   discovered
                   the
                   deceipt
                   of
                   the
                   Argument
                   ,
                   and
                   shewn
                   its
                   fallacy
                   ;
                   It
                   remaineth
                   now
                   to
                   examine
                   
                   the
                   second
                   :
                   to
                   which
                   in
                   the
                   first
                   place
                   I
                   say
                   ,
                   that
                   one
                   of
                   the
                   first
                   things
                   that
                   I
                   proposed
                   in
                   this
                   affair
                   was
                   ,
                   that
                   I
                   held
                   it
                   impossible
                   to
                   do
                   any
                   act
                   ,
                   though
                   never
                   so
                   beneficial
                   ,
                   that
                   was
                   not
                   also
                   accompanied
                   by
                   some
                   inconvenience
                   and
                   mischief
                   ;
                   and
                   therefore
                   we
                   are
                   to
                   consider
                   well
                   the
                   profit
                   ,
                   and
                   the
                   losse
                   and
                   prejudice
                   ;
                   and
                   they
                   both
                   being
                   weighed
                   ,
                   we
                   shall
                   be
                   able
                   to
                   choose
                   the
                   lesser
                   evil
                   :
                   Secondly
                   ,
                   I
                   admit
                   it
                   to
                   be
                   most
                   true
                   ,
                   that
                   Brent
                   is
                   at
                   some
                   times
                   muddy
                   ,
                   but
                   it
                   is
                   also
                   true
                   ,
                   that
                   for
                   the
                   greater
                   part
                   of
                   the
                   year
                   it
                   is
                   not
                   muddy
                   .
                   Thirdly
                   ,
                   I
                   do
                   not
                   see
                   nor
                   understand
                   what
                   strength
                   this
                   objection
                   hath
                   ,
                   being
                   taken
                   so
                   at
                   large
                   ,
                   and
                   in
                   general
                   ;
                   and
                   methinks
                   that
                   it
                   is
                   not
                   enough
                   to
                   say
                   ,
                   that
                   the
                   Brent
                   runneth
                   muddy
                   ,
                   and
                   to
                   assert
                   that
                   it
                   deposeth
                   its
                   Muddinesse
                   in
                   the
                   Lake
                   ,
                   but
                   we
                   ought
                   moreover
                   to
                   proceed
                   to
                   particulars
                   ,
                   and
                   shew
                   how
                   much
                   this
                   Mud
                   is
                   ,
                   and
                   in
                   what
                   time
                   this
                   choaking
                   up
                   of
                   the
                   Ports
                   may
                   be
                   effected
                   .
                   For
                   the
                   Reasons
                   are
                   but
                   too
                   apparent
                   and
                   particular
                   ,
                   that
                   conclude
                   the
                   ruine
                   of
                   the
                   Lake
                   ,
                   and
                   that
                   in
                   a
                   very
                   short
                   time
                   ,
                   (
                   for
                   mention
                   is
                   made
                   of
                   dayes
                   )
                   the
                   Waters
                   diversion
                   being
                   made
                   ,
                   and
                   moreover
                   we
                   have
                   the
                   circumstance
                   of
                   an
                   Experiment
                   ,
                   the
                   state
                   of
                   things
                   being
                   observed
                   to
                   have
                   grown
                   worse
                   since
                   the
                   said
                   diversion
                   .
                   And
                   I
                   have
                   demonstrated
                   ,
                   that
                   in
                   case
                   the
                   Diversion
                   of
                   the
                   Sile
                   and
                   the
                   other
                   Rivers
                   should
                   be
                   put
                   in
                   execution
                   ,
                   the
                   Lake
                   would
                   in
                   a
                   few
                   dayes
                   become
                   almost
                   dry
                   ;
                   and
                   the
                   Ports
                   would
                   be
                   lost
                   ,
                   with
                   other
                   mischievous
                   consequences
                   .
                   But
                   on
                   the
                   other
                   side
                   ,
                   although
                   that
                   we
                   did
                   grant
                   the
                   choaking
                   of
                   them
                   ,
                   we
                   may
                   very
                   probably
                   say
                   ,
                   that
                   it
                   will
                   not
                   happen
                   ,
                   save
                   onely
                   in
                   the
                   succession
                   of
                   many
                   and
                   many
                   Centuries
                   of
                   years
                   .
                   Nor
                   can
                   I
                   think
                   it
                   prudent
                   counsel
                   to
                   take
                   a
                   resolution
                   and
                   imbrace
                   a
                   Designe
                   now
                   ,
                   to
                   obtain
                   a
                   benefit
                   very
                   uncertain
                   ,
                   and
                   more
                   than
                   that
                   ,
                   which
                   only
                   shall
                   concern
                   those
                   who
                   are
                   to
                   come
                   very
                   many
                   Ages
                   after
                   us
                   ,
                   and
                   thereby
                   bring
                   a
                   cetain
                   inconvenience
                   upon
                   our selves
                   ,
                   and
                   upon
                   our
                   children
                   that
                   are
                   now
                   alive
                   and
                   present
                   .
                
                 
                   Let
                   it
                   be
                   alledged
                   therefore
                   ,
                   (
                   although
                   I
                   hold
                   it
                   false
                   )
                   that
                   by
                   the
                   diversions
                   of
                   the
                   Rivers
                   the
                   Lake
                   may
                   be
                   kept
                   in
                   good
                   condition
                   for
                   several
                   years
                   to
                   come
                   .
                
                 
                   But
                   I
                   say
                   confidently
                   ,
                   and
                   hope
                   to
                   demonstrate
                   it
                   ;
                   That
                   the
                   Diversions
                   will
                   bring
                   the
                   Lake
                   ,
                   even
                   in
                   our
                   dayes
                   ,
                   to
                   be
                   almost
                   dry
                   ,
                   and
                   at
                   least
                   will
                   leave
                   so
                   little
                   water
                   in
                   it
                   ,
                   that
                   it
                   shall
                   cease
                   to
                   be
                   Navigable
                   ,
                   and
                   the
                   Ports
                   shall
                   most
                   infallibly
                   be
                   choaked
                   up
                   .
                   I
                   will
                   therefore
                   say
                   upon
                   experience
                   ,
                   in
                   answer
                   to
                   this
                   Objection
                   ,
                   that
                   it
                   is
                   very
                   necessary
                   first
                   well
                   to
                   discourse
                   ,
                   and
                   rationally
                   to
                   particularize
                   and
                   ascertain
                   the
                   best
                   that
                   may
                   be
                   this
                   point
                   of
                   the
                   quantity
                   of
                   this
                   sinking
                   Mud
                   or
                   Sand.
                   
                
                 
                   Now
                   I
                   fear
                   I
                   shall
                   make
                   my self
                   ridiculous
                   to
                   those
                   ,
                   who
                   measuring
                   the
                   things
                   of
                   Nature
                   with
                   the
                   shallownesse
                   of
                   their
                   brains
                   
                   do
                   think
                   that
                   it
                   is
                   absolutely
                   impossible
                   to
                   make
                   this
                   enquiry
                   ,
                   and
                   will
                   say
                   unto
                   me
                   ,
                   
                     Quis
                     mensus
                     est
                     pugillo
                     aquas
                     ,
                     &
                     terram
                     palmo
                     ponderavit
                     ?
                  
                   Yet
                   nevertheless
                   I
                   will
                   propound
                   a
                   way
                   whereby
                   ,
                   at
                   least
                   in
                   gross
                   ,
                   one
                   may
                   find
                   out
                   the
                   same
                   .
                
                 
                   Take
                   a
                   Vessel
                   of
                   Cylindrical
                   Figure
                   ,
                   holding
                   two
                   barrels
                   of
                   water
                   ,
                   or
                   thereabouts
                   ;
                   and
                   then
                   fill
                   it
                   with
                   the
                   water
                   of
                   Brent
                   ,
                   at
                   its
                   Mouth
                   or
                   Fall
                   into
                   the
                   Lake
                   ;
                   but
                   in
                   the
                   Lake
                   at
                   the
                   time
                   that
                   the
                   Brent
                   runneth
                   muddy
                   ,
                   and
                   after
                   it
                   hath
                   begun
                   to
                   run
                   muddy
                   for
                   eight
                   or
                   ten
                   hours
                   ,
                   to
                   give
                   the
                   mud
                   time
                   to
                   go
                   as
                   far
                   as
                   S.
                   Nicolo
                   ,
                   to
                   issue
                   into
                   the
                   Sea
                   ;
                   and
                   at
                   the
                   same
                   time
                   take
                   another
                   Vessel
                   ,
                   like
                   ,
                   and
                   equal
                   to
                   the
                   first
                   ,
                   and
                   fill
                   it
                   with
                   the
                   water
                   of
                   the
                   Lake
                   towards
                   S.
                   Nicolo
                   ,
                   (
                   but
                   take
                   notice
                   that
                   this
                   operation
                   ought
                   to
                   be
                   made
                   at
                   the
                   time
                   when
                   the
                   waters
                   go
                   out
                   ,
                   and
                   when
                   the
                   Sea
                   is
                   calm
                   )
                   and
                   then
                   ,
                   when
                   the
                   waters
                   shall
                   have
                   setled
                   in
                   the
                   aforesaid
                   Vessels
                   ,
                   take
                   out
                   the
                   clear
                   water
                   ,
                   and
                   consider
                   the
                   quantity
                   of
                   Sand
                   that
                   remains
                   behind
                   ,
                   and
                   let
                   it
                   be
                   set
                   down
                   ,
                   or
                   kept
                   in
                   mind
                   :
                   And
                   I
                   am
                   easily
                   induced
                   to
                   think
                   ,
                   that
                   that
                   shall
                   be
                   a
                   greater
                   quantity
                   of
                   Sand
                   which
                   shall
                   be
                   left
                   in
                   the
                   first
                   Vessel
                   ,
                   than
                   that
                   left
                   in
                   the
                   second
                   Vessel
                   .
                   Afterwards
                   when
                   the
                   Brent
                   shall
                   come
                   to
                   be
                   clear
                   ,
                   let
                   both
                   the
                   operations
                   be
                   repeated
                   ,
                   and
                   observe
                   the
                   quantity
                   of
                   Sand
                   in
                   the
                   aforesaid
                   Vessels
                   ;
                   for
                   if
                   the
                   Sand
                   in
                   the
                   first
                   Vessel
                   should
                   be
                   most
                   ,
                   it
                   would
                   be
                   a
                   sign
                   ,
                   that
                   in
                   the
                   revolution
                   of
                   a
                   year
                   the
                   Brent
                   would
                   depose
                   Sand
                   in
                   the
                   Lake
                   :
                   And
                   in
                   this
                   manner
                   one
                   may
                   calculate
                   to
                   a
                   small
                   matter
                   what
                   proportion
                   the
                   Sand
                   that
                   entreth
                   into
                   the
                   Lake
                   ,
                   hath
                   to
                   that
                   which
                   remains
                   :
                   And
                   by
                   that
                   proportion
                   one
                   may
                   judge
                   how
                   expedient
                   it
                   shall
                   be
                   for
                   publick
                   benefit
                   .
                   And
                   if
                   at
                   several
                   times
                   of
                   the
                   year
                   you
                   carefully
                   repeat
                   the
                   same
                   operations
                   ,
                   or
                   rather
                   observations
                   ,
                   you
                   would
                   come
                   to
                   a
                   more
                   exact
                   knowledge
                   in
                   this
                   business
                   :
                   And
                   it
                   would
                   be
                   good
                   to
                   make
                   the
                   said
                   operations
                   at
                   those
                   times
                   ,
                   when
                   the
                   Lake
                   is
                   disturbed
                   by
                   strong
                   high
                   Winds
                   ,
                   and
                   made
                   muddy
                   by
                   its
                   own
                   Mud
                   ,
                   raised
                   by
                   the
                   commotion
                   of
                   the
                   Waters
                   .
                
                 
                   This
                   notion
                   would
                   give
                   us
                   great
                   light
                   ,
                   if
                   the
                   same
                   observations
                   should
                   be
                   made
                   towards
                   the
                   Mouth
                   of
                   Lio
                   ,
                   at
                   such
                   time
                   as
                   the
                   waters
                   flow
                   and
                   ebb
                   ,
                   in
                   calm
                   seasons
                   ;
                   for
                   so
                   one
                   should
                   come
                   to
                   know
                   whether
                   the
                   waters
                   of
                   the
                   Lake
                   are
                   more
                   thick
                   at
                   the
                   going
                   out
                   ,
                   than
                   at
                   the
                   entrance
                   .
                   I
                   have
                   propounded
                   the
                   foregoing
                   way
                   of
                   measuring
                   Sands
                   and
                   Mud
                   ,
                   to
                   shew
                   that
                   we
                   are
                   not
                   so
                   generally
                   ,
                   and
                   inconsiderately
                   to
                   pronounce
                   any
                   sentence
                   ,
                   but
                   proceed
                   to
                   stricter
                   inquiries
                   ,
                   and
                   then
                   deliberate
                   what
                   shall
                   be
                   most
                   expedient
                   to
                   be
                   done
                   .
                   Others
                   may
                   propose
                   more
                   equisite
                   examinations
                   ,
                   but
                   this
                   shall
                   serve
                   me
                   for
                   the
                   present
                   .
                
                 
                   I
                   will
                   add
                   onely
                   ,
                   that
                   if
                   any
                   one
                   had
                   greater
                   curiosity
                   (
                   it
                   would
                   be
                   profitable
                   to
                   have
                   it
                   )
                   in
                   investigating
                   more
                   exactly
                   the
                   quantity
                   
                   of
                   the
                   Water
                   that
                   entereth
                   into
                   the
                   Lake
                   ,
                   by
                   the
                   means
                   that
                   I
                   have
                   shewen
                   in
                   the
                   beginning
                   of
                   this
                   Book
                   :
                   When
                   he
                   shall
                   have
                   found
                   the
                   proportion
                   of
                   the
                   quantity
                   of
                   water
                   to
                   the
                   quantity
                   of
                   Sand
                   or
                   Mud
                   ,
                   he
                   shall
                   come
                   to
                   know
                   how
                   much
                   Sand
                   the
                   Brent
                   shall
                   leave
                   in
                   the
                   Lake
                   in
                   the
                   space
                   of
                   a
                   year
                   .
                   But
                   to
                   perform
                   these
                   things
                   ,
                   there
                   are
                   required
                   persons
                   of
                   discretion
                   ,
                   and
                   fidelity
                   ,
                   and
                   that
                   are
                   imployed
                   by
                   publick
                   Order
                   ;
                   for
                   there
                   would
                   thence
                   result
                   eminent
                   benefit
                   and
                   profit
                   .
                
                 
                   Here
                   are
                   wanting
                   LETTERS
                   from
                   several
                   persons
                   .
                
                 
                   
                     
                       To
                       the
                       Reverend
                       Father
                       ,
                       Francesco
                       di
                       S.
                       GIUSEPPE
                       .
                    
                     
                       IN
                       execution
                       of
                       the
                       command
                       that
                       you
                       laid
                       upon
                       me
                       in
                       your
                       former
                       Letters
                       ,
                       by
                       order
                       from
                       the
                       most
                       Serene
                       ,
                       my
                       Lord
                       ,
                       
                         Prince
                         Leopold
                      
                       ;
                       that
                       I
                       should
                       speak
                       my
                       judgement
                       concerning
                       the
                       disimboguement
                       of
                       the
                       River
                       called
                       
                         Fiume
                         morto
                      
                       ,
                       whether
                       it
                       ought
                       to
                       be
                       let
                       into
                       the
                       Sea
                       ,
                       or
                       into
                       Serchio
                       ;
                       I
                       say
                       ,
                       that
                       I
                       chanced
                       18.
                       years
                       since
                       to
                       be
                       present
                       ,
                       when
                       the
                       said
                       Mouth
                       was
                       opened
                       into
                       the
                       Sea
                       ,
                       and
                       that
                       of
                       Serchio
                       stopt
                       ;
                       which
                       work
                       was
                       done
                       to
                       remedy
                       the
                       great
                       Innundation
                       that
                       was
                       made
                       in
                       all
                       that
                       Country
                       ,
                       and
                       Plain
                       of
                       Pisa
                       ,
                       that
                       lyeth
                       between
                       the
                       River
                       Arno
                       ,
                       and
                       the
                       Mountains
                       of
                       
                         S.
                         Giuliano
                      
                       ,
                       and
                       the
                       River
                       Serchio
                       ;
                       which
                       Plain
                       continued
                       long
                       under
                       water
                       ,
                       insomuch
                       that
                       not
                       onely
                       in
                       the
                       Winter
                       ,
                       but
                       also
                       for
                       a
                       great
                       part
                       of
                       the
                       Summer
                       ,
                       those
                       fields
                       were
                       overflowed
                       ;
                       and
                       when
                       that
                       the
                       Mouth
                       of
                       
                         Fiume
                         morto
                      
                       was
                       effectually
                       opened
                       into
                       the
                       Sea
                       ,
                       the
                       place
                       was
                       presently
                       freed
                       from
                       the
                       waters
                       .
                       and
                       drained
                       ,
                       to
                       the
                       great
                       satisfaction
                       of
                       the
                       Owners
                       of
                       those
                       Grounds
                       .
                       And
                       here
                       I
                       judge
                       it
                       worth
                       your
                       notice
                       ,
                       that
                       for
                       the
                       generality
                       of
                       those
                       that
                       possess
                       estates
                       in
                       those
                       parts
                       ,
                       they
                       desired
                       that
                       the
                       Mouth
                       of
                       
                         Fiume
                         morto
                      
                       might
                       stand
                       open
                       to
                       the
                       Sea
                       ,
                       and
                       those
                       who
                       would
                       have
                       it
                       open
                       into
                       Serchio
                       ,
                       are
                       persons
                       that
                       have
                       no
                       other
                       concernment
                       there
                       ,
                       save
                       the
                       hopes
                       of
                       gaining
                       by
                       having
                       the
                       dispose
                       of
                       Commissions
                       ,
                       and
                       the
                       like
                       ,
                       &c
                       ,
                    
                     
                       But
                       for
                       the
                       more
                       plain
                       understanding
                       of
                       that
                       which
                       is
                       to
                       be
                       said
                       ,
                       it
                       must
                       be
                       known
                       ,
                       That
                       the
                       resolution
                       of
                       opening
                       the
                       said
                       Mouth
                       into
                       Serchio
                       ,
                       was
                       taken
                       in
                       the
                       time
                       of
                       the
                       Great
                       Duke
                       Ferdinando
                       the
                       first
                       ,
                       upon
                       the
                       same
                       motives
                       that
                       are
                       at
                       this
                       time
                       again
                       proposed
                       ,
                       as
                       your
                       Letters
                       tell
                       me
                       ,
                       Since
                       that
                       ,
                       it
                       manifestly
                       appearing
                       ,
                       that
                       
                         Fiume
                         morto
                      
                       had
                       ,
                       and
                       hath
                       its
                       Mouth
                       open
                       to
                       the
                       Sea
                       ,
                       the
                       Plain
                       hath
                       been
                       kept
                       dry
                       ;
                       and
                       it
                       being
                       also
                       true
                       ,
                       that
                       
                       the
                       fury
                       of
                       the
                       South
                       ,
                       and
                       South-West-Winds
                       carryed
                       such
                       abundance
                       of
                       sand
                       into
                       the
                       Mouth
                       ,
                       or
                       Out-let
                       of
                       
                         Fiume
                         morto
                      
                       ,
                       that
                       it
                       wholly
                       stopt
                       it
                       up
                       :
                       especially
                       when
                       the
                       waters
                       on
                       Pisa
                       side
                       were
                       low
                       and
                       shallow
                       ,
                       And
                       they
                       think
                       ,
                       that
                       turning
                       the
                       Lake
                       of
                       
                         Fiume
                         morto
                      
                       into
                       Serchio
                       ,
                       and
                       the
                       Serchio
                       maintaining
                       continually
                       its
                       own
                       Mouth
                       with
                       the
                       force
                       of
                       its
                       waters
                       open
                       to
                       the
                       Sea
                       ,
                       and
                       consequently
                       also
                       
                         Fiume
                         morto
                      
                       ,
                       they
                       would
                       have
                       had
                       the
                       Out-let
                       clear
                       and
                       open
                       ;
                       and
                       in
                       this
                       manner
                       they
                       think
                       ,
                       that
                       the
                       Plain
                       of
                       Pisa
                       would
                       have
                       been
                       freed
                       from
                       the
                       waters
                       .
                       The
                       business
                       passeth
                       for
                       current
                       ,
                       at
                       first
                       sight
                       ;
                       but
                       experience
                       proveth
                       the
                       contrary
                       ,
                       and
                       Reason
                       confirmeth
                       the
                       same
                       :
                       For
                       the
                       height
                       of
                       the
                       water
                       of
                       those
                       Plains
                       ,
                       was
                       regulated
                       by
                       the
                       height
                       of
                       the
                       waters
                       in
                       the
                       Mouth
                       of
                       
                         Fiume
                         morto
                      
                       ;
                       that
                       is
                       ,
                       The
                       waters
                       at
                       the
                       Mouth
                       being
                       high
                       ,
                       the
                       waters
                       also
                       do
                       rise
                       in
                       the
                       fields
                       ;
                       and
                       when
                       the
                       waters
                       at
                       the
                       Mouth
                       are
                       low
                       ,
                       the
                       waters
                       of
                       the
                       fields
                       do
                       likewise
                       abate
                       :
                       Nor
                       is
                       it
                       enough
                       to
                       say
                       ,
                       That
                       the
                       Out-let
                       or
                       Vent
                       of
                       
                         Fiume
                         morto
                      
                       is
                       continual
                       ,
                       but
                       it
                       must
                       be
                       very
                       low
                       :
                       Now
                       if
                       
                         Fiume
                         morto
                      
                       did
                       determine
                       in
                       Serchio
                       ,
                       it
                       is
                       manifest
                       that
                       it
                       would
                       determine
                       high
                       ;
                       for
                       Serchio
                       terminating
                       in
                       the
                       Sea
                       ,
                       when
                       ever
                       it
                       more
                       and
                       more
                       aboundeth
                       with
                       water
                       ,
                       and
                       riseth
                       ,
                       it
                       is
                       necessary
                       that
                       also
                       
                         Fiume
                         morto
                      
                       hath
                       its
                       level
                       higher
                       ,
                       and
                       consequently
                       shall
                       keep
                       the
                       waters
                       in
                       the
                       Plains
                       higher
                       .
                       Nay
                       ,
                       it
                       hath
                       happened
                       sometimes
                       (
                       and
                       I
                       speak
                       it
                       upon
                       my
                       own
                       sight
                       )
                       that
                       
                         Fiume
                         morto
                      
                       hath
                       reversed
                       its
                       course
                       upwards
                       towards
                       Pisa
                       ;
                       which
                       case
                       will
                       ever
                       happen
                       ,
                       whensoever
                       the
                       Pisan
                       waters
                       chance
                       to
                       be
                       lower
                       than
                       the
                       level
                       of
                       those
                       of
                       Serchio
                       ;
                       for
                       in
                       that
                       case
                       the
                       waters
                       of
                       Serchio
                       return
                       back
                       upon
                       the
                       Plains
                       thorow
                       
                         Fiume
                         morto
                      
                       in
                       such
                       sort
                       ,
                       that
                       the
                       Muddinesses
                       ,
                       and
                       the
                       Serchio
                       have
                       been
                       observed
                       to
                       be
                       carried
                       by
                       this
                       return
                       as
                       farr
                       as
                       the
                       Walls
                       of
                       Pisa
                       ;
                       and
                       then
                       before
                       such
                       time
                       as
                       so
                       great
                       waters
                       can
                       be
                       asswaged
                       ,
                       which
                       come
                       in
                       with
                       great
                       fury
                       ,
                       and
                       go
                       out
                       by
                       little
                       and
                       little
                       ,
                       there
                       do
                       pass
                       very
                       many
                       days
                       ,
                       and
                       moneths
                       ,
                       nay
                       sometimes
                       one
                       being
                       never
                       able
                       to
                       find
                       the
                       waters
                       of
                       Serchio
                       ,
                       when
                       at
                       the
                       shallowest
                       ,
                       so
                       low
                       as
                       the
                       Sea
                       in
                       level
                       ;
                       (
                       which
                       is
                       the
                       lowest
                       place
                       of
                       the
                       waters
                       )
                       it
                       thence
                       doth
                       follow
                       ,
                       that
                       the
                       waters
                       of
                       
                         Fiume
                         morto
                      
                       should
                       never
                       at
                       any
                       time
                       of
                       the
                       year
                       ,
                       so
                       long
                       as
                       they
                       determine
                       in
                       Serchio
                       ,
                       be
                       so
                       low
                       ;
                       as
                       they
                       come
                       to
                       be
                       when
                       the
                       same
                       
                         Fiume
                         morto
                      
                       determineth
                       in
                       the
                       Sea.
                       T
                       is
                       true
                       indeed
                       ,
                       that
                       the
                       Mouth
                       of
                       
                         Fiume
                         morto
                      
                       ,
                       opened
                       into
                       the
                       Sea
                       ,
                       is
                       subject
                       to
                       the
                       inconvenience
                       of
                       being
                       stopt
                       up
                       by
                       the
                       force
                       of
                       Winds
                       :
                       But
                       in
                       this
                       case
                       ,
                       it
                       is
                       necessary
                       to
                       take
                       some
                       pains
                       in
                       opening
                       it
                       ;
                       which
                       may
                       easily
                       be
                       done
                       ,
                       by
                       cutting
                       that
                       Sand
                       a
                       little
                       which
                       stayeth
                       in
                       the
                       Mouth
                       ,
                       after
                       that
                       the
                       Wind
                       is
                       laid
                       ,
                       and
                       it
                       is
                       enough
                       if
                       you
                       make
                       a
                       Trench
                       little
                       more
                       than
                       two
                       Palms
                       in
                       breadth
                       ;
                       for
                       the
                       water
                       once
                       beginning
                       to
                       run
                       into
                       it
                       ,
                       it
                       will
                       in
                       a
                       few
                       hours
                       carry
                       
                       that
                       Sand
                       away
                       with
                       it
                       ,
                       and
                       there
                       will
                       ensue
                       a
                       deep
                       and
                       broad
                       Trench
                       that
                       will
                       drain
                       away
                       all
                       the
                       water
                       of
                       the
                       Plains
                       in
                       very
                       little
                       time
                       .
                       And
                       I
                       have
                       found
                       by
                       practice
                       ,
                       that
                       there
                       having
                       been
                       a
                       great
                       quantity
                       of
                       Sand
                       driven
                       back
                       ,
                       by
                       the
                       fury
                       of
                       the
                       South-West-Wind
                       ,
                       into
                       the
                       Mouth
                       of
                       
                         Fiume
                         morto
                      
                       ,
                       I
                       having
                       caused
                       the
                       little
                       gutter
                       to
                       be
                       made
                       in
                       the
                       Morning
                       ,
                       somewhat
                       before
                       Noon
                       ,
                       a
                       Mouth
                       hath
                       been
                       opened
                       of
                       40.
                       
                       Braces
                       wide
                       ,
                       and
                       notably
                       deep
                       ,
                       insomuch
                       that
                       the
                       water
                       ,
                       which
                       before
                       had
                       incommoded
                       all
                       the
                       Champian
                       ran
                       away
                       in
                       less
                       than
                       three
                       dayes
                       ,
                       and
                       left
                       the
                       Country
                       free
                       and
                       dry
                       ,
                       to
                       the
                       admiration
                       of
                       all
                       men
                       .
                       There
                       was
                       present
                       upon
                       the
                       place
                       ,
                       at
                       this
                       business
                       ,
                       on
                       the
                       same
                       day
                       that
                       I
                       opened
                       the
                       Mouth
                       ,
                       the
                       most
                       Serene
                       great
                       Duke
                       ,
                       the
                       most
                       Serene
                       Arch-Dutchess
                       Mother
                       ,
                       all
                       the
                       Commissioners
                       of
                       Sewers
                       ;
                       with
                       many
                       other
                       Persons
                       and
                       Peasants
                       of
                       those
                       parts
                       ;
                       and
                       they
                       all
                       saw
                       very
                       well
                       ,
                       that
                       it
                       was
                       never
                       possible
                       that
                       a
                       little
                       Bark
                       of
                       eight
                       Oars
                       ,
                       which
                       was
                       come
                       from
                       Legorn
                       to
                       wait
                       upon
                       the
                       great
                       Duke
                       ,
                       should
                       ever
                       be
                       able
                       to
                       master
                       the
                       Current
                       ,
                       and
                       to
                       make
                       up
                       into
                       
                         Fiume
                         morto
                      
                       ;
                       and
                       his
                       Highness
                       ,
                       who
                       came
                       with
                       an
                       intent
                       to
                       cause
                       the
                       said
                       Mouth
                       towards
                       the
                       Sea
                       to
                       be
                       stopt
                       ;
                       and
                       that
                       into
                       Serchio
                       to
                       be
                       opened
                       ,
                       changed
                       his
                       judgement
                       ,
                       giving
                       order
                       that
                       it
                       should
                       be
                       left
                       open
                       towards
                       the
                       Sea
                       ,
                       as
                       it
                       was
                       done
                       .
                       And
                       if
                       at
                       this
                       day
                       it
                       shall
                       return
                       into
                       Serchio
                       ,
                       I
                       am
                       very
                       certain
                       that
                       it
                       will
                       be
                       necessary
                       to
                       open
                       it
                       again
                       into
                       the
                       Sea.
                       And
                       there
                       was
                       also
                       charge
                       and
                       order
                       given
                       to
                       a
                       person
                       appointed
                       for
                       the
                       purpose
                       ,
                       that
                       he
                       should
                       take
                       care
                       to
                       open
                       the
                       said
                       Mouth
                       ,
                       as
                       hath
                       been
                       said
                       upon
                       occasion
                       .
                       And
                       thus
                       things
                       have
                       succeeded
                       very
                       well
                       unto
                       this
                       very
                       time
                       .
                       But
                       from
                       the
                       middle
                       of
                       October
                       ,
                       until
                       this
                       first
                       of
                       February
                       ,
                       there
                       having
                       continued
                       high
                       South
                       ,
                       and
                       South-West-Winds
                       ,
                       with
                       frequent
                       and
                       abundant
                       Rains
                       ;
                       it
                       is
                       no
                       wonder
                       that
                       some
                       innundation
                       hath
                       happened
                       ;
                       but
                       yet
                       I
                       will
                       affirm
                       ,
                       that
                       greater
                       mischiefs
                       would
                       have
                       followed
                       ,
                       if
                       the
                       Mouth
                       had
                       been
                       opened
                       into
                       Serchio
                       .
                       This
                       which
                       I
                       have
                       hitherto
                       said
                       ,
                       is
                       very
                       clear
                       and
                       intelligible
                       to
                       all
                       such
                       as
                       have
                       but
                       competent
                       insight
                       ,
                       and
                       indifferent
                       skill
                       in
                       these
                       affairs
                       .
                       But
                       that
                       which
                       I
                       am
                       now
                       about
                       to
                       propose
                       farther
                       ,
                       will
                       ,
                       I
                       am
                       very
                       certain
                       ,
                       be
                       understood
                       by
                       your self
                       ,
                       but
                       it
                       will
                       seem
                       strange
                       and
                       unlikely
                       to
                       many
                       others
                       .
                       The
                       point
                       is
                       ,
                       that
                       I
                       say
                       ,
                       That
                       by
                       raising
                       the
                       level
                       of
                       
                         Fiume
                         morto
                      
                       ,
                       one
                       half
                       Brace
                       ,
                       onely
                       at
                       its
                       Mouth
                       ,
                       (
                       it
                       will
                       penipenitrate
                       into
                       Serchio
                       farther
                       than
                       it
                       would
                       into
                       the
                       Sea
                       )
                       it
                       shall
                       cause
                       the
                       waters
                       to
                       rise
                       three
                       ,
                       or
                       perhaps
                       more
                       Braces
                       upon
                       the
                       fields
                       towards
                       Pisa
                       ,
                       and
                       still
                       more
                       by
                       degrees
                       as
                       they
                       shall
                       recede
                       farther
                       from
                       the
                       Sea-side
                       ;
                       and
                       thus
                       there
                       will
                       follow
                       very
                       great
                       Innundations
                       ,
                       and
                       considerable
                       mischiefs
                       .
                       And
                       to
                       know
                       that
                       this
                       is
                       true
                       ,
                       you
                       are
                       to
                       take
                       notice
                       of
                       an
                       accident
                       ,
                       which
                       I
                       give
                       warning
                       of
                       in
                       my
                       discourse
                       of
                       the
                       Measure
                       of
                       Running
                       Waters
                       :
                       
                       where
                       also
                       I
                       give
                       the
                       reason
                       thereof
                       ,
                       *
                       Coroll
                       .
                       14.
                       
                       The
                       accident
                       is
                       this
                       ,
                       That
                       there
                       coming
                       a
                       Land-Flood
                       ,
                       for
                       example
                       ,
                       into
                       Arno
                       ,
                       which
                       maketh
                       it
                       to
                       rise
                       above
                       its
                       ordinary
                       Mouth
                       wthin
                       Pisa
                       ,
                       or
                       a
                       little
                       above
                       or
                       below
                       the
                       City
                       six
                       or
                       seven
                       Braces
                       ;
                       this
                       same
                       height
                       becometh
                       alwaies
                       lesser
                       and
                       lesser
                       ,
                       the
                       more
                       we
                       approach
                       towards
                       the
                       Sea-side
                       ;
                       insomuch
                       ,
                       that
                       near
                       to
                       the
                       Sea
                       the
                       said
                       River
                       shall
                       be
                       raised
                       hardly
                       half
                       a
                       Brace
                       :
                       Whence
                       it
                       followeth
                       of
                       necessary
                       consequence
                       ,
                       that
                       should
                       I
                       again
                       be
                       at
                       the
                       Sea-side
                       ,
                       and
                       knowing
                       nothing
                       of
                       what
                       hapneth
                       ,
                       should
                       see
                       the
                       River
                       Arno
                       raised
                       by
                       the
                       accession
                       of
                       a
                       Land-flood
                       ,
                       one
                       third
                       of
                       a
                       Brace
                       ;
                       I
                       could
                       certainly
                       infer
                       ,
                       that
                       the
                       same
                       River
                       was
                       raised
                       in
                       Pisa
                       those
                       same
                       six
                       or
                       seven
                       Braces
                       .
                       And
                       that
                       which
                       I
                       say
                       of
                       Arno
                       ,
                       is
                       true
                       of
                       all
                       Rivers
                       that
                       fall
                       into
                       the
                       Sea.
                       Which
                       thing
                       being
                       true
                       ,
                       it
                       is
                       necessary
                       to
                       make
                       great
                       account
                       of
                       every
                       small
                       rising
                       ,
                       that
                       
                         Fiume
                         morto
                      
                       maketh
                       towards
                       the
                       Sea-side
                       by
                       falling
                       into
                       Serchio
                       .
                       For
                       although
                       the
                       rising
                       of
                       
                         Fiume
                         morto
                      
                       ,
                       by
                       being
                       to
                       disgorge
                       its
                       Waters
                       into
                       Serchio
                       ,
                       towards
                       the
                       Sea
                       ,
                       were
                       onely
                       a
                       quarter
                       of
                       a
                       Brace
                       ;
                       we
                       might
                       very
                       well
                       be
                       sure
                       ,
                       that
                       farr
                       from
                       the
                       Sea
                       ,
                       about
                       Pisa
                       ,
                       and
                       upon
                       those
                       fields
                       the
                       rise
                       shall
                       be
                       much
                       greater
                       ,
                       and
                       shall
                       become
                       two
                       or
                       three
                       Braces
                       :
                       And
                       because
                       the
                       Countrey
                       lyeth
                       low
                       ,
                       that
                       same
                       ●ise
                       will
                       cause
                       a
                       continual
                       Innundation
                       ▪
                       of
                       the
                       Plains
                       ,
                       like
                       as
                       it
                       did
                       before
                       ;
                       I
                       caused
                       the
                       Mouth
                       to
                       be
                       opened
                       into
                       the
                       Sea.
                       And
                       therefore
                       I
                       conclude
                       that
                       the
                       Mouth
                       of
                       
                         Fiume
                         morto
                      
                       ,
                       ought
                       by
                       no
                       means
                       to
                       be
                       opened
                       into
                       Serchio
                       ;
                       but
                       ought
                       to
                       be
                       continued
                       into
                       the
                       Sea
                       ,
                       using
                       all
                       diligence
                       to
                       keep
                       it
                       open
                       after
                       the
                       manner
                       aforesaid
                       ,
                       so
                       soon
                       as
                       ever
                       the
                       Wind
                       shall
                       be
                       laid
                       .
                       And
                       if
                       they
                       shall
                       do
                       otherwise
                       ,
                       I
                       confidently
                       affirm
                       ,
                       that
                       there
                       will
                       daily
                       follow
                       greater
                       damages
                       ;
                       not
                       onely
                       in
                       the
                       Plains
                       ,
                       but
                       also
                       in
                       the
                       wholesomness
                       of
                       the
                       Air
                       ;
                       as
                       hath
                       been
                       seen
                       in
                       times
                       past
                       .
                       And
                       again
                       ,
                       It
                       oughs
                       with
                       all
                       care
                       to
                       be
                       procured
                       ,
                       that
                       no
                       waters
                       do
                       by
                       any
                       means
                       run
                       or
                       fall
                       from
                       the
                       Trench
                       of
                       Libra
                       ,
                       into
                       the
                       Plain
                       of
                       Pisa
                       ,
                       for
                       these
                       Waters
                       being
                       to
                       discharge
                       into
                       
                         Fiume
                         morto
                      
                       ,
                       they
                       maintain
                       it
                       much
                       higher
                       than
                       is
                       imagined
                       ,
                       according
                       to
                       that
                       which
                       I
                       have
                       demonstrated
                       in
                       my
                       consideration
                       upon
                       the
                       state
                       of
                       the
                       Lake
                       of
                       Venice
                       .
                       I
                       have
                       said
                       but
                       little
                       ,
                       but
                       I
                       speak
                       to
                       you
                       ,
                       who
                       understandeth
                       much
                       ,
                       and
                       I
                       submit
                       all
                       to
                       the
                       most
                       refined
                       judgment
                       of
                       our
                       most
                       Serene
                       Prince
                       Leopold
                       ,
                       whose
                       hands
                       I
                       beseech
                       you
                       in
                       all
                       humility
                       to
                       kiss
                       in
                       my
                       name
                       ,
                       and
                       implore
                       the
                       continuance
                       of
                       his
                       Princely
                       favour
                       to
                       me
                       ;
                       and
                       so
                       desiring
                       your
                       prayers
                       to
                       God
                       for
                       me
                       ,
                       I
                       take
                       my
                       leave
                       .
                    
                     
                       
                         Rome
                         
                           1.
                           
                           Feb.
                           1642.
                           
                        
                      
                       
                         Your
                         most
                         affectionate
                         Servants
                         ,
                         D.
                         BENEDETTO
                         CASTELLI
                         .
                      
                    
                  
                
                 
                   
                     
                     
                       The
                       answer
                       to
                       a
                       Letter
                       written
                       by
                       BARTOLOTTI
                       ,
                       touching
                       the
                       difficultyes
                       observed
                       .
                    
                     
                       The
                       former
                       part
                       of
                       the
                       Letter
                       is
                       omitted
                       ,
                       and
                       the
                       discourse
                       beginneth
                       at
                       the
                       first
                       Head.
                       
                    
                     
                       ANd
                       first
                       I
                       say
                       ,
                       Whereas
                       I
                       suppose
                       that
                       the
                       level
                       of
                       the
                       Serchio
                       is
                       higher
                       than
                       that
                       of
                       
                         Fiume
                         morto
                      
                       ;
                       this
                       is
                       most
                       true
                       ,
                       at
                       such
                       time
                       as
                       the
                       waters
                       of
                       
                         Fiume
                         morto
                      
                       are
                       discharged
                       into
                       the
                       Sea
                       ;
                       but
                       I
                       did
                       never
                       say
                       that
                       things
                       could
                       never
                       be
                       brought
                       to
                       that
                       pass
                       ,
                       as
                       that
                       the
                       level
                       of
                       
                         Fiume
                         morto
                      
                       should
                       be
                       higher
                       than
                       Serchio
                       :
                       and
                       so
                       I
                       grant
                       that
                       it
                       will
                       follow
                       ,
                       that
                       the
                       waters
                       of
                       
                         Fiume
                         morto
                      
                       shall
                       go
                       into
                       Serchio
                       ,
                       and
                       it
                       s
                       very
                       possible
                       ,
                       that
                       the
                       Drain
                       of
                       
                         Fiume
                         morto
                      
                       into
                       Serchio
                       may
                       be
                       continuate
                       ;
                       and
                       I
                       farther
                       grant
                       ,
                       that
                       its
                       possible
                       ,
                       that
                       the
                       Serchio
                       doth
                       never
                       disgorge
                       thorow
                       
                         Fiume
                         morto
                      
                       towards
                       Pisa
                       ;
                       Nay
                       ,
                       I
                       will
                       yet
                       farther
                       grant
                       that
                       it
                       might
                       have
                       happened
                       ,
                       that
                       
                         Fiume
                         morto
                      
                       might
                       have
                       had
                       such
                       a
                       fall
                       into
                       Serchio
                       ,
                       as
                       would
                       have
                       sufficed
                       to
                       have
                       turned
                       Mills
                       :
                       But
                       then
                       I
                       add
                       withall
                       ,
                       that
                       the
                       Plains
                       of
                       Pisa
                       ,
                       and
                       the
                       City
                       it self
                       must
                       be
                       a
                       meer
                       Lake
                       .
                    
                     
                       2.
                       
                       
                         Signore
                         Bartolotti
                      
                       saith
                       confidently
                       ,
                       that
                       when
                       the
                       Sea
                       swelleth
                       by
                       the
                       South-West
                       ,
                       or
                       other
                       Winds
                       ,
                       the
                       level
                       of
                       Serchio
                       in
                       the
                       place
                       marked
                       A
                       in
                       the
                       Platt
                       ,
                       distant
                       about
                       200.
                       
                       Braces
                       ,
                       riseth
                       very
                       little
                       :
                       But
                       that
                       
                         Fiume
                         morto
                      
                       in
                       D
                       ,
                       and
                       in
                       E
                       ,
                       many
                       miles
                       more
                       up
                       into
                       Land
                       riseth
                       very
                       much
                       ,
                       and
                       that
                       certain
                       Fishermen
                       confirm
                       this
                       ,
                       and
                       shew
                       him
                       the
                       signes
                       of
                       the
                       rising
                       of
                       the
                       Water
                       .
                       I
                       grant
                       it
                       to
                       be
                       very
                       true
                       ,
                       and
                       I
                       have
                       seen
                       it
                       with
                       my
                       own
                       eyes
                       :
                       But
                       this
                       cometh
                       to
                       pass
                       ,
                       when
                       the
                       Mouth
                       of
                       
                         Fiume
                         morto
                      
                       is
                       stopt
                       up
                       by
                       the
                       Sea
                       ;
                       as
                       I
                       shall
                       shew
                       by
                       and
                       by
                       .
                       And
                       this
                       rising
                       near
                       the
                       Sea-side
                       ,
                       is
                       of
                       no
                       considerable
                       prejudice
                       to
                       the
                       fields
                       .
                       And
                       this
                       is
                       as
                       much
                       as
                       I
                       find
                       to
                       be
                       true
                       in
                       the
                       assertion
                       of
                       
                         Signore
                         Bartolotti
                      
                       ,
                       (
                       without
                       his
                       confirming
                       it
                       by
                       any
                       other
                       proof
                       ;
                       as
                       indeed
                       it
                       needs
                       none
                       )
                       That
                       the
                       level
                       of
                       
                         Fiume
                         morto
                      
                       riseth
                       in
                       E
                       ,
                       and
                       many
                       miles
                       farther
                       upwards
                       it
                       riseth
                       much
                       ;
                       nor
                       did
                       I
                       ever
                       affirm
                       the
                       contrary
                       .
                    
                     
                       3.
                       
                       Concerning
                       the
                       difficulty
                       of
                       opening
                       the
                       Mouth
                       of
                       
                         Fiume
                         morto
                      
                       into
                       the
                       Sea
                       ,
                       that
                       which
                       
                         Il
                         Castellano
                      
                       saith
                       is
                       most
                       certain
                       ;
                       namely
                       ,
                       That
                       at
                       the
                       entrance
                       upon
                       the
                       opening
                       of
                       the
                       Mouth
                       ,
                       it
                       is
                       necessary
                       to
                       make
                       a
                       deep
                       Trench
                       :
                       But
                       I
                       say
                       ,
                       that
                       at
                       that
                       time
                       it
                       is
                       difficult
                       to
                       open
                       it
                       ,
                       unless
                       upon
                       great
                       occasions
                       ;
                       for
                       that
                       the
                       
                       difficulty
                       proceedeth
                       from
                       the
                       waters
                       of
                       
                         Fiume
                         morto
                      
                       being
                       low
                       ,
                       and
                       the
                       fields
                       drained
                       .
                    
                     
                       4.
                       
                       As
                       to
                       the
                       particular
                       of
                       the
                       Causes
                       that
                       you
                       tell
                       me
                       men
                       press
                       so
                       much
                       unto
                       the
                       most
                       
                         Serene
                         Grand
                         Duke
                      
                       ,
                       and
                       to
                       the
                       Prince
                       ,
                       I
                       have
                       not
                       much
                       to
                       say
                       ,
                       because
                       it
                       is
                       not
                       my
                       profession
                       ;
                       nor
                       have
                       I
                       considered
                       of
                       the
                       same
                       :
                       Yet
                       I
                       believe
                       ,
                       that
                       when
                       the
                       Prince
                       and
                       his
                       Highnesse
                       see
                       the
                       benefit
                       of
                       his
                       People
                       and
                       Subjects
                       in
                       one
                       scale
                       of
                       the
                       Ballance
                       ,
                       and
                       the
                       accomodation
                       of
                       Huntsmen
                       in
                       the
                       other
                       ,
                       his
                       Highnesse
                       will
                       incline
                       to
                       the
                       profit
                       of
                       his
                       subjects
                       ;
                       such
                       have
                       I
                       alwayes
                       found
                       his
                       Clemency
                       and
                       Noblenesse
                       of
                       minde
                       .
                       But
                       if
                       I
                       were
                       to
                       put
                       in
                       my
                       vote
                       upon
                       this
                       businesse
                       ,
                       I
                       would
                       say
                       ,
                       that
                       the
                       points
                       of
                       Spears
                       ,
                       and
                       the
                       mouths
                       of
                       Guns
                       ,
                       the
                       yelping
                       of
                       Dogs
                       ,
                       the
                       wilynesse
                       of
                       Huntsmen
                       ,
                       who
                       run
                       thorow
                       and
                       narrowly
                       search
                       all
                       those
                       Woods
                       ,
                       Thickets
                       and
                       Heathes
                       ,
                       are
                       the
                       true
                       destroyers
                       of
                       Bucks
                       and
                       Boares
                       ,
                       and
                       not
                       a
                       little
                       Salt-water
                       ,
                       which
                       setleth
                       at
                       last
                       in
                       some
                       low
                       places
                       ,
                       and
                       spreadeth
                       not
                       very
                       far
                       .
                       Yet
                       neverthelesse
                       ,
                       I
                       will
                       not
                       enter
                       upon
                       any
                       such
                       point
                       ,
                       but
                       confine
                       my self
                       solely
                       to
                       the
                       businesse
                       before
                       me
                       .
                    
                     
                       5.
                       
                       That
                       Experiment
                       of
                       joyning
                       together
                       the
                       water
                       of
                       
                         Fiume
                         morto
                      
                       ,
                       and
                       that
                       of
                       Serchio
                       by
                       a
                       little
                       trench
                       to
                       see
                       what
                       advantage
                       the
                       Level
                       E
                       hath
                       upon
                       the
                       Level
                       I
                       ,
                       doth
                       not
                       give
                       me
                       full
                       satisfaction
                       ,
                       taken
                       so
                       particularly
                       ,
                       for
                       it
                       may
                       come
                       to
                       passe
                       ,
                       that
                       sometimes
                       E
                       may
                       be
                       higher
                       ,
                       and
                       sometimes
                       A
                       lower
                       ,
                       and
                       I
                       do
                       not
                       question
                       but
                       that
                       when
                       Serchio
                       is
                       low
                       ,
                       and
                       
                         Fiume
                         morto
                      
                       full
                       of
                       Water
                       ,
                       the
                       level
                       of
                       
                         Fiume
                         morto
                      
                       will
                       be
                       higher
                       than
                       that
                       of
                       Serchio
                       .
                       But
                       Serchio
                       being
                       full
                       ,
                       and
                       
                         Fiume
                         morto
                      
                       scant
                       of
                       Water
                       ,
                       the
                       contrary
                       will
                       follow
                       ,
                       if
                       the
                       Mouth
                       shall
                       be
                       opened
                       to
                       the
                       Sea.
                       And
                       here
                       it
                       should
                       seem
                       to
                       me
                       ,
                       that
                       it
                       ought
                       to
                       be
                       considered
                       ,
                       that
                       there
                       is
                       as
                       much
                       advantage
                       from
                       E
                       to
                       the
                       Sea
                       through
                       the
                       little
                       Trench
                       opened
                       anew
                       into
                       Serchio
                       ,
                       as
                       from
                       E
                       to
                       the
                       Sea
                       by
                       the
                       Mouth
                       of
                       
                         Fiume
                         morto
                      
                       .
                       But
                       the
                       difficulty
                       (
                       which
                       is
                       that
                       we
                       are
                       to
                       regard
                       in
                       our
                       case
                       )
                       is
                       ,
                       that
                       the
                       course
                       of
                       the
                       Waters
                       thorow
                       the
                       Trench
                       is
                       three
                       times
                       longer
                       than
                       the
                       course
                       of
                       the
                       Mouth
                       of
                       
                         Fiume
                         morto
                      
                       ,
                       as
                       appeareth
                       by
                       the
                       Draught
                       or
                       Plat
                       which
                       you
                       sent
                       me
                       ,
                       which
                       I
                       know
                       to
                       be
                       very
                       exactly
                       drawn
                       ,
                       for
                       that
                       the
                       situation
                       of
                       those
                       places
                       are
                       fresh
                       in
                       my
                       memory
                       .
                       Here
                       I
                       must
                       give
                       notice
                       ,
                       that
                       the
                       waters
                       of
                       
                         Fiume
                         morto
                      
                       determining
                       thorow
                       the
                       Trench
                       in
                       Serchio
                       (
                       the
                       waters
                       of
                       which
                       
                         Fiume
                         morto
                      
                       are
                       ,
                       for
                       certain
                       ,
                       never
                       so
                       low
                       as
                       the
                       Sea
                       )
                       their
                       pendency
                       or
                       declivity
                       shall
                       ,
                       for
                       two
                       causes
                       ,
                       be
                       lesse
                       than
                       the
                       pendency
                       of
                       those
                       waters
                       through
                       the
                       Mouth
                       towards
                       the
                       Sea
                       ,
                       that
                       is
                       ,
                       because
                       of
                       the
                       length
                       of
                       the
                       line
                       through
                       the
                       Trench
                       ,
                       and
                       because
                       of
                       the
                       height
                       of
                       their
                       entrance
                       into
                       Serchio
                       ,
                       a
                       thing
                       which
                       is
                       of
                       very
                       great
                       import
                       in
                       discharging
                       the
                       waters
                       which
                       come
                       suddenly
                       ,
                       as
                       
                       he
                       shall
                       plainly
                       see
                       ,
                       who
                       shall
                       have
                       understood
                       my
                       Book
                       of
                       the
                       Measure
                       of
                       Running
                       Waters
                       .
                       And
                       this
                       was
                       the
                       Reason
                       why
                       all
                       the
                       Countrey
                       did
                       grow
                       dry
                       upon
                       the
                       opening
                       of
                       the
                       Mouth
                       into
                       the
                       Sea.
                       And
                       here
                       I
                       propose
                       to
                       consideration
                       that
                       which
                       the
                       Peasants
                       about
                       Pisa
                       relate
                       ,
                       namely
                       ,
                       That
                       the
                       Water
                       in
                       the
                       Fields
                       doth
                       no
                       considerable
                       harm
                       by
                       continuing
                       there
                       five
                       or
                       six
                       ,
                       yea
                       ,
                       or
                       eight
                       dayes
                       .
                       And
                       therefore
                       the
                       work
                       of
                       the
                       Countrey
                       is
                       to
                       open
                       the
                       Mouth
                       of
                       
                         Fiume
                         morto
                      
                       ,
                       in
                       such
                       manner
                       ,
                       that
                       the
                       Water
                       being
                       come
                       ,
                       they
                       may
                       have
                       the
                       Trench
                       free
                       and
                       ready
                       ,
                       when
                       that
                       the
                       Water
                       cometh
                       it
                       may
                       have
                       a
                       free
                       drain
                       ,
                       and
                       may
                       not
                       stay
                       there
                       above
                       eight
                       or
                       nine
                       dayes
                       ,
                       for
                       then
                       the
                       overflowings
                       become
                       hurtful
                       .
                       It
                       is
                       to
                       be
                       desired
                       also
                       ,
                       that
                       if
                       any
                       Proposition
                       is
                       produced
                       touching
                       these
                       affairs
                       ,
                       it
                       might
                       be
                       propounded
                       the
                       most
                       distinctly
                       that
                       may
                       be
                       possible
                       ,
                       and
                       not
                       consist
                       in
                       generals
                       ,
                       especially
                       when
                       the
                       Dispute
                       is
                       of
                       the
                       risings
                       ,
                       of
                       velocity
                       ,
                       of
                       tardity
                       ,
                       of
                       much
                       and
                       little
                       water
                       ;
                       things
                       that
                       are
                       all
                       to
                       be
                       specified
                       by
                       measures
                       .
                    
                     
                       6.
                       
                       Your
                       Letter
                       saith
                       ,
                       in
                       the
                       next
                       place
                       ,
                       that
                       
                         Signore
                         Bartolotti
                      
                       confesseth
                       ,
                       that
                       if
                       the
                       Mouth
                       of
                       the
                       
                         Fiume
                         morto
                      
                       might
                       alwayes
                       be
                       kept
                       open
                       ,
                       it
                       would
                       be
                       better
                       to
                       let
                       it
                       continue
                       as
                       it
                       is
                       :
                       the
                       which
                       ,
                       that
                       I
                       may
                       not
                       yield
                       to
                       him
                       in
                       courtesie
                       ,
                       I
                       confesse
                       ,
                       for
                       the
                       keeping
                       it
                       stopt
                       on
                       all
                       sides
                       would
                       be
                       a
                       thing
                       most
                       pernicious
                       .
                       But
                       admitting
                       of
                       his
                       confession
                       I
                       again
                       reply
                       ,
                       that
                       
                         Fiume
                         morto
                      
                       ought
                       not
                       to
                       be
                       let
                       into
                       Serchio
                       ,
                       but
                       immediately
                       into
                       the
                       Sea
                       ;
                       because
                       although
                       sometimes
                       the
                       Mouth
                       to
                       Sea-wards
                       be
                       stopt
                       up
                       ,
                       yet
                       for
                       all
                       that
                       ,
                       the
                       raising
                       of
                       the
                       Bank
                       above
                       the
                       Plains
                       (
                       which
                       is
                       all
                       the
                       businesse
                       of
                       importance
                       )
                       shall
                       be
                       ever
                       lesser
                       ,
                       if
                       we
                       make
                       use
                       of
                       the
                       Mouth
                       leading
                       to
                       the
                       Sea
                       ,
                       than
                       using
                       that
                       of
                       Serchio
                       .
                    
                     
                       7.
                       
                       I
                       will
                       not
                       omit
                       to
                       mention
                       a
                       kinde
                       of
                       scruple
                       that
                       I
                       have
                       concerning
                       the
                       position
                       of
                       
                         Sign
                         .
                         Bartolotti
                      
                       ,
                       that
                       is
                       ,
                       where
                       he
                       saith
                       that
                       the
                       two
                       Mouths
                       A
                       and
                       D
                       are
                       equal
                       to
                       the
                       like
                       Mouths
                       into
                       the
                       Sea
                       ;
                       Now
                       it
                       seems
                       to
                       me
                       ,
                       that
                       the
                       Mouth
                       A
                       of
                       
                         Fiume
                         morto
                      
                       into
                       Serchio
                       is
                       absolutely
                       within
                       Serchio
                       ,
                       nor
                       can
                       it
                       be
                       made
                       lower
                       ,
                       and
                       is
                       regulated
                       by
                       the
                       height
                       of
                       Serchio
                       :
                       But
                       the
                       Mouth
                       of
                       
                         Fiume
                         morto
                      
                       terminates
                       ,
                       and
                       ought
                       to
                       be
                       understood
                       to
                       terminate
                       in
                       the
                       Sea
                       it self
                       ,
                       the
                       lowest
                       place
                       .
                       And
                       this
                       I
                       believe
                       was
                       very
                       well
                       perceived
                       by
                       
                         Sig.
                         Bartolotti
                      
                       ,
                       but
                       I
                       cannot
                       tell
                       why
                       he
                       past
                       it
                       over
                       without
                       declaring
                       it
                       :
                       and
                       we
                       see
                       not
                       that
                       the
                       Mouth
                       D
                       falleth
                       far
                       from
                       the
                       Sea
                       ,
                       which
                       Mouth
                       ought
                       to
                       be
                       let
                       into
                       the
                       Sea
                       it self
                       ,
                       and
                       so
                       the
                       advantage
                       of
                       the
                       Mouth
                       into
                       the
                       Sea
                       more
                       clearly
                       appeareth
                       .
                    
                     
                       8.
                       
                       That
                       which
                       
                         Sig.
                         Bartolotti
                      
                       addeth
                       ,
                       that
                       when
                       it
                       is
                       high
                       Waters
                       ,
                       at
                       such
                       time
                       as
                       the
                       Waters
                       are
                       out
                       ,
                       and
                       when
                       Winds
                       choak
                       up
                       
                         Fiume
                         morto
                      
                       ,
                       they
                       not
                       only
                       retard
                       it
                       ,
                       but
                       return
                       the
                       
                       course
                       of
                       the
                       Waters
                       upwards
                       very
                       leasurely
                       ,
                       perswadeth
                       me
                       more
                       readily
                       to
                       believe
                       that
                       
                         Sig.
                         Bartolotti
                      
                       knoweth
                       very
                       well
                       ,
                       that
                       the
                       Mouth
                       of
                       
                         Fiume
                         morto
                      
                       let
                       into
                       Serchio
                       is
                       hurtful
                       :
                       for
                       by
                       this
                       he
                       acknowledgeth
                       that
                       the
                       Mouth
                       towards
                       the
                       Sea
                       doth
                       in
                       such
                       sort
                       drain
                       the
                       Countrey
                       of
                       the
                       Waters
                       ,
                       as
                       that
                       they
                       become
                       very
                       low
                       ;
                       and
                       therefore
                       upon
                       every
                       little
                       impetus
                       the
                       waters
                       turn
                       their
                       course
                       :
                       And
                       from
                       the
                       motions
                       ,
                       being
                       exceeding
                       slow
                       ,
                       is
                       inferred
                       ,
                       that
                       the
                       abundance
                       of
                       Sea-water
                       that
                       cometh
                       into
                       
                         Fiume
                         morto
                      
                       ,
                       is
                       so
                       much
                       as
                       is
                       believed
                       ,
                       and
                       as
                       
                         Sig.
                         Bartolotti
                      
                       affirmeth
                       .
                    
                     
                       9.
                       
                       After
                       that
                       
                         Sig.
                         Bartolotti
                      
                       hath
                       said
                       what
                       he
                       promiseth
                       above
                       ,
                       namely
                       ,
                       that
                       when
                       the
                       Windes
                       blowing
                       strongly
                       do
                       stop
                       up
                       
                         Fiume
                         morto
                      
                       ,
                       and
                       not
                       onely
                       retard
                       but
                       turn
                       the
                       course
                       upwards
                       ,
                       the
                       time
                       being
                       Rainy
                       ,
                       and
                       the
                       Mouth
                       of
                       
                         Fiume
                         morto
                      
                       shut
                       up
                       ,
                       the
                       Waves
                       of
                       the
                       Sea
                       passe
                       over
                       the
                       Bank
                       of
                       
                         Fiume
                         morto
                      
                       ;
                       at
                       that
                       time
                       ,
                       saith
                       
                         Signore
                         Bartolotti
                      
                       ,
                       the
                       Champain
                       shall
                       know
                       the
                       benefit
                       of
                       
                         Fiume
                         morto
                      
                       discharged
                       into
                       Serchio
                       ,
                       and
                       the
                       mouth
                       A
                       shall
                       stand
                       alwayes
                       open
                       ;
                       and
                       
                         Fiume
                         morto
                      
                       may
                       alwayes
                       constantly
                       run
                       out
                       ,
                       as
                       also
                       the
                       Rains
                       and
                       Rain-waters
                       ,
                       although
                       the
                       hurtful
                       Tempest
                       should
                       last
                       many
                       dayes
                       ,
                       &c.
                       
                       And
                       I
                       reply
                       ,
                       that
                       all
                       the
                       Art
                       consists
                       in
                       this
                       ;
                       for
                       the
                       benefit
                       of
                       those
                       Fields
                       doth
                       not
                       depend
                       on
                       ,
                       or
                       consist
                       in
                       saying
                       ,
                       that
                       
                         Fiume
                         morto
                      
                       is
                       alwayes
                       open
                       ,
                       and
                       
                         Fiume
                         morto
                      
                       draineth
                       continually
                       ;
                       But
                       all
                       the
                       businesse
                       of
                       profit
                       lyeth
                       and
                       consisteth
                       in
                       maintaining
                       the
                       Waters
                       low
                       in
                       those
                       Plaines
                       ,
                       and
                       those
                       Ditches
                       ,
                       which
                       shall
                       never
                       be
                       effected
                       whilst
                       the
                       World
                       stands
                       ,
                       if
                       you
                       let
                       
                         Fiume
                         morto
                      
                       into
                       Serchio
                       ;
                       but
                       yet
                       it
                       may
                       ,
                       by
                       opening
                       the
                       mouth
                       into
                       the
                       Sea
                       :
                       and
                       so
                       much
                       reason
                       and
                       nature
                       proveth
                       ,
                       and
                       (
                       which
                       importeth
                       )
                       Experience
                       confirmeth
                       .
                    
                     
                       10.
                       
                       In
                       the
                       tenth
                       place
                       I
                       come
                       to
                       consider
                       the
                       answer
                       that
                       was
                       made
                       to
                       another
                       Proposition
                       in
                       the
                       Letter
                       which
                       I
                       writ
                       to
                       Father
                       Francesco
                       ,
                       which
                       prudently
                       of
                       it self
                       alone
                       might
                       serve
                       to
                       clear
                       this
                       whole
                       businesse
                       .
                       I
                       said
                       in
                       my
                       Letter
                       ,
                       That
                       great
                       account
                       is
                       to
                       be
                       made
                       of
                       every
                       small
                       rising
                       and
                       ebbing
                       of
                       the
                       Waters
                       neer
                       to
                       the
                       Sea
                       in
                       
                         Fiume
                         morto
                      
                       ,
                       for
                       that
                       these
                       risings
                       and
                       fallings
                       ,
                       although
                       that
                       they
                       be
                       small
                       neer
                       to
                       the
                       Sea-side
                       ,
                       yet
                       neverthelesse
                       ,
                       they
                       operate
                       and
                       are
                       accompanied
                       by
                       notable
                       risings
                       and
                       fallings
                       within
                       Land
                       ,
                       and
                       far
                       from
                       the
                       Sea-side
                       ,
                       and
                       I
                       have
                       declared
                       by
                       an
                       example
                       of
                       Arno
                       ,
                       in
                       which
                       a
                       Land-flood
                       falling
                       ,
                       that
                       made
                       it
                       increase
                       above
                       its
                       ordinary
                       height
                       within
                       Pisa
                       six
                       or
                       seven
                       Braces
                       ,
                       that
                       this
                       height
                       of
                       the
                       same
                       Flood
                       becometh
                       still
                       lesser
                       ,
                       the
                       neerer
                       we
                       approach
                       to
                       the
                       Sea-coasts
                       .
                       Nor
                       shall
                       the
                       said
                       River
                       be
                       raised
                       hardly
                       half
                       a
                       Brace
                       ;
                       whereupon
                       it
                       necessrily
                       followeth
                       ,
                       that
                       if
                       I
                       should
                       return
                       to
                       the
                       Sea-side
                       ,
                       and
                       not
                       knowing
                       any
                       think
                       of
                       that
                       which
                       happeneth
                       at
                       Pisa
                       ,
                       and
                       seeing
                       
                       the
                       River
                       Arno
                       raised
                       by
                       a
                       Land-flood
                       half
                       a
                       Brace
                       ,
                       I
                       might
                       confidently
                       affirm
                       the
                       said
                       River
                       to
                       be
                       raised
                       in
                       Pisa
                       those
                       six
                       or
                       seven
                       Braces
                       ,
                       &c.
                       
                       From
                       such
                       like
                       accidents
                       I
                       conclude
                       in
                       the
                       same
                       Letter
                       ,
                       that
                       it
                       is
                       necessary
                       to
                       make
                       great
                       account
                       of
                       every
                       little
                       rise
                       that
                       
                         Fiume
                         morto
                      
                       shall
                       make
                       towards
                       the
                       Sea.
                       Now
                       cometh
                       Bartolotti
                       (
                       and
                       perhaps
                       because
                       I
                       knew
                       not
                       how
                       to
                       express
                       my self
                       better
                       ,
                       understandeth
                       not
                       my
                       Proposition
                       )
                       and
                       speaketh
                       that
                       which
                       indeed
                       is
                       true
                       ,
                       but
                       yet
                       besides
                       our
                       case
                       :
                       Nor
                       have
                       I
                       ever
                       said
                       the
                       contrary
                       ;
                       and
                       withall
                       doth
                       not
                       apply
                       it
                       to
                       his
                       purpose
                       .
                       Nay
                       I
                       say
                       ,
                       that
                       if
                       he
                       had
                       well
                       applyed
                       it
                       ,
                       this
                       alone
                       had
                       been
                       able
                       to
                       have
                       made
                       him
                       change
                       his
                       opinion
                       .
                       And
                       because
                       he
                       saith
                       ,
                       that
                       I
                       said
                       ,
                       that
                       it
                       is
                       true
                       ,
                       when
                       the
                       abatement
                       proceedeth
                       from
                       some
                       cause
                       above
                       ,
                       as
                       namely
                       by
                       Rain
                       ,
                       or
                       opening
                       of
                       Lakes
                       ;
                       But
                       when
                       the
                       cause
                       is
                       from
                       below
                       ,
                       that
                       is
                       ,
                       by
                       some
                       stop
                       ,
                       as
                       for
                       instance
                       some
                       Fishers
                       Wears
                       or
                       Locks
                       ,
                       or
                       some
                       impediment
                       remote
                       from
                       the
                       Sea
                       ,
                       although
                       at
                       the
                       Level
                       it
                       shall
                       rise
                       some
                       Braces
                       where
                       the
                       impediment
                       is
                       ,
                       yet
                       that
                       rising
                       shall
                       go
                       upwards
                       ;
                       and
                       here
                       he
                       finisheth
                       his
                       Discourse
                       ,
                       and
                       concludeth
                       not
                       any
                       thing
                       more
                       .
                       To
                       which
                       I
                       say
                       first
                       ,
                       that
                       I
                       have
                       also
                       said
                       the
                       same
                       in
                       the
                       Proposition
                       ,
                       namely
                       ,
                       that
                       a
                       Flood
                       coming
                       (
                       which
                       maketh
                       Arno
                       to
                       rise
                       in
                       Pisa
                       six
                       or
                       seven
                       Braces
                       (
                       which
                       I
                       take
                       to
                       be
                       a
                       superiour
                       cause
                       whether
                       it
                       be
                       Rain
                       or
                       the
                       opening
                       of
                       Lakes
                       ,
                       as
                       best
                       pleaseth
                       Bartolotti
                       )
                       in
                       such
                       a
                       case
                       I
                       say
                       ,
                       and
                       in
                       no
                       other
                       (
                       for
                       towards
                       the
                       Sea-coasts
                       it
                       shall
                       not
                       cause
                       a
                       rising
                       of
                       full
                       half
                       a
                       Brace
                       ;
                       and
                       therefore
                       seeing
                       Arno
                       at
                       the
                       Sea-side
                       to
                       be
                       raised
                       by
                       a
                       Flood
                       ,
                       whether
                       of
                       Rain
                       ,
                       or
                       of
                       opening
                       of
                       Lakes
                       half
                       a
                       Brace
                       )
                       it
                       may
                       be
                       inferred
                       ,
                       that
                       at
                       Pisa
                       it
                       shall
                       be
                       raised
                       those
                       six
                       or
                       seven
                       Braces
                       ;
                       which
                       variety
                       ,
                       well
                       considered
                       ,
                       explaineth
                       all
                       this
                       affair
                       in
                       favour
                       of
                       my
                       opinion
                       :
                       For
                       the
                       rising
                       that
                       is
                       made
                       by
                       the
                       impediment
                       placed
                       below
                       ,
                       of
                       Fishing
                       Weares
                       and
                       Locks
                       ,
                       operateth
                       at
                       the
                       beginning
                       ,
                       raising
                       the
                       Waters
                       that
                       are
                       neer
                       to
                       the
                       impediment
                       ;
                       and
                       afterwards
                       less
                       and
                       less
                       ,
                       as
                       we
                       retire
                       upwards
                       from
                       the
                       impediment
                       :
                       provided
                       yet
                       that
                       we
                       speak
                       not
                       of
                       a
                       Flood
                       that
                       commeth
                       by
                       accession
                       ,
                       but
                       onely
                       of
                       the
                       ordinary
                       Water
                       impeded
                       .
                       But
                       there
                       being
                       a
                       new
                       accession
                       ,
                       as
                       in
                       our
                       case
                       ,
                       then
                       the
                       Water
                       of
                       the
                       Flood
                       ,
                       I
                       say
                       ,
                       shall
                       make
                       a
                       greater
                       rising
                       in
                       the
                       parts
                       superiour
                       ,
                       far
                       from
                       the
                       impediment
                       ;
                       and
                       these
                       impediments
                       shall
                       come
                       to
                       be
                       those
                       that
                       shall
                       overflow
                       the
                       Plains
                       ,
                       as
                       happened
                       eighteen
                       or
                       nineteen
                       years
                       ago
                       ,
                       before
                       the
                       opening
                       of
                       
                         Fiume
                         morto
                      
                       into
                       the
                       Sea
                       ,
                       The
                       same
                       will
                       certainly
                       follow
                       ,
                       if
                       
                         Fiume
                         morto
                      
                       be
                       let
                       into
                       Serchio
                       .
                       Here
                       I
                       could
                       alledge
                       a
                       very
                       pretty
                       case
                       that
                       befell
                       me
                       in
                       la
                       *
                       
                         Campagna
                         di
                         Roma
                      
                       ,
                       neer
                       to
                       the
                       Sea-side
                       .
                       where
                       I
                       drained
                       a
                       Bog
                       or
                       Fen
                       ,
                       of
                       the
                       nature
                       of
                       the
                       Waters
                       of
                       Pisa
                       ,
                       and
                       I
                       succeeded
                       in
                       the
                       enterprize
                       ,
                       the
                       Waters
                       in
                       their
                       site
                       towards
                       the
                       Sea
                       abating
                       only
                       three
                       Palmes
                       ,
                       and
                       yet
                       in
                       the
                       
                       Fen
                       they
                       fell
                       more
                       than
                       fifteen
                       Palmes
                       .
                       But
                       the
                       businesse
                       would
                       be
                       long
                       ,
                       and
                       not
                       so
                       easily
                       to
                       be
                       declared
                       ,
                       and
                       I
                       am
                       certain
                       that
                       
                         Sig.
                         Bartolotti
                      
                       having
                       considered
                       this
                       ,
                       would
                       alter
                       his
                       judgment
                       ,
                       and
                       withall
                       would
                       know
                       that
                       remitting
                       that
                       impediment
                       anew
                       ,
                       which
                       I
                       had
                       left
                       for
                       lesse
                       than
                       three
                       I
                       almes
                       towards
                       the
                       Sea
                       ,
                       the
                       Waters
                       in
                       the
                       Fen
                       would
                       return
                       with
                       the
                       first
                       Floods
                       and
                       Raines
                       to
                       the
                       same
                       height
                       as
                       before
                       ,
                       as
                       likewise
                       
                         Fiume
                         morto
                      
                       will
                       do
                       if
                       it
                       shall
                       be
                       let
                       again
                       into
                       Serchio
                       .
                    
                     
                       Here
                       I
                       intreat
                       your
                       Honour
                       to
                       do
                       me
                       the
                       favour
                       to
                       importune
                       
                         P.
                         Francesco
                      
                       in
                       my
                       behalf
                       ,
                       that
                       he
                       would
                       be
                       pleased
                       to
                       declare
                       my
                       meaning
                       in
                       the
                       aforesaid
                       Letter
                       to
                       
                         Sig.
                         Bartolotti
                      
                       ,
                       for
                       I
                       hope
                       that
                       if
                       he
                       will
                       understand
                       this
                       point
                       ,
                       he
                       will
                       be
                       no
                       longer
                       so
                       tenacious
                       in
                       his
                       opinion
                       .
                    
                     
                       Next
                       that
                       these
                       Lords
                       in
                       the
                       Commission
                       of
                       Sewers
                       ,
                       with
                       the
                       Right
                       Honourable
                       the
                       Marquesse
                       of
                       S.
                       Angelo
                       ,
                       and
                       your
                       Honour
                       do
                       approve
                       of
                       my
                       judgment
                       ,
                       doth
                       very
                       much
                       rejoyce
                       me
                       ;
                       but
                       because
                       that
                       I
                       know
                       that
                       they
                       do
                       it
                       not
                       in
                       design
                       to
                       complement
                       me
                       ,
                       but
                       onely
                       to
                       serve
                       his
                       Highness
                       our
                       Grand
                       Duke
                       ,
                       I
                       freely
                       profess
                       that
                       I
                       will
                       pretend
                       no
                       farther
                       obligations
                       from
                       them
                       therein
                       ,
                       than
                       I
                       account
                       my self
                       to
                       owe
                       to
                       those
                       whose
                       opinions
                       are
                       contrary
                       to
                       mine
                       ,
                       for
                       that
                       I
                       know
                       that
                       they
                       have
                       the
                       same
                       end
                       .
                       The
                       definitive
                       sentence
                       of
                       this
                       whole
                       business
                       is
                       ,
                       that
                       they
                       give
                       these
                       Plains
                       ,
                       these
                       Draines
                       ,
                       and
                       these
                       Waters
                       farre
                       fetcht
                       appellations
                       .
                    
                     
                       11.
                       
                       As
                       to
                       the
                       quantity
                       of
                       the
                       Water
                       that
                       
                         Fiume
                         morto
                      
                       dischargeth
                       into
                       the
                       Sea
                       ,
                       there
                       are
                       very
                       great
                       disputes
                       about
                       it
                       ,
                       and
                       I
                       have
                       been
                       present
                       at
                       some
                       of
                       them
                       .
                       But
                       let
                       your
                       Honour
                       believe
                       me
                       ,
                       that
                       as
                       this
                       is
                       not
                       continual
                       ,
                       but
                       only
                       during
                       a
                       few
                       dayes
                       ,
                       so
                       it
                       will
                       never
                       be
                       of
                       any
                       great
                       prejudice
                       to
                       these
                       Fields
                       ;
                       and
                       if
                       your
                       Lordship
                       would
                       be
                       ascertained
                       thereof
                       ,
                       you
                       may
                       please
                       to
                       go
                       to
                       
                         Fiume
                         morto
                      
                       at
                       about
                       a
                       mile's
                       distance
                       from
                       the
                       Sea
                       ,
                       in
                       the
                       time
                       of
                       these
                       strong
                       Windes
                       ,
                       and
                       observe
                       the
                       current
                       from
                       thence
                       upwards
                       ,
                       for
                       you
                       shall
                       finde
                       it
                       extream
                       slow
                       ,
                       and
                       consequently
                       will
                       know
                       that
                       the
                       quantity
                       of
                       the
                       Water
                       that
                       is
                       repuls'd
                       is
                       very
                       small
                       .
                       And
                       this
                       seems
                       to
                       be
                       contradicted
                       by
                       the
                       rule
                       of
                       Risings
                       proceeding
                       from
                       causes
                       below
                       ,
                       which
                       occasion
                       no
                       considerable
                       alteration
                       far
                       from
                       the
                       Sea.
                       
                    
                     
                       I
                       am
                       necessitated
                       to
                       go
                       to
                       morrow
                       out
                       of
                       Rome
                       with
                       his
                       Eminence
                       Cardinal
                       Gaetano
                       about
                       certain
                       affairs
                       touching
                       Waters
                       ,
                       therefore
                       I
                       shall
                       not
                       farther
                       inlarge
                       ,
                       but
                       for
                       a
                       close
                       to
                       this
                       tedious
                       Discourse
                       ,
                       I
                       conclude
                       in
                       few
                       words
                       ,
                       that
                       
                         Fiume
                         morto
                      
                       is
                       by
                       no
                       means
                       to
                       be
                       let
                       into
                       Serchio
                       ,
                       nor
                       are
                       there
                       any
                       means
                       intermediate
                       courses
                       to
                       be
                       taken
                       ,
                       for
                       they
                       will
                       alwayes
                       be
                       prejudicial
                       ;
                       but
                       
                         Fiume
                         morto
                      
                       is
                       to
                       be
                       discharged
                       immediately
                       into
                       the
                       Sea.
                       When
                       it
                       is
                       stopt
                       up
                       by
                       the
                       fury
                       of
                       the
                       Sea-waves
                       ,
                       I
                       affirm
                       that
                       it
                       is
                       a
                       
                       sign
                       that
                       there
                       is
                       no
                       need
                       of
                       opening
                       it
                       ;
                       and
                       if
                       there
                       be
                       any
                       occasion
                       to
                       open
                       it
                       ,
                       it
                       is
                       easily
                       done
                       .
                       As
                       for
                       the
                       rest
                       your
                       Lordship
                       may
                       please
                       to
                       keep
                       account
                       of
                       all
                       the
                       particulars
                       that
                       occur
                       ,
                       for
                       the
                       memory
                       of
                       things
                       past
                       is
                       our
                       Tutresse
                       in
                       those
                       that
                       are
                       to
                       come
                       .
                       If
                       occasion
                       shall
                       offer
                       ,
                       I
                       intreat
                       you
                       to
                       bow
                       humbly
                       in
                       my
                       name
                       to
                       His
                       Highness
                       the
                       Grand
                       Duke
                       ,
                       and
                       the
                       most
                       Serene
                       Prince
                       Leopold
                       ;
                       and
                       to
                       attend
                       the
                       service
                       of
                       Their
                       Highnesses
                       ,
                       for
                       you
                       serve
                       Princes
                       of
                       extraordinary
                       merit
                       ;
                       And
                       to
                       whom
                       I
                       my self
                       am
                       also
                       exceedingly
                       obliged
                       .
                       In
                       the
                       controversies
                       that
                       arise
                       respect
                       the
                       pious
                       end
                       of
                       speaking
                       the
                       Truth
                       ,
                       for
                       then
                       every
                       thing
                       will
                       succeed
                       happily
                       .
                       I
                       kiss
                       the
                       hands
                       of
                       
                         Padre
                         Francesco
                      
                       ,
                       of
                       
                         Sig.
                         Bartolotti
                      
                       ,
                       and
                       of
                       your
                       Lordship
                       .
                    
                     
                       
                         Rome
                         ,
                         
                           14.
                           
                           March
                           1642.
                           
                        
                      
                       
                         Your
                         Honours
                         most
                         Obliged
                         Servant
                         D.
                         BENEDETTO
                         CASTELLI
                         .
                      
                    
                  
                
                 
                   Vpon
                   this
                   occasion
                   I
                   will
                   here
                   insert
                   a
                   Discourse
                   that
                   I
                   made
                   upon
                   the
                   Draining
                   and
                   improvement
                   of
                   the
                   
                     Pontine
                     Fens
                  
                   ,
                   for
                   that
                   I
                   think
                   that
                   whatsoever
                   may
                   be
                   done
                   well
                   and
                   to
                   purpose
                   in
                   this
                   matter
                   hath
                   absolute
                   dependance
                   on
                   the
                   perfect
                   knowledge
                   of
                   that
                   so
                   important
                   Proposition
                   ,
                   by
                   me
                   demonstrated
                   and
                   explained
                   in
                   my
                   Treatise
                   of
                   the
                   Mensuration
                   of
                   
                     Running
                     Waters
                  
                   ,
                   namely
                   ,
                   That
                   the
                   same
                   water
                   of
                   a
                   River
                   doth
                   continually
                   change
                   Measures
                   ,
                   according
                   as
                   it
                   altereth
                   and
                   changeth
                   the
                   velocity
                   of
                   its
                   course
                   ;
                   so
                   that
                   the
                   measure
                   of
                   the
                   thicknesse
                   of
                   a
                   River
                   in
                   one
                   Site
                   ,
                   to
                   the
                   measure
                   of
                   the
                   same
                   River
                   in
                   another
                   Site
                   ,
                   hath
                   the
                   same
                   proportion
                   reciprocally
                   that
                   the
                   velocity
                   in
                   this
                   site
                   hath
                   to
                   the
                   velocity
                   in
                   the
                   first
                   site
                   .
                   And
                   this
                   is
                   a
                   Truth
                   so
                   constant
                   and
                   unchangeable
                   ,
                   that
                   it
                   altereth
                   not
                   in
                   the
                   least
                   point
                   on
                   any
                   occurrences
                   of
                   the
                   Waters
                   that
                   change
                   :
                   and
                   being
                   well
                   understood
                   ,
                   it
                   openeth
                   the
                   way
                   to
                   the
                   knowledge
                   of
                   sundry
                   advertisements
                   in
                   these
                   matters
                   ,
                   which
                   are
                   all
                   resolved
                   by
                   this
                   sole
                   Principle
                   ;
                   and
                   from
                   it
                   are
                   derived
                   very
                   considerable
                   benefits
                   ;
                   and
                   without
                   these
                   it
                   is
                   impossible
                   to
                   do
                   any
                   thing
                   with
                   absolute
                   perfection
                   .
                
              
            
             
               
               
               
                 A
                 CONSIDERATION
                 Upon
                 the
                 DRAINING
                 OF
                 THE
                 Pontine
                 Fenns
                 .
                 BY
                 D.
                 BENEDETTO
                 CASTELLI
                 ,
                 Abbot
                 of
                 S.
                 BENEDETTO
                 ALOISIO
                 ,
                 and
                 Professor
                 of
                 the
                 Methematicks
                 to
                 P.
                 Vrban
                 VIII
                 .
                 in
                 the
                 University
                 of
                 ROME
                 .
              
               
                 CONSIDERATION
                 III.
                 
              
               
                 AMongst
                 the
                 enterprizes
                 by
                 me
                 esteemed
                 ,
                 if
                 not
                 absolutely
                 impossible
                 ,
                 ,
                 at
                 least
                 exceeding
                 difficult
                 ,
                 one
                 was
                 that
                 famous
                 one
                 of
                 Draining
                 the
                 
                   Pontine
                   Fenns
                
                 ;
                 and
                 therefore
                 I
                 was
                 thorowly
                 resolved
                 never
                 to
                 apply
                 my
                 minde
                 thereunto
                 ,
                 although
                 by
                 my
                 Patrons
                 I
                 should
                 be
                 commanded
                 to
                 the
                 same
                 :
                 accounting
                 that
                 it
                 was
                 an
                 occasion
                 rather
                 of
                 losing
                 reputation
                 by
                 the
                 miscarriage
                 of
                 the
                 attempt
                 ,
                 than
                 of
                 gaining
                 fame
                 by
                 reducing
                 things
                 to
                 a
                 better
                 pass
                 then
                 they
                 now
                 are
                 at
                 .
                 Yet
                 nevertheless
                 ,
                 having
                 of
                 late
                 years
                 observed
                 the
                 place
                 ,
                 and
                 sailed
                 through
                 those
                 Chanels
                 ,
                 and
                 those
                 Waters
                 ;
                 after
                 I
                 had
                 made
                 some
                 reflection
                 thereupon
                 ,
                 I
                 thought
                 that
                 the
                 enterprize
                 was
                 not
                 so
                 difficult
                 as
                 I
                 had
                 at
                 first
                 conceited
                 it
                 to
                 be
                 ;
                 and
                 I
                 am
                 the
                 more
                 confirmed
                 in
                 this
                 opinion
                 ,
                 upon
                 the
                 inducement
                 of
                 that
                 which
                 I
                 have
                 written
                 
                 Geometrically
                 in
                 my
                 Treatise
                 of
                 the
                 Mensuration
                 of
                 Running
                 Waters
                 ;
                 so
                 that
                 talking
                 with
                 several
                 persons
                 ,
                 I
                 adventured
                 to
                 affirm
                 ,
                 in
                 discoures
                 ,
                 that
                 this
                 improvement
                 might
                 possibly
                 be
                 brought
                 into
                 a
                 good
                 estate
                 .
              
               
                 Now
                 I
                 have
                 resolved
                 to
                 set
                 down
                 my
                 thoughts
                 in
                 writing
                 ,
                 and
                 to
                 honour
                 this
                 my
                 Paper
                 with
                 the
                 Noble
                 Name
                 of
                 your
                 Lordship
                 ,
                 to
                 render
                 it
                 the
                 more
                 credible
                 and
                 conspicuous
                 at
                 the
                 first
                 view
                 ,
                 if
                 it
                 should
                 chance
                 that
                 the
                 Subject
                 I
                 treat
                 of
                 ,
                 were
                 not
                 of
                 such
                 moment
                 ,
                 as
                 that
                 it
                 did
                 deserve
                 to
                 be
                 valued
                 for
                 any
                 other
                 reason
                 .
                 Pardon
                 me
                 ,
                 Sir
                 ,
                 if
                 I
                 have
                 been
                 too
                 bold
                 ,
                 and
                 continue
                 me
                 in
                 the
                 number
                 of
                 your
                 Servants
                 .
              
               
                 The
                 enterprize
                 of
                 Draining
                 a
                 great
                 part
                 of
                 the
                 Territories
                 of
                 the
                 
                   Pontine
                   Fenns
                
                 ,
                 hath
                 been
                 undertaken
                 both
                 in
                 the
                 time
                 of
                 the
                 antient
                 Romans
                 ,
                 and
                 last
                 of
                 all
                 ,
                 in
                 our
                 days
                 ;
                 yea
                 in
                 the
                 late
                 times
                 by
                 Sixtus
                 V.
                 I
                 do
                 not
                 doubt
                 in
                 the
                 least
                 ,
                 but
                 that
                 it
                 will
                 be
                 possible
                 yet
                 to
                 reduce
                 things
                 to
                 a
                 very
                 good
                 pass
                 ;
                 and
                 if
                 I
                 be
                 not
                 mistaken
                 ,
                 with
                 a
                 very
                 small
                 charge
                 in
                 comparison
                 of
                 the
                 profit
                 that
                 would
                 be
                 received
                 from
                 those
                 rich
                 Grounds
                 .
                 This
                 improvement
                 was
                 of
                 great
                 expence
                 in
                 the
                 time
                 of
                 
                   Sixtus
                   Quintus
                
                 ,
                 but
                 by
                 reason
                 the
                 thing
                 was
                 not
                 rightly
                 understood
                 ,
                 there
                 were
                 made
                 many
                 Drains
                 ;
                 a
                 great
                 part
                 of
                 which
                 were
                 unprofitable
                 and
                 vain
                 :
                 and
                 amongst
                 so
                 many
                 operations
                 ,
                 there
                 hapned
                 some
                 to
                 be
                 made
                 that
                 succeeded
                 ,
                 as
                 was
                 desired
                 ;
                 but
                 not
                 being
                 understood
                 ,
                 they
                 were
                 held
                 in
                 no
                 account
                 ;
                 and
                 thus
                 the
                 business
                 being
                 neglected
                 ,
                 the
                 waters
                 are
                 returned
                 into
                 the
                 same
                 state
                 as
                 they
                 were
                 at
                 first
                 ,
                 before
                 the
                 improvement
                 .
                 Here
                 I
                 have
                 by
                 familiar
                 discourses
                 with
                 my
                 friends
                 ,
                 explained
                 this
                 enterprize
                 undertaken
                 by
                 Sixtus
                 V.
                 and
                 haply
                 also
                 by
                 some
                 more
                 antient
                 ,
                 with
                 the
                 example
                 of
                 the
                 Fable
                 of
                 Orilo
                 ,
                 in
                 Ariosto
                 .
                 This
                 Monster
                 was
                 made
                 up
                 with
                 such
                 enchantment
                 ,
                 that
                 men
                 fought
                 with
                 him
                 alwayes
                 in
                 vain
                 ;
                 for
                 though
                 in
                 the
                 Combate
                 he
                 were
                 cut
                 in
                 pieces
                 ,
                 those
                 divided
                 Members
                 presently
                 re-united
                 ,
                 and
                 returned
                 to
                 the
                 fight
                 more
                 fierce
                 then
                 ever
                 .
                 But
                 the
                 
                   Paladine
                   Astolfo
                
                 coming
                 to
                 undertake
                 him
                 ,
                 after
                 a
                 long
                 dispute
                 ,
                 at
                 the
                 end
                 he
                 cut
                 his
                 head
                 sheer
                 off
                 from
                 the
                 shoulders
                 at
                 one
                 blow
                 ;
                 and
                 nimbly
                 alighting
                 from
                 his
                 Horse
                 ,
                 took
                 the
                 Monstrous
                 head
                 ,
                 and
                 mounting
                 again
                 ,
                 as
                 he
                 rid
                 away
                 he
                 fell
                 to
                 shave
                 the
                 Pole
                 of
                 that
                 Monster
                 ,
                 and
                 so
                 he
                 lost
                 the
                 Lock
                 of
                 Hair
                 ,
                 in
                 which
                 alone
                 the
                 enchantment
                 lay
                 ;
                 and
                 then
                 the
                 horrible
                 Head
                 in
                 an
                 instant
                 manifested
                 signs
                 of
                 death
                 ,
                 and
                 the
                 trunk
                 which
                 ran
                 ,
                 seeking
                 to
                 reunite
                 to
                 it
                 anew
                 ,
                 gave
                 the
                 last
                 gasp
                 ,
                 and
                 in
                 this
                 manner
                 the
                 enchantment
                 ended
                 .
                 The
                 Book
                 of
                 Fate
                 served
                 admirably
                 to
                 the
                 Paladine
                 ,
                 whereby
                 he
                 came
                 to
                 understand
                 that
                 Charm
                 ;
                 for
                 by
                 shaving
                 his
                 whole
                 head
                 ,
                 the
                 enchanted
                 hairs
                 came
                 to
                 be
                 cut
                 off
                 amongst
                 the
                 rest
                 :
                 In
                 the
                 same
                 manner
                 ,
                 I
                 say
                 ,
                 that
                 i●
                 hath
                 sometimes
                 happened
                 in
                 Draining
                 those
                 Fields
                 ;
                 
                 for
                 that
                 amongst
                 so
                 many
                 tryals
                 as
                 have
                 been
                 made
                 ,
                 that
                 also
                 was
                 light
                 upon
                 ,
                 on
                 which
                 the
                 improvement
                 and
                 remedy
                 to
                 the
                 disorder
                 did
                 depend
                 .
                 And
                 to
                 us
                 my
                 fore-named
                 Treatise
                 shall
                 serve
                 for
                 a
                 Rule
                 ,
                 which
                 being
                 well
                 understood
                 ,
                 shall
                 make
                 us
                 to
                 know
                 wherein
                 consisteth
                 ,
                 and
                 whereon
                 dependeth
                 this
                 miscarriage
                 ,
                 and
                 consequently
                 it
                 will
                 be
                 easie
                 to
                 apply
                 thereunto
                 a
                 seasonable
                 remedy
                 .
              
               
               
                 Another
                 head
                 to
                 which
                 these
                 harms
                 may
                 be
                 reduced
                 ,
                 but
                 proceeding
                 from
                 the
                 same
                 Root
                 ,
                 which
                 hath
                 a
                 great
                 part
                 in
                 this
                 disorder
                 ,
                 is
                 the
                 impediment
                 of
                 those
                 Wears
                 in
                 the
                 River
                 which
                 are
                 made
                 by
                 heightning
                 the
                 bed
                 of
                 the
                 same
                 ,
                 for
                 placing
                 of
                 fishing-nets
                 ;
                 of
                 which
                 Piscaries
                 I
                 reckoned
                 above
                 ten
                 ,
                 when
                 I
                 made
                 a
                 voyage
                 thorow
                 those
                 waters
                 to
                 Sandolo
                 .
                 And
                 these
                 Fishing-Wears
                 are
                 such
                 impediments
                 ,
                 that
                 some
                 one
                 of
                 them
                 makes
                 the
                 water
                 of
                 the
                 River
                 in
                 the
                 upper
                 part
                 to
                 rise
                 half
                 a
                 Palm
                 ,
                 and
                 sometimes
                 a
                 whole
                 Palm
                 ,
                 and
                 more
                 ;
                 so
                 that
                 when
                 they
                 are
                 all
                 gathered
                 together
                 ,
                 these
                 impediments
                 amount
                 to
                 more
                 than
                 seven
                 ,
                 or
                 possibly
                 than
                 eight
                 Palms
                 .
              
               
                 There
                 concurreth
                 for
                 a
                 third
                 most
                 Potent
                 Cause
                 of
                 the
                 waters
                 continuing
                 high
                 in
                 the
                 evacuating
                 ,
                 or
                 Draining
                 Chanel
                 ,
                 and
                 consequently
                 on
                 the
                 Plains
                 ;
                 The
                 great
                 abundance
                 of
                 water
                 that
                 issueth
                 from
                 
                   Fiume
                   Sisto
                
                 ,
                 the
                 waters
                 of
                 which
                 do
                 not
                 keep
                 within
                 its
                 Banks
                 when
                 they
                 are
                 abundant
                 ;
                 but
                 encreasing
                 above
                 its
                 Chanel
                 ,
                 they
                 unite
                 with
                 those
                 of
                 the
                 Evacuator
                 ,
                 and
                 dispersing
                 thorow
                 
                 the
                 Fens
                 are
                 raised
                 with
                 great
                 prejudice
                 ,
                 and
                 much
                 greater
                 than
                 is
                 conceived
                 ,
                 according
                 to
                 what
                 hath
                 been
                 demonstrated
                 in
                 the
                 Second
                 Consideration
                 upon
                 the
                 
                   Lake
                   of
                   Venice
                
                 .
                 Nor
                 is
                 it
                 to
                 any
                 purpose
                 to
                 say
                 ,
                 that
                 if
                 we
                 should
                 measure
                 all
                 the
                 Waters
                 that
                 disimbogue
                 from
                 
                   Fiume
                   Sisto
                
                 ,
                 and
                 gather
                 them
                 into
                 one
                 summe
                 ,
                 we
                 should
                 not
                 finde
                 them
                 to
                 be
                 such
                 ,
                 as
                 that
                 they
                 shall
                 be
                 able
                 to
                 make
                 the
                 Waters
                 of
                 the
                 Fens
                 to
                 increase
                 ,
                 by
                 reason
                 of
                 the
                 great
                 expansion
                 of
                 them
                 ,
                 over
                 which
                 that
                 body
                 of
                 water
                 is
                 to
                 distend
                 :
                 for
                 to
                 this
                 instance
                 we
                 answer
                 with
                 that
                 which
                 we
                 have
                 given
                 notice
                 of
                 in
                 the
                 First
                 Consideration
                 touching
                 the
                 
                   Lake
                   of
                   Venice
                
                 ,
                 treating
                 of
                 the
                 abatement
                 that
                 is
                 caused
                 by
                 the
                 Brent
                 let
                 into
                 the
                 Lake
                 .
                 And
                 moreover
                 ,
                 if
                 I
                 shall
                 adde
                 thereto
                 that
                 which
                 I
                 write
                 in
                 the
                 Second
                 Consideration
                 ,
                 it
                 will
                 be
                 very
                 apparent
                 how
                 greatly
                 harmfull
                 and
                 prejudicial
                 these
                 excursions
                 of
                 Waters
                 from
                 
                   Fiume
                   Sisto
                
                 may
                 be
                 ,
                 which
                 are
                 not
                 kept
                 under
                 ,
                 and
                 confined
                 within
                 the
                 River
                 :
                 Therefore
                 ,
                 proceeding
                 to
                 the
                 provisions
                 ,
                 and
                 operations
                 that
                 are
                 to
                 be
                 accounted
                 Principall
                 ,
                 I
                 reduce
                 them
                 to
                 three
                 Heads
                 .
              
               
                 In
                 the
                 first
                 place
                 it
                 is
                 necessary
                 to
                 throw
                 down
                 those
                 Weares
                 ,
                 and
                 to
                 take
                 the
                 Pisciaries
                 quite
                 away
                 ,
                 observing
                 a
                 Maxime
                 ,
                 in
                 my
                 judgment
                 ,
                 infallible
                 ,
                 that
                 Fishing
                 and
                 Sowing
                 are
                 two
                 things
                 that
                 can
                 never
                 consist
                 together
                 ;
                 Fishing
                 being
                 on
                 the
                 Water
                 ,
                 and
                 Sowing
                 on
                 land
                 .
              
               
                 Secondly
                 ,
                 it
                 will
                 be
                 necessary
                 to
                 cut
                 under
                 Water
                 in
                 the
                 bottome
                 of
                 the
                 River
                 those
                 Weeds
                 and
                 Plants
                 that
                 grow
                 and
                 increase
                 in
                 the
                 River
                 ,
                 and
                 leave
                 them
                 to
                 be
                 carried
                 into
                 the
                 Sea
                 by
                 the
                 Stream
                 ;
                 for
                 by
                 this
                 means
                 these
                 Reeds
                 shall
                 not
                 spring
                 up
                 and
                 distend
                 along
                 the
                 bottome
                 of
                 the
                 River
                 ,
                 by
                 means
                 of
                 the
                 Beasts
                 treading
                 upon
                 them
                 ;
                 And
                 the
                 same
                 ought
                 to
                 be
                 done
                 often
                 ,
                 and
                 with
                 care
                 ,
                 and
                 must
                 not
                 be
                 delaied
                 till
                 the
                 mischief
                 increase
                 ,
                 and
                 the
                 Champain
                 Grounds
                 be
                 drowned
                 ,
                 but
                 one
                 ought
                 to
                 order
                 matters
                 so
                 ,
                 as
                 that
                 they
                 may
                 not
                 drown
                 .
                 And
                 I
                 will
                 affirm
                 ,
                 that
                 otherwise
                 this
                 principal
                 point
                 would
                 become
                 a
                 most
                 considerable
                 inconvenience
                 .
              
               
                 Thirdly
                 ,
                 it
                 is
                 necessary
                 to
                 make
                 good
                 the
                 Banks
                 of
                 
                   Fiume
                   Sisto
                
                 on
                 the
                 left
                 hand
                 ,
                 and
                 to
                 procure
                 that
                 those
                 Waters
                 may
                 run
                 in
                 the
                 Chanel
                 ,
                 and
                 not
                 break
                 forth
                 .
                 And
                 it
                 is
                 to
                 be
                 noted
                 ,
                 that
                 it
                 is
                 not
                 enough
                 to
                 do
                 one
                 or
                 two
                 of
                 those
                 things
                 ,
                 but
                 we
                 are
                 to
                 put
                 them
                 all
                 in
                 execution
                 ;
                 for
                 omitting
                 any
                 thing
                 ,
                 the
                 whole
                 machine
                 will
                 be
                 out
                 of
                 tune
                 ,
                 and
                 spoiled
                 .
                 But
                 proceeding
                 with
                 due
                 care
                 ,
                 you
                 shall
                 not
                 only
                 Drain
                 the
                 
                   Pontine
                   Fens
                
                 ,
                 but
                 by
                 means
                 of
                 this
                 last
                 particular
                 the
                 Current
                 of
                 
                   Fiume
                   Sisto
                
                 shall
                 scowr
                 its
                 own
                 Chanel
                 of
                 its
                 self
                 ,
                 even
                 to
                 the
                 carrying
                 part
                 of
                 it
                 away
                 :
                 and
                 haply
                 with
                 this
                 abundance
                 of
                 water
                 that
                 it
                 shall
                 
                 bear
                 ,
                 the
                 Mouth
                 
                   della
                   Torre
                
                 may
                 be
                 opened
                 ,
                 and
                 kept
                 open
                 into
                 the
                 Sea.
                 And
                 it
                 would
                 ,
                 last
                 of
                 all
                 ,
                 be
                 of
                 admirable
                 benefit
                 to
                 cleanse
                 
                   Fiume
                   Sisto
                
                 from
                 many
                 Trees
                 and
                 Bushes
                 wherewith
                 it
                 is
                 overgrown
                 .
              
               
                 And
                 with
                 this
                 I
                 conclude
                 ,
                 that
                 the
                 Improvement
                 or
                 Drain
                 possible
                 to
                 be
                 made
                 consisteth
                 in
                 these
                 three
                 particulars
                 .
                 First
                 ,
                 in
                 taking
                 away
                 the
                 Fishing
                 Weares
                 ,
                 leaving
                 the
                 Course
                 of
                 the
                 Waters
                 free
                 .
                 Secondly
                 ,
                 in
                 keeping
                 the
                 Principal
                 Rivers
                 clear
                 from
                 Weeds
                 and
                 Plants
                 .
                 Thirdly
                 ,
                 in
                 keeping
                 the
                 water
                 of
                 
                   Fiume
                   Sisto
                
                 in
                 its
                 own
                 Chanel
                 .
                 All
                 which
                 are
                 things
                 that
                 may
                 be
                 done
                 with
                 very
                 little
                 charge
                 ,
                 and
                 to
                 the
                 manifest
                 benefit
                 of
                 the
                 whole
                 Country
                 ,
                 and
                 to
                 the
                 rendering
                 the
                 Air
                 wholsomer
                 in
                 all
                 those
                 Places
                 adjoyning
                 to
                 the
                 
                   Pontine
                   Fens
                
                 .
              
            
             
               
               
                 A
                 CONSIDERATION
                 Upon
                 the
                 DRAINING
                 Of
                 the
                 Territories
                 of
                 Bologna
                 ,
                 Ferrara
                 ,
                 AND
                 Romagna
                 .
              
               
                 BY
                 D.
                 BENEDETTO
                 CASTELLI
                 ,
                 Abbot
                 of
                 S.
                 BENEDETTO
                 ALOISIO
                 ,
                 Mathematician
                 to
                 P.
                 Vrban
                 VIII
                 .
                 and
                 Professor
                 in
                 the
                 University
                 of
                 ROME
                 .
              
               
                 THe
                 weghty
                 businesse
                 of
                 the
                 Draining
                 of
                 the
                 Territories
                 of
                 
                   Bologna
                   ,
                   Ferrara
                
                 ,
                 and
                 Romagna
                 having
                 been
                 punctually
                 handled
                 and
                 declared
                 in
                 writing
                 from
                 the
                 excellent
                 memory
                 of
                 the
                 Right
                 Honourable
                 and
                 Noble
                 
                   Monsignore
                   Corsini
                
                 ,
                 who
                 was
                 heretofore
                 Deputed
                 Commissary
                 General
                 ,
                 and
                 Visitor
                 of
                 those
                 Waters
                 ;
                 I
                 am
                 not
                 able
                 to
                 make
                 such
                 another
                 Discourse
                 upon
                 the
                 same
                 Subject
                 ,
                 but
                 will
                 only
                 say
                 somewhat
                 for
                 farther
                 confirmation
                 of
                 that
                 which
                 I
                 have
                 said
                 in
                 this
                 Book
                 upon
                 the
                 
                   Lake
                   of
                   Venice
                
                 ,
                 upon
                 the
                 
                   Pontine
                   Fens
                
                 ,
                 and
                 upon
                 the
                 Draining
                 of
                 those
                 Plains
                 of
                 Pisa
                 ,
                 lying
                 between
                 the
                 Rivers
                 Arno
                 and
                 Serchio
                 ;
                 whereby
                 it
                 is
                 manifest
                 ,
                 that
                 in
                 all
                 the
                 
                 aforementioned
                 Cases
                 ,
                 and
                 in
                 the
                 present
                 one
                 that
                 we
                 are
                 in
                 hand
                 with
                 ,
                 there
                 have
                 ,
                 in
                 times
                 past
                 ,
                 very
                 grosse
                 Errours
                 been
                 committed
                 ,
                 through
                 the
                 not
                 having
                 ever
                 well
                 understood
                 the
                 true
                 measure
                 of
                 Running
                 waters
                 ;
                 and
                 here
                 it
                 is
                 to
                 be
                 noted
                 ,
                 that
                 the
                 businesse
                 is
                 ,
                 that
                 in
                 Venice
                 ,
                 the
                 diversion
                 of
                 the
                 waters
                 of
                 the
                 Lake
                 ,
                 by
                 diverting
                 the
                 Brent
                 was
                 debated
                 ,
                 and
                 in
                 part
                 executed
                 ,
                 without
                 consideration
                 had
                 how
                 great
                 abatement
                 of
                 water
                 might
                 follow
                 in
                 the
                 Lake
                 ,
                 if
                 the
                 Brent
                 were
                 diverted
                 ,
                 as
                 I
                 have
                 shewn
                 in
                 the
                 first
                 Consideration
                 upon
                 this
                 particular
                 ,
                 from
                 which
                 act
                 there
                 hath
                 insued
                 very
                 bad
                 consequences
                 ,
                 not
                 only
                 the
                 difficulty
                 of
                 Navigation
                 ,
                 but
                 it
                 hath
                 infected
                 the
                 wholsomnesse
                 of
                 the
                 Air
                 ,
                 and
                 caused
                 the
                 stoppage
                 of
                 the
                 Ports
                 of
                 Venice
                 .
                 And
                 on
                 the
                 contrary
                 ,
                 the
                 same
                 inadvertency
                 of
                 not
                 considering
                 what
                 rising
                 of
                 the
                 Water
                 the
                 Reno
                 ,
                 and
                 other
                 Rivers
                 being
                 opened
                 into
                 the
                 Valleys
                 of
                 Bologna
                 and
                 Ferrara
                 ,
                 might
                 cause
                 in
                 the
                 said
                 Valleys
                 ,
                 is
                 the
                 certain
                 cause
                 that
                 so
                 many
                 rich
                 and
                 fertile
                 Fields
                 are
                 drowned
                 under
                 water
                 ,
                 converting
                 the
                 happy
                 habitations
                 and
                 dwellings
                 of
                 men
                 into
                 miserable
                 receptacles
                 for
                 Fishes
                 :
                 Things
                 which
                 doubtlesse
                 would
                 never
                 have
                 happened
                 ,
                 if
                 those
                 Rivers
                 had
                 been
                 kept
                 at
                 their
                 height
                 ,
                 and
                 Reno
                 had
                 been
                 turn'd
                 into
                 Main-Po
                 ,
                 and
                 the
                 other
                 Rivers
                 into
                 that
                 of
                 Argenta
                 ,
                 and
                 of
                 Volano
                 .
                 Now
                 there
                 having
                 sufficient
                 been
                 spoken
                 by
                 the
                 above-named
                 
                   Monsig
                   .
                   Corsini
                
                 in
                 his
                 Relation
                 ,
                 I
                 will
                 only
                 adde
                 one
                 conceit
                 of
                 my
                 own
                 ,
                 which
                 after
                 the
                 Rivers
                 should
                 be
                 regulated
                 ,
                 as
                 hath
                 been
                 said
                 ,
                 I
                 verily
                 believe
                 would
                 be
                 of
                 extraordinary
                 profit
                 ,
                 I
                 much
                 doubt
                 indeed
                 that
                 I
                 shall
                 finde
                 it
                 a
                 hard
                 matter
                 to
                 perswade
                 men
                 to
                 be
                 of
                 my
                 mind
                 ,
                 but
                 yet
                 nevertheless
                 I
                 will
                 not
                 question
                 ,
                 but
                 that
                 those
                 ,
                 at
                 least
                 ,
                 who
                 shall
                 have
                 understood
                 what
                 I
                 have
                 said
                 and
                 demonstrated
                 concerning
                 the
                 manners
                 and
                 proportions
                 ,
                 according
                 to
                 which
                 the
                 abatements
                 and
                 risings
                 of
                 Running
                 waters
                 proceed
                 ,
                 that
                 are
                 made
                 by
                 the
                 Diversions
                 and
                 Introductions
                 of
                 VVaters
                 ,
                 will
                 apprehend
                 that
                 my
                 conjecture
                 is
                 grounded
                 upon
                 Reason
                 ,
                 And
                 although
                 I
                 descend
                 not
                 to
                 the
                 exactnesse
                 of
                 particulars
                 ,
                 I
                 will
                 open
                 the
                 way
                 to
                 others
                 ,
                 who
                 having
                 observed
                 the
                 requisite
                 Rules
                 of
                 considering
                 the
                 quantity
                 of
                 the
                 waters
                 that
                 are
                 introduced
                 ,
                 or
                 that
                 happen
                 to
                 be
                 diverted
                 ,
                 shall
                 be
                 able
                 with
                 punctuality
                 to
                 examine
                 the
                 whole
                 businesse
                 ,
                 and
                 then
                 resolve
                 on
                 that
                 which
                 shall
                 be
                 expedient
                 to
                 be
                 done
                 .
              
               
                 Reflecting
                 therefore
                 upon
                 the
                 first
                 Proposition
                 ,
                 that
                 the
                 Risings
                 of
                 a
                 Running
                 Water
                 made
                 by
                 the
                 accession
                 of
                 new
                 water
                 into
                 the
                 River
                 ,
                 are
                 to
                 one
                 another
                 ,
                 as
                 the
                 Square-Roots
                 of
                 the
                 quantity
                 of
                 the
                 water
                 that
                 runneth
                 ;
                 and
                 consequently
                 ,
                 that
                 the
                 same
                 cometh
                 to
                 pass
                 in
                 the
                 Diversions
                 :
                 Insomuch
                 ,
                 that
                 a
                 River
                 running
                 in
                 height
                 one
                 such
                 a
                 certain
                 measure
                 ,
                 to
                 make
                 it
                 encrease
                 double
                 in
                 height
                 ,
                 the
                 water
                 is
                 to
                 be
                 encreased
                 to
                 three
                 times
                 as
                 
                 much
                 as
                 it
                 ran
                 before
                 ;
                 so
                 that
                 when
                 the
                 water
                 shall
                 be
                 quadruple
                 ,
                 the
                 height
                 shall
                 be
                 double
                 ;
                 and
                 if
                 the
                 water
                 were
                 centuple
                 ,
                 the
                 height
                 would
                 be
                 decuple
                 onely
                 ,
                 and
                 so
                 from
                 one
                 quantity
                 to
                 another
                 :
                 And
                 on
                 the
                 contrary
                 ,
                 in
                 the
                 Diversions
                 ;
                 If
                 of
                 the
                 100.
                 parts
                 of
                 water
                 that
                 run
                 thorow
                 a
                 River
                 ,
                 there
                 shall
                 be
                 diverted
                 19
                 /
                 100
                 ,
                 the
                 height
                 of
                 the
                 River
                 diminisheth
                 onely
                 1
                 /
                 10
                 ,
                 and
                 continuing
                 to
                 divert
                 17
                 /
                 100
                 ,
                 the
                 height
                 of
                 the
                 River
                 abateth
                 likewise
                 1
                 /
                 10
                 ,
                 and
                 so
                 proceeding
                 to
                 divert
                 15
                 /
                 100
                 and
                 then
                 13
                 /
                 100
                 ,
                 and
                 then
                 11
                 /
                 100
                 ,
                 and
                 then
                 9
                 /
                 100
                 ,
                 and
                 then
                 7
                 /
                 100
                 ,
                 and
                 then
                 5
                 /
                 100
                 ,
                 and
                 then
                 3
                 /
                 100
                 ,
                 alwaies
                 by
                 each
                 of
                 these
                 diversions
                 ,
                 the
                 height
                 of
                 the
                 Running
                 Water
                 diminisheth
                 the
                 tenth
                 part
                 :
                 although
                 that
                 the
                 diversions
                 be
                 so
                 unequal
                 .
                 Reflecting
                 I
                 say
                 upon
                 this
                 infallible
                 Truth
                 ,
                 I
                 have
                 had
                 a
                 conceit
                 ,
                 that
                 though
                 the
                 Reno
                 and
                 other
                 Rivers
                 were
                 diverted
                 from
                 the
                 Valleyes
                 ,
                 and
                 there
                 was
                 onely
                 left
                 the
                 
                   Chanel
                   of
                   Navigation
                
                 ,
                 which
                 was
                 onely
                 the
                 1
                 /
                 20
                 part
                 of
                 the
                 whole
                 water
                 that
                 falleth
                 into
                 the
                 Valleys
                 ;
                 yet
                 nevertheless
                 ,
                 the
                 water
                 in
                 those
                 same
                 Valleyes
                 would
                 retain
                 a
                 tenth
                 part
                 of
                 that
                 height
                 that
                 became
                 conjoyned
                 by
                 the
                 concourse
                 of
                 all
                 the
                 Rivers
                 :
                 And
                 therefore
                 I
                 should
                 think
                 that
                 it
                 were
                 the
                 best
                 resolution
                 to
                 maintain
                 the
                 
                   Chanel
                   of
                   Navigation
                
                 (
                 if
                 it
                 were
                 possible
                 )
                 continuate
                 unto
                 the
                 Po
                 of
                 Ferrara
                 ,
                 and
                 from
                 thence
                 to
                 carry
                 it
                 into
                 the
                 Po
                 of
                 Volano
                 ,
                 for
                 besides
                 that
                 it
                 would
                 be
                 of
                 very
                 great
                 ease
                 in
                 the
                 Navigation
                 of
                 Bologna
                 ,
                 and
                 Ferrara
                 ,
                 the
                 said
                 water
                 would
                 render
                 the
                 Po
                 of
                 Volano
                 navigable
                 as
                 far
                 as
                 to
                 the
                 very
                 Walls
                 of
                 Ferrara
                 ,
                 and
                 consequently
                 the
                 Navigation
                 would
                 be
                 continuate
                 from
                 Bologna
                 to
                 the
                 Sea-side
                 .
              
               
                 But
                 to
                 manage
                 this
                 enterprize
                 well
                 ,
                 it
                 is
                 necessary
                 to
                 measure
                 the
                 quantity
                 of
                 the
                 Water
                 that
                 the
                 Rivers
                 discharge
                 into
                 the
                 Valleys
                 ,
                 and
                 that
                 which
                 the
                 
                   Chanel
                   of
                   Navigation
                
                 carryeth
                 ,
                 in
                 manner
                 as
                 I
                 have
                 demonstrated
                 at
                 the
                 beginning
                 of
                 this
                 Book
                 ;
                 for
                 this
                 once
                 known
                 ,
                 we
                 shall
                 also
                 come
                 to
                 know
                 ,
                 how
                 profitable
                 this
                 diversion
                 of
                 the
                 
                   Chanel
                   of
                   Navigation
                
                 from
                 the
                 Valleys
                 is
                 like
                 to
                 prove
                 ;
                 which
                 yet
                 would
                 still
                 be
                 unprofitable
                 ,
                 if
                 so
                 be
                 that
                 all
                 the
                 Rivers
                 that
                 discharge
                 their
                 waters
                 into
                 the
                 Valleys
                 ,
                 should
                 not
                 first
                 be
                 Drained
                 ,
                 according
                 to
                 what
                 hath
                 been
                 above
                 advertised
                 .
              
               
                 
                   Abbot
                   CASTELLI
                
                 ,
                 in
                 the
                 present
                 consideration
                 referring
                 himself
                 to
                 the
                 Relation
                 of
                 
                   Monsig
                   .
                   Corsini
                
                 ,
                 grounded
                 upon
                 the
                 Observations
                 and
                 Precepts
                 of
                 the
                 said
                 Abbot
                 ;
                 as
                 is
                 seen
                 in
                 the
                 present
                 Discourse
                 .
                 I
                 thought
                 it
                 convenient
                 for
                 the
                 compleating
                 of
                 the
                 Work
                 of
                 our
                 Authour
                 ,
                 upon
                 these
                 subjects
                 ,
                 to
                 insert
                 it
                 in
                 this
                 place
                 .
              
            
             
               
               
                 A
                 Relation
                 of
                 the
                 Waters
                 in
                 the
                 Territories
                 of
                 Bologna
                 and
                 Ferrara
                 .
              
               
                 BY
                 The
                 Right
                 Honourable
                 and
                 Illustrious
                 ,
                 Monsignore
                 CORSINI
                 ,
                 a
                 Native
                 of
                 Tuscany
                 ,
                 Superintendent
                 of
                 the
                 general
                 DRAINS
                 ,
                 and
                 President
                 of
                 Romagna
                 .
              
               
                 THe
                 Rheno
                 ,
                 and
                 other
                 Brooks
                 of
                 Romagna
                 ,
                 were
                 by
                 the
                 advice
                 of
                 
                   P.
                   Agostino
                   Spernazzati
                
                 the
                 Jesuite
                 ,
                 towards
                 the
                 latter
                 end
                 of
                 the
                 time
                 of
                 
                   Pope
                   Clement
                
                 VIII
                 .
                 notwithstanding
                 the
                 opposition
                 of
                 the
                 Bolognesi
                 ,
                 and
                 others
                 concerned
                 therein
                 ,
                 diverted
                 from
                 their
                 Chanels
                 ,
                 for
                 the
                 more
                 commodious
                 cleansing
                 of
                 the
                 Po
                 of
                 Ferrara
                 ,
                 and
                 of
                 its
                 two
                 Branches
                 of
                 Primaro
                 ,
                 and
                 Volano
                 ;
                 in
                 order
                 to
                 the
                 introducing
                 the
                 water
                 of
                 the
                 Main-Po
                 into
                 them
                 ,
                 to
                 the
                 end
                 that
                 their
                 wonted
                 Torrents
                 being
                 restored
                 ,
                 they
                 might
                 carry
                 the
                 Muddy-water
                 thence
                 into
                 the
                 Sea
                 ,
                 and
                 restore
                 to
                 the
                 City
                 the
                 Navigation
                 which
                 was
                 last
                 ,
                 as
                 is
                 manifest
                 by
                 the
                 Brief
                 of
                 the
                 said
                 
                   Pope
                   Clement
                
                 ,
                 directed
                 to
                 the
                 
                   Cardinal
                   San
                   Clemence
                
                 ,
                 bearing
                 date
                 the
                 22.
                 of
                 August
                 ,
                 1604.
                 
              
               
                 The
                 work
                 of
                 the
                 said
                 cleansing
                 ,
                 and
                 introducing
                 of
                 the
                 said
                 Po
                 ,
                 either
                 as
                 being
                 such
                 in
                 it self
                 ,
                 or
                 by
                 the
                 contention
                 of
                 the
                 
                   Cardinal
                   Legates
                
                 then
                 in
                 these
                 parts
                 ;
                 and
                 the
                 jarrings
                 that
                 hapned
                 betwixt
                 them
                 ,
                 proved
                 so
                 difficult
                 ,
                 that
                 after
                 the
                 expence
                 of
                 vast
                 summs
                 in
                 the
                 space
                 of
                 21.
                 years
                 ,
                 there
                 hath
                 been
                 nothing
                 done
                 ,
                 save
                 the
                 rendring
                 of
                 it
                 the
                 more
                 difficult
                 to
                 be
                 effected
                 .
              
               
                 Interim
                 ,
                 the
                 Torrents
                 with
                 their
                 waters
                 ,
                 both
                 muddy
                 and
                 clear
                 ,
                 have
                 damaged
                 the
                 Grounds
                 lying
                 on
                 the
                 right
                 hand
                 of
                 the
                 Po
                 of
                 Argenta
                 ,
                 and
                 the
                 Rheno
                 those
                 on
                 its
                 Banks
                 ;
                 of
                 which
                 I
                 will
                 speak
                 in
                 the
                 first
                 place
                 ,
                 as
                 of
                 that
                 which
                 is
                 of
                 greater
                 importance
                 ,
                 and
                 from
                 which
                 the
                 principal
                 cause
                 of
                 the
                 mischiefs
                 that
                 result
                 from
                 the
                 rest
                 doth
                 proceed
                 .
              
               
                 This
                 Rheno
                 having
                 overflowed
                 the
                 *
                 Tennency
                 of
                 Sanmartina
                 ,
                 in
                 circumference
                 about
                 fourteen
                 miles
                 given
                 it
                 before
                 ,
                 and
                 part
                 of
                 that
                 of
                 Cominale
                 given
                 it
                 afterwards
                 ,
                 as
                 it
                 were
                 ,
                 for
                 a
                 receptacle
                 ;
                 from
                 whence
                 ,
                 having
                 deposed
                 the
                 matter
                 of
                 its
                 muddiness
                 ,
                 it
                 issued
                 clear
                 by
                 the
                 Mouths
                 of
                 Masi
                 ,
                 and
                 of
                 Lievaloro
                 ,
                 into
                 the
                 Po
                 of
                 Primaro
                 ,
                 and
                 of
                 Volano
                 ;
                 did
                 break
                 down
                 the
                 encompassing
                 
                 Bank
                 or
                 Dam
                 towards
                 S.
                 Martino
                 ,
                 and
                 that
                 of
                 its
                 new
                 Chanel
                 on
                 the
                 right
                 hand
                 neer
                 to
                 
                   Torre
                   del
                   Fondo
                
                 .
              
               
                 By
                 the
                 breaches
                 on
                 this
                 side
                 it
                 streamed
                 out
                 in
                 great
                 abundance
                 from
                 the
                 upper
                 part
                 of
                 Cominale
                 ,
                 and
                 in
                 the
                 parts
                 about
                 
                   Raveda
                   ,
                   Pioggio
                   ,
                   Caprara
                   ,
                   Ghiare
                   di
                   Reno
                   ,
                   Sant
                   '
                   Agostino
                   ,
                   San
                   Prospero
                   ,
                   San
                   Vincenzo
                   ,
                
                 and
                 others
                 ,
                 and
                 made
                 them
                 to
                 become
                 incultivable
                 :
                 it
                 made
                 also
                 those
                 places
                 above
                 but
                 little
                 fruitful
                 ,
                 by
                 reason
                 of
                 the
                 impediments
                 that
                 their
                 Draines
                 received
                 ,
                 finding
                 the
                 Conveyances
                 called
                 Riolo
                 and
                 Scorsuro
                 ,
                 not
                 only
                 filled
                 by
                 
                   la
                   Motta
                
                 and
                 
                   la
                   Belletta
                
                 ,
                 but
                 that
                 they
                 turned
                 backwards
                 of
                 themselves
                 .
              
               
                 But
                 by
                 the
                 Mouths
                 in
                 the
                 inclosing
                 Bank
                 or
                 Dam
                 at
                 
                   Borgo
                   di
                
                 S.
                 Martino
                 issuing
                 with
                 violence
                 ,
                 it
                 first
                 gave
                 obstruction
                 to
                 the
                 ancient
                 Navigation
                 of
                 
                   la
                   Torre
                   de
                   la
                   Fossa
                
                 ,
                 and
                 afterwards
                 to
                 the
                 moderne
                 of
                 the
                 mouth
                 of
                 Masi
                 ,
                 so
                 that
                 at
                 present
                 the
                 Commerce
                 between
                 Bologna
                 and
                 Ferrara
                 is
                 lost
                 ,
                 nor
                 can
                 it
                 ever
                 be
                 in
                 any
                 durable
                 way
                 renewed
                 ,
                 whilst
                 that
                 this
                 exceeds
                 its
                 due
                 bounds
                 ,
                 and
                 what
                 ever
                 moneys
                 shall
                 be
                 imployed
                 about
                 the
                 same
                 shall
                 be
                 without
                 any
                 equivalent
                 benefit
                 ,
                 and
                 to
                 the
                 manifest
                 and
                 notable
                 prejudice
                 of
                 the
                 *
                 Apostolick
                 Chamber
                 .
              
               
                 Thence
                 passing
                 into
                 the
                 Valley
                 of
                 Marzara
                 ,
                 it
                 swelleth
                 higher
                 ,
                 not
                 only
                 by
                 the
                 rising
                 of
                 the
                 water
                 ,
                 but
                 by
                 the
                 raising
                 of
                 the
                 bottome
                 ,
                 by
                 reason
                 of
                 the
                 matter
                 sunk
                 thither
                 after
                 Land-floods
                 ,
                 and
                 dilateth
                 so
                 ,
                 that
                 it
                 covereth
                 all
                 the
                 Meadows
                 thereabouts
                 ,
                 nor
                 doth
                 it
                 receive
                 with
                 the
                 wonted
                 facility
                 the
                 Drains
                 of
                 the
                 upper
                 Grounds
                 ,
                 of
                 which
                 the
                 next
                 unto
                 it
                 lying
                 under
                 the
                 waters
                 that
                 return
                 upwards
                 by
                 the
                 Conveyances
                 ,
                 and
                 the
                 more
                 remote
                 ,
                 not
                 finding
                 a
                 passage
                 for
                 Rain-waters
                 that
                 settle
                 ,
                 become
                 either
                 altogether
                 unprofitable
                 or
                 little
                 better
                 .
              
               
                 From
                 this
                 Valley
                 ,
                 by
                 the
                 Trench
                 or
                 Ditch
                 of
                 Marzara
                 ,
                 or
                 of
                 
                   la
                   Duca
                
                 by
                 
                   la
                   Buova
                
                 ,
                 or
                 mouth
                 of
                 
                   Castaldo
                   de
                   Rossi
                
                 ,
                 and
                 by
                 the
                 new
                 passage
                 it
                 falleth
                 into
                 the
                 Po
                 of
                 Argenta
                 ,
                 which
                 being
                 to
                 receive
                 it
                 clear
                 ,
                 that
                 so
                 it
                 may
                 sink
                 farther
                 therein
                 ,
                 and
                 receiving
                 it
                 muddy
                 ,
                 because
                 it
                 hath
                 acquired
                 a
                 quicker
                 course
                 ,
                 there
                 will
                 arise
                 a
                 very
                 contrary
                 effect
                 .
              
               
                 Here
                 therefore
                 the
                 superficies
                 of
                 the
                 water
                 keeping
                 high
                 ,
                 until
                 it
                 come
                 to
                 the
                 Sea
                 ,
                 hindereth
                 the
                 Valleys
                 of
                 Ravenna
                 ,
                 where
                 the
                 River
                 Senio
                 ,
                 those
                 of
                 
                   San
                   Bernardino
                
                 where
                 Santerno
                 was
                 turned
                 ,
                 those
                 of
                 
                   Buon
                   '
                   acquisto
                
                 ,
                 and
                 those
                 of
                 Marmorto
                 ,
                 where
                 the
                 
                   Idice
                   ,
                   Quaderna
                   ,
                   Sellero
                
                 fall
                 in
                 ,
                 from
                 swallowing
                 and
                 taking
                 in
                 their
                 Waters
                 by
                 their
                 usual
                 In-lets
                 ,
                 yet
                 many
                 times
                 ,
                 as
                 I
                 my self
                 have
                 seen
                 in
                 the
                 Visitation
                 ,
                 they
                 drink
                 them
                 up
                 plentifully
                 ,
                 whereupon
                 ,
                 being
                 conjoyned
                 with
                 the
                 muddinesse
                 of
                 those
                 Rivers
                 that
                 fall
                 into
                 the
                 same
                 ,
                 they
                 swell
                 ,
                 and
                 dilate
                 ,
                 and
                 overflow
                 some
                 grounds
                 ,
                 and
                 deprive
                 others
                 of
                 their
                 Drains
                 in
                 like
                 manner
                 
                 as
                 hath
                 been
                 said
                 of
                 that
                 of
                 Marrara
                 ,
                 insomuch
                 that
                 from
                 the
                 Point
                 of
                 S.
                 Giorgio
                 ,
                 as
                 far
                 as
                 S.
                 Alberto
                 all
                 those
                 that
                 are
                 between
                 the
                 Valleys
                 and
                 Po
                 are
                 spoiled
                 ,
                 of
                 those
                 that
                 are
                 between
                 Valley
                 and
                 Valley
                 many
                 are
                 in
                 a
                 very
                 bad
                 condition
                 ,
                 and
                 those
                 that
                 are
                 some
                 considerable
                 space
                 above
                 not
                 a
                 little
                 damnified
                 .
              
               
                 In
                 fine
                 ,
                 by
                 raising
                 the
                 bottom
                 or
                 sand
                 of
                 the
                 Valleys
                 ,
                 and
                 the
                 bed
                 of
                 Reno
                 ,
                 and
                 the
                 too
                 great
                 repletion
                 of
                 the
                 Po
                 of
                 Primaro
                 with
                 waters
                 ,
                 the
                 Valleys
                 of
                 Comacchio
                 (
                 on
                 which
                 side
                 the
                 Banks
                 are
                 very
                 bad
                 )
                 and
                 *
                 
                   Polesine
                   di
                
                 S.
                 Giorgio
                 are
                 threatned
                 with
                 a
                 danger
                 ,
                 that
                 may
                 in
                 time
                 ,
                 if
                 it
                 be
                 not
                 remedied
                 ,
                 become
                 irreparable
                 ,
                 and
                 at
                 present
                 feeleth
                 the
                 incommodity
                 of
                 the
                 Waters
                 ,
                 which
                 penetrating
                 thorow
                 the
                 pores
                 of
                 the
                 Earth
                 do
                 spring
                 up
                 in
                 the
                 same
                 ,
                 which
                 they
                 call
                 Purlings
                 ,
                 which
                 is
                 all
                 likely
                 to
                 redound
                 to
                 the
                 prejudice
                 of
                 Ferrara
                 ,
                 so
                 noble
                 a
                 City
                 of
                 Italy
                 ,
                 and
                 so
                 important
                 to
                 the
                 
                   Ecclesiastick
                   State.
                
                 
              
               
                 Which
                 particulars
                 all
                 appear
                 to
                 be
                 attested
                 under
                 the
                 hand
                 of
                 a
                 Notary
                 in
                 the
                 Visitation
                 which
                 I
                 made
                 upon
                 the
                 command
                 of
                 His
                 Holinesse
                 ,
                 and
                 are
                 withall
                 known
                 to
                 be
                 true
                 by
                 the
                 *
                 Ferraresi
                 themselves
                 ,
                 of
                 whom
                 (
                 besides
                 the
                 request
                 of
                 the
                 Bolognesi
                 )
                 the
                 greater
                 part
                 beg
                 compassion
                 with
                 sundry
                 Memorials
                 ,
                 and
                 remedies
                 ,
                 aswell
                 for
                 the
                 mischiefs
                 past
                 ,
                 as
                 also
                 for
                 those
                 in
                 time
                 to
                 come
                 ,
                 from
                 which
                 I
                 hold
                 it
                 a
                 duty
                 of
                 Conscience
                 ,
                 and
                 of
                 Charity
                 to
                 deliver
                 them
                 .
              
               
                 Pope
                 Clement
                 judged
                 ,
                 that
                 the
                 sufficient
                 means
                 ,
                 to
                 effect
                 this
                 was
                 the
                 said
                 Introduction
                 of
                 the
                 
                   Main
                   Po
                
                 into
                 the
                 Chanel
                 of
                 Ferrara
                 ;
                 a
                 resolution
                 truly
                 Heroical
                 ,
                 and
                 of
                 no
                 lesse
                 beauty
                 than
                 benefit
                 to
                 that
                 City
                 ,
                 of
                 which
                 I
                 speak
                 not
                 at
                 present
                 ,
                 because
                 I
                 think
                 that
                 there
                 is
                 need
                 of
                 a
                 readier
                 and
                 more
                 accomodate
                 remedy
                 .
              
               
                 So
                 that
                 I
                 see
                 not
                 how
                 any
                 other
                 thing
                 can
                 be
                 so
                 much
                 considerable
                 as
                 the
                 removal
                 of
                 Reno
                 ,
                 omitting
                 for
                 this
                 time
                 to
                 speak
                 of
                 *
                 inclosing
                 it
                 from
                 Valley
                 to
                 Valley
                 untill
                 it
                 come
                 to
                 the
                 Sea
                 ,
                 as
                 the
                 Dukes
                 of
                 Ferrara
                 did
                 design
                 ,
                 forasmuch
                 as
                 all
                 those
                 Ferraresi
                 that
                 have
                 interest
                 in
                 the
                 
                   Polesine
                   di
                
                 S.
                 Giorgio
                 ,
                 and
                 on
                 the
                 right
                 hand
                 of
                 the
                 Po
                 of
                 Argenta
                 do
                 not
                 desire
                 it
                 ,
                 and
                 do
                 ,
                 but
                 too
                 openly
                 ,
                 protest
                 against
                 it
                 ;
                 and
                 because
                 that
                 before
                 the
                 Chanel
                 were
                 made
                 as
                 far
                 as
                 the
                 Sea
                 ,
                 many
                 hundreds
                 of
                 years
                 would
                 be
                 spent
                 ,
                 and
                 yet
                 would
                 not
                 remedy
                 the
                 dammages
                 of
                 those
                 who
                 now
                 are
                 agrieved
                 ,
                 but
                 would
                 much
                 increase
                 them
                 ,
                 in
                 regard
                 the
                 Valleys
                 would
                 continue
                 submerged
                 ,
                 the
                 Drains
                 stopped
                 ,
                 and
                 the
                 other
                 Brooks
                 obstructed
                 ,
                 which
                 would
                 of
                 necessity
                 drown
                 not
                 a
                 few
                 Lands
                 that
                 lie
                 between
                 Valley
                 and
                 Valley
                 ;
                 and
                 in
                 fine
                 ,
                 in
                 regard
                 it
                 hath
                 not
                 from
                 
                   San
                   Martina
                
                 to
                 the
                 Sea
                 for
                 a
                 space
                 of
                 fifty
                 miles
                 a
                 greater
                 fall
                 then
                 19
                 ,
                 8
                 ,
                 6
                 ,
                 feet
                 ,
                 it
                 would
                 want
                 that
                 force
                 which
                 they
                 themselves
                 who
                 propound
                 this
                 project
                 do
                 require
                 it
                 to
                 
                 have
                 ,
                 that
                 so
                 it
                 may
                 not
                 depose
                 the
                 matter
                 of
                 the
                 muddiness
                 when
                 it
                 is
                 intended
                 to
                 be
                 let
                 into
                 Volana
                 .
              
               
                 So
                 that
                 making
                 the
                 Line
                 of
                 the
                 bottome
                 neer
                 to
                 Vigarano
                 ,
                 it
                 would
                 rise
                 to
                 those
                 prodigious
                 termes
                 that
                 they
                 do
                 make
                 bigger
                 ,
                 and
                 they
                 may
                 thence
                 expect
                 those
                 mischiefs
                 ,
                 for
                 which
                 they
                 will
                 not
                 admit
                 of
                 introducing
                 it
                 into
                 the
                 said
                 Po
                 of
                 Volana
                 .
              
               
                 Amongst
                 the
                 wayes
                 therefore
                 that
                 I
                 have
                 thought
                 of
                 for
                 effecting
                 that
                 same
                 remotion
                 ,
                 and
                 which
                 I
                 have
                 caused
                 to
                 be
                 viewed
                 by
                 skilful
                 men
                 that
                 have
                 taken
                 a
                 level
                 thereof
                 ,
                 (
                 with
                 the
                 assistance
                 of
                 the
                 venerable
                 Father
                 ,
                 
                   D.
                   Benedetto
                   Castelli
                
                 of
                 Casina
                 ,
                 a
                 man
                 of
                 much
                 fidelity
                 and
                 honesty
                 ,
                 and
                 no
                 less
                 expert
                 in
                 such
                 like
                 affairs
                 touching
                 waters
                 ,
                 than
                 perfect
                 in
                 the
                 Mathematick
                 Disciplines
                 )
                 two
                 onely
                 ,
                 the
                 rest
                 being
                 either
                 too
                 tedious
                 ,
                 or
                 too
                 dangerous
                 to
                 the
                 City
                 ,
                 have
                 seemed
                 to
                 me
                 worthy
                 ,
                 and
                 one
                 of
                 them
                 also
                 more
                 than
                 the
                 other
                 ,
                 to
                 offer
                 to
                 your
                 Lordship
                 .
              
               
                 The
                 one
                 is
                 to
                 remit
                 it
                 into
                 the
                 Chanel
                 of
                 Volana
                 ,
                 thorow
                 which
                 it
                 goeth
                 of
                 its
                 own
                 accord
                 to
                 the
                 Sea.
                 
              
               
                 The
                 other
                 is
                 to
                 turn
                 it
                 into
                 Main-Po
                 at
                 Stellata
                 ,
                 for
                 ,
                 as
                 at
                 other
                 times
                 it
                 hath
                 done
                 ,
                 it
                 will
                 carry
                 it
                 to
                 the
                 Sea
                 happily
                 .
              
               
                 As
                 to
                 what
                 concerns
                 the
                 making
                 choice
                 of
                 the
                 first
                 way
                 ,
                 that
                 which
                 seemeth
                 to
                 perswade
                 us
                 to
                 it
                 is
                 ,
                 that
                 we
                 therein
                 do
                 nothing
                 that
                 is
                 new
                 ,
                 in
                 that
                 it
                 is
                 but
                 restored
                 to
                 the
                 place
                 whence
                 it
                 was
                 removed
                 in
                 the
                 year
                 1522.
                 in
                 the
                 time
                 of
                 Pope
                 Adrian
                 ,
                 by
                 an
                 agreement
                 made
                 in
                 way
                 of
                 contract
                 ,
                 between
                 Alfonso
                 ,
                 Duke
                 of
                 Ferrara
                 ,
                 and
                 the
                 Bolognesi
                 ;
                 and
                 that
                 it
                 was
                 diverted
                 for
                 reasons
                 ,
                 that
                 are
                 either
                 out
                 of
                 date
                 ,
                 or
                 else
                 have
                 been
                 too
                 long
                 time
                 deferred
                 .
              
               
                 In
                 like
                 manner
                 the
                 facility
                 wherewith
                 it
                 may
                 be
                 effected
                 ,
                 letting
                 it
                 run
                 into
                 the
                 divided
                 Po
                 ,
                 whereby
                 it
                 will
                 be
                 turned
                 to
                 Ferrara
                 ,
                 or
                 else
                 carrying
                 it
                 by
                 
                   Torre
                   del
                   Fondo
                
                 ,
                 to
                 the
                 mouth
                 of
                 Masi
                 ,
                 and
                 from
                 thence
                 thorow
                 the
                 Trench
                 made
                 by
                 the
                 Ferraresi
                 ,
                 along
                 by
                 Panaro
                 ,
                 where
                 also
                 finding
                 an
                 ample
                 Bed
                 ,
                 and
                 high
                 and
                 thick
                 Banks
                 ,
                 that
                 will
                 serve
                 at
                 other
                 times
                 for
                 it
                 ,
                 and
                 for
                 the
                 waters
                 of
                 Po
                 ,
                 there
                 may
                 a
                 great
                 expence
                 be
                 spared
                 .
              
               
                 That
                 what
                 ever
                 its
                 Fall
                 be
                 ,
                 it
                 would
                 maintain
                 the
                 same
                 ,
                 not
                 having
                 other
                 Rivers
                 ,
                 which
                 with
                 their
                 Floods
                 can
                 hinder
                 it
                 ;
                 and
                 that
                 running
                 confined
                 between
                 good
                 Banks
                 ,
                 without
                 doubt
                 it
                 would
                 not
                 leave
                 
                   la
                   Motto
                
                 by
                 the
                 way
                 ;
                 but
                 especially
                 ,
                 that
                 it
                 would
                 be
                 sufficient
                 if
                 it
                 came
                 to
                 Codigoro
                 ,
                 where
                 being
                 assisted
                 by
                 the
                 Ebbing
                 and
                 Flowing
                 of
                 the
                 Sea
                 ,
                 it
                 would
                 run
                 no
                 hazard
                 of
                 having
                 its
                 Chanel
                 filled
                 up
                 from
                 thence
                 downwards
                 .
              
               
                 That
                 there
                 might
                 thence
                 many
                 benefits
                 be
                 derived
                 to
                 the
                 City
                 ,
                 by
                 means
                 of
                 the
                 Running
                 Waters
                 ,
                 and
                 also
                 no
                 mean
                 Navigation
                 might
                 be
                 expected
                 .
              
               
                 On
                 the
                 contrary
                 it
                 is
                 objected
                 ,
                 That
                 it
                 is
                 not
                 convenient
                 to
                 
                 think
                 of
                 returning
                 this
                 Torrent
                 into
                 the
                 divided
                 Po
                 ,
                 by
                 reason
                 of
                 the
                 peril
                 that
                 would
                 thence
                 redound
                 to
                 this
                 City
                 .
              
               
                 And
                 that
                 going
                 by
                 
                   Torre
                   del
                   Fondo
                
                 ,
                 through
                 Sanmartina
                 to
                 the
                 Mouth
                 
                   de
                   Masi
                
                 by
                 the
                 Chappel
                 of
                 Vigarano
                 unto
                 the
                 Sea
                 ,
                 it
                 is
                 by
                 this
                 way
                 70.
                 miles
                 ;
                 nor
                 is
                 the
                 Fall
                 greater
                 than
                 26.
                 5.
                 6.
                 
                 Feet
                 ,
                 so
                 that
                 it
                 would
                 come
                 to
                 fall
                 but
                 4.
                 inches
                 &
                 an
                 half
                 ,
                 or
                 thereabouts
                 in
                 a
                 mile
                 ;
                 whereas
                 the
                 common
                 opinion
                 of
                 the
                 skilfull
                 (
                 to
                 the
                 end
                 that
                 the
                 Torrents
                 may
                 not
                 depose
                 their
                 sand
                 that
                 they
                 bring
                 with
                 them
                 in
                 Land-Floods
                 )
                 requireth
                 the
                 twenty
                 fourth
                 part
                 of
                 the
                 hundredth
                 part
                 of
                 their
                 whole
                 length
                 ,
                 which
                 in
                 our
                 case
                 ,
                 accounting
                 according
                 to
                 the
                 measure
                 of
                 these
                 places
                 ,
                 is
                 16.
                 inches
                 a
                 *
                 mile
                 ;
                 whereupon
                 the
                 sinking
                 of
                 the
                 Mud
                 and
                 Sand
                 would
                 most
                 certainly
                 follow
                 ,
                 and
                 so
                 an
                 immense
                 heightning
                 of
                 the
                 Line
                 of
                 the
                 Bottom
                 ,
                 and
                 consequently
                 a
                 necessity
                 of
                 raising
                 the
                 Banks
                 ,
                 the
                 impossibility
                 of
                 maintaining
                 them
                 ,
                 the
                 danger
                 of
                 breaches
                 and
                 decayes
                 ,
                 things
                 very
                 prejudicial
                 to
                 the
                 Islets
                 of
                 this
                 City
                 ,
                 and
                 of
                 
                   San
                   Giorgio
                
                 ,
                 the
                 obstruction
                 of
                 the
                 Drains
                 ,
                 which
                 from
                 the
                 Tower
                 of
                 Tienne
                 downwards
                 ,
                 fall
                 into
                 the
                 said
                 Chanel
                 ;
                 to
                 wit
                 ,
                 those
                 of
                 the
                 Sluices
                 of
                 Goro
                 ,
                 and
                 the
                 Drains
                 ,
                 of
                 the
                 Meadows
                 of
                 Ferrara
                 :
                 And
                 moreover
                 ,
                 the
                 damages
                 that
                 would
                 arise
                 unto
                 the
                 said
                 Islet
                 of
                 S.
                 Giorgio
                 ,
                 and
                 the
                 Valleys
                 of
                 Comachio
                 ,
                 by
                 the
                 waters
                 that
                 should
                 enter
                 into
                 the
                 Goro
                 or
                 Dam
                 of
                 the
                 Mills
                 of
                 Belriguardo
                 ,
                 thorow
                 the
                 Trenches
                 of
                 Quadrea
                 ,
                 which
                 cannot
                 be
                 stopt
                 ,
                 because
                 they
                 belong
                 to
                 the
                 Duke
                 of
                 Modena
                 ,
                 who
                 hath
                 right
                 of
                 diverting
                 the
                 waters
                 of
                 that
                 place
                 at
                 his
                 pleasure
                 to
                 the
                 work
                 of
                 turning
                 Mills
                 .
              
               
                 The
                 greater
                 part
                 of
                 which
                 Objections
                 ,
                 others
                 pretend
                 to
                 prove
                 frivolous
                 ,
                 by
                 saying
                 ,
                 that
                 its
                 running
                 there
                 till
                 at
                 the
                 last
                 it
                 was
                 turned
                 another
                 way
                 ,
                 is
                 a
                 sign
                 that
                 it
                 had
                 made
                 such
                 an
                 elevation
                 of
                 the
                 Line
                 ,
                 of
                 its
                 Bed
                 as
                 it
                 required
                 ;
                 denying
                 that
                 it
                 needeth
                 so
                 great
                 a
                 declivity
                 as
                 is
                 mentioned
                 above
                 ;
                 and
                 that
                 for
                 the
                 future
                 it
                 would
                 rise
                 no
                 more
                 .
              
               
                 That
                 the
                 said
                 Dra●ns
                 and
                 Ditches
                 did
                 empty
                 into
                 the
                 same
                 ,
                 whilst
                 Po
                 was
                 there
                 ;
                 so
                 that
                 they
                 must
                 needs
                 be
                 more
                 able
                 to
                 do
                 so
                 when
                 onely
                 Reno
                 runs
                 that
                 way
                 .
              
               
                 That
                 there
                 would
                 no
                 Breaches
                 follow
                 ,
                 or
                 if
                 they
                 did
                 ,
                 they
                 would
                 be
                 onely
                 of
                 the
                 water
                 of
                 Reno
                 ,
                 which
                 in
                 few
                 hours
                 might
                 be
                 taken
                 away
                 (
                 in
                 those
                 parts
                 they
                 call
                 damming
                 up
                 of
                 Breaches
                 ,
                 and
                 mending
                 the
                 Bank
                 ,
                 
                   taking
                   away
                   the
                   Breaches
                
                 )
                 and
                 it
                 s
                 a
                 question
                 whether
                 they
                 would
                 procure
                 more
                 inconvenience
                 than
                 benefit
                 ,
                 for
                 that
                 its
                 Mud
                 and
                 Sand
                 might
                 in
                 many
                 places
                 ,
                 by
                 filling
                 them
                 up
                 ,
                 occasion
                 a
                 seasonable
                 improvement
                 .
              
               
                 Now
                 omitting
                 to
                 discourse
                 of
                 the
                 solidity
                 of
                 the
                 reasons
                 on
                 the
                 oneside
                 ,
                 or
                 on
                 the
                 other
                 ,
                 I
                 will
                 produce
                 those
                 that
                 move
                 me
                 to
                 suspend
                 my
                 allowance
                 of
                 this
                 design
                 .
              
               
               
                 The
                 first
                 is
                 ,
                 that
                 although
                 I
                 dare
                 not
                 subscribe
                 to
                 the
                 opinion
                 of
                 those
                 that
                 require
                 16.
                 inches
                 Declivity
                 in
                 a
                 mile
                 to
                 Reno
                 ,
                 to
                 prevent
                 its
                 deposing
                 of
                 Mud
                 ;
                 yet
                 would
                 I
                 not
                 be
                 the
                 Author
                 that
                 should
                 make
                 a
                 trial
                 of
                 it
                 with
                 so
                 much
                 hazard
                 ,
                 for
                 having
                 to
                 satisfie
                 my self
                 in
                 some
                 particulars
                 caused
                 a
                 Level
                 to
                 be
                 taken
                 of
                 the
                 Rivers
                 
                   L'amone
                   ,
                   Senio
                
                 ,
                 and
                 Santerno
                 ,
                 by
                 
                   Bernardino
                   Aleotti
                
                 ,
                 we
                 found
                 that
                 they
                 have
                 more
                 Declivity
                 by
                 much
                 than
                 Artists
                 require
                 ,
                 as
                 also
                 the
                 Reno
                 hath
                 from
                 
                   la
                   Botta
                   de
                   Ghislieri
                
                 to
                 the
                 Chappel
                 of
                 Vigarano
                 ,
                 for
                 in
                 the
                 space
                 of
                 four
                 miles
                 its
                 Bottom-Line
                 falleth
                 five
                 feet
                 and
                 five
                 inches
                 .
                 So
                 that
                 I
                 hold
                 it
                 greater
                 prudence
                 to
                 depend
                 upon
                 that
                 example
                 ,
                 than
                 to
                 go
                 contrary
                 to
                 a
                 common
                 opinion
                 ,
                 especially
                 since
                 ,
                 that
                 the
                 effects
                 caused
                 by
                 Reno
                 it self
                 do
                 confirm
                 me
                 in
                 the
                 same
                 ,
                 for
                 when
                 it
                 was
                 forsaken
                 by
                 the
                 Po
                 ,
                 after
                 a
                 few
                 years
                 ,
                 either
                 because
                 it
                 had
                 choaked
                 up
                 its
                 Chanel
                 with
                 Sand
                 ,
                 or
                 because
                 it
                 s
                 too
                 long
                 journey
                 did
                 increase
                 it
                 ,
                 it
                 also
                 naturally
                 turned
                 aside
                 ,
                 and
                 took
                 the
                 way
                 of
                 the
                 said
                 Po
                 towards
                 Stellata
                 .
                 Nay
                 ,
                 in
                 those
                 very
                 years
                 that
                 it
                 did
                 run
                 that
                 way
                 ,
                 it
                 only
                 began
                 (
                 as
                 relations
                 say
                 )
                 to
                 make
                 Breaches
                 ,
                 an
                 evident
                 sign
                 that
                 it
                 doth
                 depose
                 Sand
                 ,
                 and
                 raise
                 its
                 Bed
                 ;
                 which
                 agreeth
                 with
                 the
                 testimony
                 of
                 some
                 that
                 were
                 examined
                 in
                 the
                 Visitation
                 of
                 the
                 Publique
                 Notary
                 ,
                 who
                 found
                 great
                 benefit
                 by
                 having
                 Running
                 Water
                 ,
                 and
                 some
                 kind
                 of
                 passage
                 for
                 Boats
                 ,
                 and
                 yet
                 nevertheless
                 affirm
                 that
                 it
                 for
                 want
                 of
                 Running
                 Water
                 had
                 made
                 too
                 high
                 Stoppages
                 and
                 Shelfes
                 of
                 Sand
                 ;
                 so
                 that
                 if
                 it
                 should
                 be
                 restored
                 to
                 the
                 Course
                 that
                 it
                 forsook
                 ,
                 I
                 much
                 fear
                 that
                 after
                 a
                 short
                 time
                 ,
                 if
                 not
                 suddenly
                 ,
                 it
                 would
                 leave
                 it
                 a-again
                 .
              
               
                 The
                 second
                 I
                 take
                 from
                 the
                 observation
                 of
                 what
                 happened
                 to
                 Panaro
                 ,
                 when
                 with
                 so
                 great
                 applause
                 of
                 the
                 Feraresi
                 ,
                 it
                 was
                 brought
                 by
                 Cardinal
                 Serra
                 into
                 the
                 said
                 Chanel
                 of
                 Volana
                 ;
                 for
                 that
                 notwithstanding
                 that
                 it
                 had
                 Running
                 Waters
                 in
                 much
                 greater
                 abundance
                 than
                 Reno
                 ;
                 yet
                 in
                 the
                 time
                 that
                 it
                 continued
                 in
                 that
                 Chanel
                 it
                 raised
                 its
                 Bed
                 well
                 neer
                 five
                 feet
                 ,
                 as
                 is
                 to
                 be
                 seen
                 below
                 the
                 Sluice
                 made
                 by
                 Cardinal
                 Capponi
                 to
                 his
                 new
                 Chanel
                 ;
                 yea
                 ,
                 the
                 said
                 Cardinal
                 Serra
                 who
                 desired
                 that
                 this
                 his
                 undertaking
                 should
                 appear
                 to
                 have
                 been
                 of
                 no
                 danger
                 nor
                 damage
                 ,
                 was
                 constrained
                 at
                 its
                 Overflowings
                 ,
                 to
                 give
                 it
                 Vent
                 into
                 Sanmartina
                 ,
                 that
                 it
                 might
                 not
                 break
                 in
                 upon
                 ,
                 and
                 prejudice
                 the
                 City
                 ;
                 which
                 danger
                 I
                 should
                 more
                 fear
                 from
                 Reno
                 ,
                 in
                 regard
                 it
                 carrieth
                 a
                 greater
                 abundance
                 of
                 Water
                 and
                 Sand.
                 
              
               
                 Thirdly
                 ,
                 I
                 am
                 much
                 troubled
                 (
                 in
                 the
                 uncertainty
                 of
                 the
                 success
                 of
                 the
                 affair
                 )
                 at
                 the
                 great
                 expence
                 thereto
                 required
                 ;
                 For
                 in
                 regard
                 I
                 do
                 not
                 approve
                 of
                 letting
                 it
                 in
                 ,
                 neer
                 to
                 the
                 Fortresse
                 ,
                 for
                 many
                 respects
                 ,
                 and
                 carrying
                 it
                 by
                 
                   la
                   Torre
                   del
                   Fondo
                
                 to
                 the
                 Mouth
                 
                   de
                   Masi
                
                 ,
                 it
                 will
                 take
                 up
                 eight
                 miles
                 of
                 double
                 Banks
                 ,
                 a
                 
                 thing
                 not
                 easie
                 to
                 be
                 procured
                 ,
                 by
                 reason
                 that
                 the
                 Grounds
                 lie
                 under
                 Water
                 ;
                 but
                 from
                 the
                 Mouth
                 
                   de
                   Masi
                
                 unto
                 Codigoro
                 ,
                 it
                 would
                 also
                 be
                 necessary
                 to
                 make
                 new
                 Scowrings
                 of
                 the
                 Chanel
                 ;
                 to
                 the
                 end
                 ,
                 that
                 the
                 Water
                 approaching
                 (
                 by
                 wearing
                 and
                 carrying
                 away
                 the
                 Earth
                 on
                 both
                 shores
                 ,
                 might
                 make
                 a
                 Bed
                 sufficient
                 for
                 its
                 Body
                 ,
                 the
                 depth
                 made
                 for
                 Panaro
                 not
                 serving
                 the
                 turn
                 ,
                 as
                 I
                 conceive
                 ;
                 and
                 if
                 it
                 should
                 suffice
                 ,
                 when
                 could
                 the
                 people
                 of
                 Ferrara
                 hope
                 to
                 be
                 re-imbursed
                 and
                 satisfied
                 for
                 the
                 charge
                 thereof
                 ?
              
               
                 Fourthly
                 ,
                 it
                 serves
                 as
                 an
                 Argument
                 with
                 me
                 ,
                 to
                 see
                 that
                 the
                 very
                 individual
                 persons
                 concerned
                 in
                 the
                 Remotion
                 or
                 Diversion
                 of
                 the
                 said
                 Torrent
                 ,
                 namely
                 ,
                 the
                 Bolognesi
                 do
                 not
                 incline
                 unto
                 it
                 ,
                 and
                 that
                 the
                 whole
                 City
                 of
                 Ferrara
                 ,
                 even
                 those
                 very
                 persons
                 who
                 at
                 present
                 receive
                 damage
                 by
                 it
                 ,
                 cannot
                 indure
                 to
                 hear
                 thereof
                 .
                 The
                 reason
                 that
                 induceth
                 these
                 last
                 named
                 to
                 be
                 so
                 averse
                 thereto
                 ,
                 is
                 ,
                 either
                 because
                 that
                 this
                 undertaking
                 will
                 render
                 the
                 introduction
                 of
                 the
                 Water
                 of
                 Main-Po
                 more
                 difficult
                 ;
                 or
                 because
                 they
                 fear
                 the
                 danger
                 thereof
                 ;
                 The
                 others
                 decline
                 the
                 Project
                 ,
                 either
                 for
                 that
                 they
                 know
                 that
                 Reno
                 cannot
                 long
                 continue
                 in
                 that
                 Course
                 ,
                 or
                 because
                 they
                 fear
                 that
                 it
                 is
                 too
                 much
                 exposed
                 to
                 those
                 mens
                 revengeful
                 Cutting
                 of
                 it
                 who
                 do
                 not
                 desire
                 it
                 should
                 ;
                 and
                 if
                 a
                 man
                 have
                 any
                 other
                 wayes
                 ,
                 he
                 ought
                 ,
                 in
                 my
                 opinion
                 ,
                 to
                 forbear
                 that
                 ,
                 which
                 to
                 such
                 as
                 stand
                 in
                 need
                 of
                 its
                 Removal
                 ,
                 is
                 lesse
                 satisfactory
                 ,
                 and
                 to
                 such
                 as
                 oppose
                 it
                 ,
                 more
                 prejudicial
                 .
              
               
                 To
                 conclude
                 ,
                 I
                 exceedingly
                 honour
                 the
                 judgment
                 of
                 Cardinal
                 Capponi
                 ,
                 who
                 having
                 to
                 his
                 Natural
                 Ability
                 and
                 Prudence
                 added
                 a
                 particular
                 Study
                 ,
                 Observation
                 ,
                 and
                 Experience
                 of
                 these
                 Waters
                 for
                 the
                 space
                 of
                 three
                 years
                 together
                 ,
                 doth
                 not
                 think
                 that
                 Reno
                 can
                 go
                 by
                 Volana
                 ;
                 to
                 which
                 agreeth
                 the
                 opinion
                 of
                 Cardinal
                 S.
                 Marcello
                 ,
                 Legate
                 of
                 this
                 City
                 ,
                 of
                 whom
                 ,
                 for
                 his
                 exquisite
                 understanding
                 ,
                 we
                 ought
                 to
                 make
                 great
                 account
                 .
                 But
                 if
                 ever
                 this
                 should
                 be
                 resolved
                 on
                 ,
                 it
                 would
                 be
                 materially
                 necessary
                 to
                 unite
                 the
                 Quick
                 and
                 Running
                 Waters
                 of
                 the
                 little
                 Chanel
                 of
                 Cento
                 ,
                 of
                 the
                 Chanel
                 Navilio
                 ,
                 of
                 Guazzaloca
                 ,
                 and
                 at
                 its
                 very
                 beginning
                 those
                 of
                 Dardagna
                 ,
                 which
                 at
                 present
                 ,
                 is
                 one
                 of
                 the
                 Springs
                 or
                 Heads
                 of
                 Panaro
                 ,
                 that
                 so
                 they
                 might
                 assist
                 it
                 in
                 carrying
                 its
                 Sand
                 ,
                 and
                 the
                 matter
                 of
                 its
                 Muddiness
                 into
                 the
                 Sea
                 ;
                 and
                 then
                 there
                 would
                 not
                 fail
                 to
                 be
                 a
                 greater
                 evacuation
                 and
                 scowring
                 ;
                 but
                 withall
                 the
                 Proprietors
                 in
                 the
                 Islet
                 of
                 
                   San
                   Giorgio
                
                 and
                 of
                 Ferrara
                 must
                 prepare
                 themselves
                 to
                 indure
                 the
                 inconveniences
                 of
                 Purlings
                 or
                 Sewings
                 of
                 the
                 Water
                 from
                 the
                 River
                 thorow
                 the
                 Boggy
                 Ground
                 thereabouts
                 .
              
               
                 I
                 should
                 more
                 easily
                 incline
                 therefore
                 to
                 carry
                 it
                 into
                 Main-Po
                 at
                 Stellata
                 ,
                 for
                 the
                 Reasons
                 that
                 Cardinal
                 Capponi
                 most
                 ingeniously
                 enumerates
                 in
                 a
                 short
                 ,
                 but
                 well-grounded
                 Tract
                 of
                 his
                 :
                 not
                 
                 because
                 that
                 indeed
                 it
                 would
                 not
                 both
                 by
                 Purlings
                 and
                 by
                 Breaches
                 occasion
                 some
                 inconvenience
                 ;
                 especially
                 ,
                 in
                 the
                 beginning
                 :
                 but
                 because
                 I
                 hold
                 this
                 for
                 the
                 incomodities
                 of
                 it
                 ,
                 to
                 be
                 a
                 far
                 less
                 evil
                 than
                 any
                 of
                 the
                 rest
                 ;
                 and
                 because
                 that
                 by
                 this
                 means
                 there
                 is
                 no
                 occasion
                 given
                 to
                 them
                 of
                 Ferrara
                 ,
                 to
                 explain
                 that
                 they
                 are
                 deprived
                 of
                 the
                 hope
                 of
                 ever
                 seeing
                 the
                 Po
                 again
                 under
                 the
                 Walls
                 of
                 their
                 City
                 :
                 To
                 whom
                 ,
                 where
                 it
                 may
                 be
                 done
                 ,
                 it
                 is
                 but
                 reason
                 that
                 satisfaction
                 should
                 be
                 given
                 .
              
               
                 It
                 is
                 certain
                 that
                 Po
                 was
                 placed
                 by
                 Nature
                 in
                 the
                 midst
                 of
                 this
                 great
                 Valley
                 made
                 by
                 the
                 Appennine
                 Hills
                 ,
                 and
                 by
                 the
                 Alps
                 ,
                 to
                 carry
                 ,
                 as
                 the
                 Master-Drain
                 to
                 the
                 Sea
                 ,
                 that
                 is
                 the
                 grand
                 receptacle
                 of
                 all
                 Waters
                 ;
                 those
                 particular
                 streams
                 which
                 descend
                 from
                 them
                 .
              
               
                 That
                 the
                 Reno
                 by
                 all
                 Geographers
                 ,
                 
                   Strabo
                   ,
                   Pliny
                   ,
                   Solimas
                   ,
                   Mella
                   ,
                
                 and
                 others
                 is
                 enumerated
                 among
                 the
                 Rivers
                 that
                 fall
                 into
                 the
                 said
                 Po.
                 
              
               
                 That
                 although
                 Po
                 should
                 of
                 it self
                 change
                 its
                 course
                 ,
                 yet
                 would
                 Reno
                 go
                 to
                 look
                 it
                 out
                 ,
                 if
                 the
                 works
                 erected
                 by
                 humane
                 industry
                 did
                 not
                 obstruct
                 its
                 passage
                 ;
                 so
                 that
                 it
                 neither
                 is
                 ,
                 nor
                 ought
                 to
                 seem
                 strange
                 ,
                 if
                 one
                 for
                 the
                 greater
                 common
                 good
                 should
                 turn
                 it
                 into
                 the
                 same
                 .
              
               
                 Now
                 at
                 Stellata
                 it
                 may
                 go
                 several
                 waies
                 into
                 Po
                 ,
                 as
                 appeareth
                 by
                 the
                 levels
                 that
                 were
                 taken
                 by
                 my
                 Order
                 ;
                 of
                 all
                 which
                 I
                 should
                 best
                 like
                 the
                 turning
                 of
                 it
                 to
                 
                   la
                   Botta
                   de'
                   
                   Ghislieri
                
                 ,
                 carrying
                 it
                 above
                 Bondeno
                 to
                 the
                 Church
                 of
                 Gambarone
                 ,
                 or
                 a
                 little
                 higher
                 or
                 lower
                 ,
                 as
                 shall
                 be
                 judged
                 least
                 prejudicial
                 ,
                 when
                 it
                 cometh
                 to
                 the
                 execution
                 ,
                 and
                 this
                 for
                 two
                 principal
                 reasons
                 :
                 The
                 one
                 because
                 that
                 then
                 it
                 will
                 run
                 along
                 by
                 the
                 confines
                 of
                 the
                 Church
                 P
                 trimony
                 ,
                 without
                 separating
                 Ferrara
                 from
                 the
                 rest
                 of
                 it
                 ;
                 The
                 other
                 is
                 ,
                 Because
                 the
                 Line
                 is
                 shorter
                 ,
                 and
                 consequently
                 the
                 fall
                 greater
                 ;
                 for
                 that
                 in
                 a
                 space
                 of
                 ten
                 miles
                 and
                 one
                 third
                 ,
                 it
                 falleth
                 twenty
                 six
                 feet
                 ,
                 more
                 by
                 much
                 than
                 is
                 required
                 by
                 Artists
                 ;
                 and
                 would
                 go
                 by
                 places
                 where
                 it
                 could
                 do
                 but
                 little
                 hurt
                 ,
                 notwithstanding
                 that
                 the
                 persons
                 interressed
                 study
                 to
                 amplifie
                 it
                 incredibly
                 .
              
               
                 On
                 the
                 contrary
                 ,
                 there
                 are
                 but
                 onely
                 two
                 objections
                 that
                 are
                 worthy
                 to
                 be
                 examined
                 ;
                 One
                 ,
                 That
                 the
                 Drains
                 and
                 Ditches
                 of
                 S.
                 Bianca
                 ,
                 of
                 the
                 Chanel
                 of
                 Cento
                 ,
                 and
                 of
                 Burana
                 ,
                 and
                 all
                 those
                 others
                 that
                 enter
                 into
                 Po
                 ,
                 do
                 hinder
                 this
                 diversion
                 of
                 Reno
                 ,
                 by
                 the
                 encreasing
                 of
                 the
                 waters
                 in
                 the
                 Po.
                 The
                 other
                 is
                 that
                 Po
                 rising
                 about
                 the
                 Transom
                 of
                 the
                 
                 Pilaster-Sluice
                 ,
                 very
                 near
                 20
                 feet
                 ,
                 the
                 Reno
                 would
                 have
                 no
                 fall
                 into
                 the
                 same
                 ;
                 whereupon
                 it
                 would
                 rise
                 to
                 a
                 terrible
                 height
                 ,
                 at
                 which
                 it
                 would
                 not
                 be
                 possible
                 to
                 make
                 ,
                 or
                 keep
                 the
                 Banks
                 made
                 ,
                 so
                 that
                 it
                 would
                 break
                 out
                 and
                 drown
                 the
                 Meadowes
                 ,
                 and
                 cause
                 mischiefs
                 ,
                 and
                 damages
                 unspeakable
                 and
                 irreparable
                 ;
                 as
                 is
                 evident
                 by
                 the
                 experiment
                 made
                 upon
                 
                 Panaro
                 ,
                 which
                 being
                 confined
                 between
                 Banks
                 ,
                 that
                 it
                 might
                 go
                 into
                 Po
                 ,
                 this
                 not
                 being
                 neither
                 in
                 its
                 greatest
                 excrescense
                 ,
                 it
                 broke
                 out
                 into
                 the
                 territories
                 of
                 Final
                 ,
                 and
                 of
                 Ferrara
                 .
                 And
                 though
                 that
                 might
                 be
                 done
                 ,
                 it
                 would
                 thereupon
                 ensue
                 ,
                 that
                 there
                 being
                 let
                 into
                 the
                 Chanel
                 of
                 Po
                 ,
                 2800.
                 square
                 feet
                 of
                 water
                 (
                 for
                 so
                 much
                 we
                 account
                 those
                 of
                 Reno
                 and
                 Panaro
                 ,
                 taken
                 together
                 in
                 their
                 greatest
                 heights
                 )
                 the
                 superficies
                 of
                 it
                 would
                 rise
                 at
                 least
                 four
                 feet
                 ,
                 insomuch
                 that
                 either
                 it
                 would
                 be
                 requisite
                 to
                 raise
                 its
                 Banks
                 all
                 the
                 way
                 unto
                 the
                 Sea
                 ,
                 to
                 the
                 same
                 height
                 ,
                 which
                 the
                 treasures
                 of
                 the
                 Indies
                 would
                 not
                 suffice
                 to
                 effect
                 ;
                 or
                 else
                 there
                 would
                 be
                 a
                 necessity
                 of
                 enduring
                 excessive
                 Breaches
                 .
                 To
                 these
                 two
                 Heads
                 are
                 the
                 Arguments
                 reduced
                 ,
                 which
                 are
                 largely
                 amplified
                 against
                 our
                 opinion
                 ;
                 and
                 I
                 shall
                 answer
                 first
                 to
                 the
                 last
                 ,
                 as
                 most
                 material
                 .
              
               
                 I
                 say
                 therefore
                 ,
                 that
                 there
                 are
                 three
                 cases
                 to
                 be
                 considered
                 :
                 First
                 ,
                 Po
                 high
                 ,
                 and
                 Reno
                 low
                 .
                 Secondly
                 ,
                 Reno
                 high
                 ,
                 and
                 Po
                 low
                 .
                 Thirdly
                 ,
                 Reno
                 and
                 Po
                 both
                 high
                 together
                 .
              
               
                 As
                 to
                 the
                 first
                 and
                 second
                 ,
                 there
                 is
                 no
                 difficulty
                 in
                 them
                 ;
                 for
                 if
                 Po
                 shall
                 not
                 be
                 at
                 its
                 greatest
                 height
                 ,
                 Reno
                 shall
                 ever
                 have
                 a
                 fall
                 into
                 it
                 ,
                 and
                 there
                 shall
                 need
                 no
                 humane
                 Artifice
                 about
                 the
                 Banks
                 :
                 And
                 if
                 Reno
                 shall
                 be
                 low
                 ,
                 Po
                 shall
                 regurgitate
                 and
                 flow
                 up
                 into
                 the
                 Chanel
                 of
                 it
                 ;
                 and
                 also
                 from
                 thence
                 no
                 inconvenience
                 shall
                 follow
                 .
                 The
                 third
                 remains
                 ,
                 from
                 which
                 there
                 are
                 expected
                 many
                 mischiefs
                 ;
                 but
                 it
                 is
                 a
                 most
                 undoubted
                 truth
                 ,
                 that
                 the
                 excrescencies
                 of
                 Reno
                 ,
                 as
                 coming
                 from
                 the
                 adjacent
                 Appennines
                 and
                 Rains
                 ,
                 are
                 to
                 continue
                 but
                 seven
                 ,
                 or
                 eight
                 hours
                 at
                 most
                 ,
                 and
                 so
                 would
                 never
                 ,
                 or
                 very
                 rarely
                 happen
                 to
                 be
                 at
                 the
                 same
                 time
                 with
                 those
                 of
                 Po
                 ,
                 caused
                 by
                 the
                 melting
                 of
                 the
                 snowes
                 of
                 the
                 Alps
                 ,
                 at
                 least
                 400.
                 miles
                 distance
                 from
                 thence
                 .
                 But
                 because
                 it
                 sometimes
                 may
                 happen
                 ,
                 I
                 reply
                 ,
                 that
                 when
                 it
                 cometh
                 to
                 pass
                 ,
                 Reno
                 shall
                 not
                 go
                 into
                 Po
                 ,
                 but
                 it
                 shall
                 have
                 allowed
                 it
                 one
                 or
                 two
                 Vents
                 ;
                 namely
                 ,
                 into
                 the
                 Chanel
                 of
                 Ferrara
                 ,
                 as
                 it
                 hath
                 ever
                 had
                 ;
                 and
                 into
                 Sanmartina
                 ,
                 where
                 it
                 runneth
                 at
                 present
                 ,
                 and
                 wherewith
                 there
                 is
                 no
                 doubt
                 ,
                 but
                 that
                 the
                 persons
                 concerned
                 will
                 be
                 well
                 pleased
                 ,
                 it
                 being
                 a
                 great
                 benefit
                 to
                 them
                 ,
                 to
                 have
                 the
                 water
                 over-flow
                 their
                 grounds
                 once
                 every
                 four
                 or
                 five
                 years
                 ,
                 instead
                 of
                 seeing
                 it
                 anoy
                 them
                 continually
                 .
                 Yea
                 ,
                 the
                 Vent
                 may
                 be
                 regulated
                 ,
                 reserving
                 for
                 it
                 the
                 Chanel
                 in
                 which
                 Reno
                 at
                 present
                 runneth
                 ;
                 and
                 instead
                 of
                 turning
                 it
                 by
                 a
                 Dam
                 at
                 
                   la
                   Betta
                   de
                   Ghislieri
                
                 ,
                 perhaps
                 ,
                 to
                 turn
                 it
                 by
                 help
                 of
                 strong
                 Sluices
                 ,
                 that
                 may
                 upon
                 all
                 occasions
                 be
                 opened
                 and
                 shut
                 .
                 And
                 for
                 my
                 part
                 ,
                 I
                 do
                 not
                 question
                 but
                 that
                 the
                 Proprietors
                 themselves
                 in
                 Sanmartina
                 would
                 make
                 a
                 Chanel
                 for
                 it
                 ;
                 which
                 receiving
                 ,
                 and
                 confining
                 it
                 in
                 the
                 time
                 of
                 the
                 Vents
                 ,
                 might
                 carry
                 the
                 Sand
                 into
                 the
                 Po
                 of
                 Primaro
                 :
                 Nor
                 need
                 there
                 thence
                 be
                 feared
                 any
                 stoppage
                 by
                 Mud
                 and
                 Sand
                 ,
                 since
                 that
                 it
                 is
                 supposed
                 that
                 there
                 will
                 but
                 very
                 seldom
                 be
                 any
                 necessity
                 of
                 using
                 it
                 ;
                 so
                 that
                 
                 time
                 would
                 be
                 allowed
                 ,
                 upon
                 occasion
                 ,
                 to
                 scowr
                 and
                 cleanse
                 it
                 .
              
               
                 And
                 in
                 this
                 manner
                 all
                 those
                 Prodigies
                 vanish
                 that
                 are
                 raised
                 with
                 so
                 much
                 fear
                 from
                 the
                 enterance
                 of
                 the
                 Water
                 of
                 Reno
                 swelled
                 into
                 Po
                 ,
                 when
                 it
                 is
                 high
                 ,
                 to
                 which
                 there
                 needeth
                 no
                 other
                 answer
                 ;
                 yet
                 neverthelesse
                 we
                 do
                 not
                 take
                 that
                 quantity
                 of
                 Water
                 ,
                 that
                 is
                 carried
                 by
                 Reno
                 ,
                 and
                 by
                 Panaro
                 ,
                 to
                 be
                 so
                 great
                 as
                 is
                 affirmed
                 :
                 For
                 that
                 P.
                 D.
                 
                   Benedetto
                   Castelli
                
                 hath
                 no
                 lesse
                 accutely
                 than
                 accurately
                 observed
                 the
                 measures
                 of
                 this
                 kind
                 ,
                 noting
                 that
                 the
                 breadth
                 and
                 depth
                 of
                 a
                 River
                 is
                 not
                 enough
                 to
                 resolve
                 the
                 question
                 truly
                 ,
                 but
                 that
                 there
                 is
                 respect
                 to
                 be
                 had
                 to
                 the
                 velocity
                 of
                 the
                 Waters
                 ,
                 and
                 the
                 term
                 of
                 time
                 ,
                 things
                 hitherto
                 not
                 considered
                 by
                 the
                 Skilful
                 in
                 these
                 affairs
                 ;
                 and
                 therefore
                 they
                 are
                 not
                 able
                 to
                 say
                 what
                 quantity
                 of
                 Waters
                 the
                 said
                 Rivers
                 carry
                 ,
                 nor
                 to
                 conclude
                 of
                 the
                 risings
                 that
                 will
                 follow
                 thereupon
                 .
                 Nay
                 ,
                 it
                 is
                 most
                 certain
                 ,
                 that
                 if
                 all
                 the
                 Rivers
                 that
                 fall
                 into
                 Po
                 ,
                 which
                 are
                 above
                 thirty
                 ,
                 should
                 rise
                 at
                 the
                 rate
                 that
                 these
                 compute
                 Reno
                 to
                 do
                 ,
                 an
                 hundred
                 feet
                 of
                 Banks
                 would
                 not
                 suffice
                 ,
                 and
                 yet
                 they
                 have
                 far
                 fewer
                 :
                 So
                 that
                 this
                 confirmes
                 the
                 Rule
                 of
                 R.
                 P.
                 D.
                 Benedetto
                 ,
                 namely
                 ,
                 that
                 the
                 proportion
                 of
                 the
                 height
                 of
                 the
                 Water
                 of
                 Reno
                 in
                 Reno
                 to
                 the
                 height
                 of
                 the
                 Water
                 of
                 Reno
                 in
                 Po
                 ,
                 is
                 compounded
                 of
                 the
                 proportion
                 of
                 the
                 breadth
                 of
                 the
                 Chanel
                 of
                 Po
                 to
                 that
                 of
                 Reno
                 ,
                 and
                 of
                 the
                 velocity
                 of
                 the
                 Water
                 of
                 Reno
                 in
                 Po
                 to
                 the
                 velccity
                 of
                 the
                 Water
                 of
                 Reno
                 in
                 Reno
                 ;
                 a
                 manifest
                 argument
                 that
                 there
                 cannot
                 in
                 it
                 ,
                 by
                 this
                 new
                 augmentation
                 of
                 Waters
                 follow
                 any
                 alteration
                 that
                 necessitates
                 the
                 raising
                 of
                 its
                 Banks
                 ,
                 as
                 appeareth
                 by
                 the
                 example
                 of
                 Panaro
                 ,
                 which
                 hath
                 been
                 so
                 far
                 from
                 swelling
                 Po
                 ,
                 that
                 it
                 hath
                 rather
                 asswaged
                 it
                 ,
                 for
                 it
                 hath
                 carried
                 away
                 many
                 Shelfs
                 and
                 many
                 Islets
                 that
                 had
                 grown
                 in
                 its
                 Bed
                 ,
                 for
                 want
                 of
                 Waters
                 sufficient
                 to
                 bear
                 away
                 the
                 matter
                 of
                 Land-floods
                 in
                 so
                 broad
                 a
                 Chanel
                 ;
                 and
                 as
                 is
                 learnt
                 by
                 the
                 trial
                 made
                 by
                 us
                 in
                 Panaro
                 with
                 the
                 Water
                 of
                 Burana
                 ;
                 for
                 erecting
                 in
                 the
                 River
                 standing
                 marks
                 ,
                 and
                 shutting
                 the
                 said
                 Sluice
                 ,
                 we
                 could
                 see
                 no
                 sensible
                 abatement
                 ,
                 nor
                 much
                 less
                 after
                 we
                 had
                 opened
                 it
                 sensible
                 increasment
                 ;
                 by
                 which
                 we
                 judge
                 that
                 the
                 same
                 is
                 to
                 succeed
                 to
                 Po
                 ,
                 by
                 letting
                 in
                 of
                 
                   Reno
                   ,
                   Burana
                
                 having
                 greater
                 proportion
                 to
                 Panaro
                 than
                 Reno
                 to
                 Po
                 ,
                 considering
                 the
                 state
                 of
                 those
                 Rivers
                 in
                 which
                 the
                 Observation
                 was
                 made
                 .
                 So
                 that
                 there
                 is
                 no
                 longer
                 any
                 occasion
                 for
                 those
                 great
                 raisings
                 of
                 Banks
                 ,
                 and
                 the
                 danger
                 of
                 the
                 ruptures
                 as
                 well
                 of
                 Reno
                 as
                 of
                 Po
                 do
                 vanish
                 ,
                 as
                 also
                 the
                 fear
                 lest
                 that
                 the
                 Sluices
                 which
                 empty
                 into
                 Po
                 should
                 receive
                 obstruction
                 :
                 which
                 if
                 they
                 should
                 ,
                 yet
                 it
                 would
                 be
                 over
                 in
                 a
                 few
                 hours
                 .
                 And
                 as
                 to
                 the
                 Breaches
                 of
                 Panaro
                 which
                 happened
                 in
                 1623.
                 
                 I
                 know
                 not
                 why
                 ,
                 seeing
                 that
                 it
                 is
                 confessed
                 that
                 the
                 Po
                 was
                 not
                 ,
                 at
                 that
                 time
                 ,
                 at
                 its
                 height
                 ,
                 one
                 should
                 rather
                 charge
                 it
                 
                 with
                 the
                 crime
                 ,
                 than
                 quit
                 it
                 thereof
                 .
                 The
                 truth
                 is
                 ,
                 that
                 the
                 Bank
                 was
                 not
                 made
                 of
                 proof
                 ,
                 since
                 that
                 the
                 same
                 now
                 continueth
                 whole
                 and
                 good
                 ,
                 and
                 Panaro
                 doth
                 not
                 break
                 out
                 ;
                 nay
                 ,
                 there
                 was
                 ,
                 when
                 it
                 brake
                 more
                 than
                 a
                 foot
                 and
                 half
                 of
                 its
                 Banks
                 above
                 the
                 Water
                 ,
                 and
                 to
                 spare
                 ;
                 but
                 it
                 broke
                 thorow
                 by
                 a
                 Moles
                 working
                 ;
                 or
                 by
                 the
                 hole
                 of
                 a
                 Water-Rat
                 ,
                 or
                 some
                 such
                 vermine
                 ;
                 and
                 by
                 occasion
                 of
                 the
                 badness
                 of
                 the
                 said
                 Banks
                 ,
                 as
                 I
                 finde
                 by
                 the
                 testimony
                 of
                 some
                 witnesses
                 examined
                 by
                 my
                 command
                 ,
                 that
                 I
                 might
                 know
                 the
                 truth
                 thereof
                 .
                 Nor
                 can
                 I
                 here
                 forbear
                 to
                 say
                 ,
                 that
                 it
                 would
                 be
                 better
                 ,
                 if
                 in
                 such
                 matters
                 men
                 were
                 more
                 candid
                 and
                 sincere
                 .
                 But
                 to
                 secure
                 our selves
                 neverthelesse
                 ,
                 to
                 the
                 utmost
                 of
                 our
                 power
                 ,
                 from
                 such
                 like
                 Breaches
                 which
                 may
                 happen
                 at
                 the
                 first
                 ,
                 by
                 reason
                 of
                 the
                 newnesse
                 of
                 the
                 Banks
                 ,
                 I
                 presuppose
                 that
                 from
                 Po
                 unto
                 the
                 place
                 whence
                 Reno
                 is
                 cut
                 ,
                 there
                 ought
                 to
                 be
                 a
                 high
                 and
                 thick
                 Fence
                 made
                 with
                 its
                 Banks
                 ,
                 so
                 that
                 there
                 would
                 be
                 no
                 cause
                 to
                 fear
                 any
                 whatsoever
                 accessions
                 of
                 Water
                 ,
                 although
                 that
                 concurrence
                 of
                 three
                 Rivers
                 ,
                 which
                 was
                 by
                 some
                 more
                 ingeniously
                 aggravated
                 than
                 faithfully
                 stated
                 by
                 that
                 which
                 was
                 said
                 above
                 were
                 true
                 ;
                 to
                 whom
                 I
                 think
                 not
                 my self
                 bound
                 to
                 make
                 any
                 farther
                 reply
                 ,
                 neither
                 to
                 those
                 who
                 say
                 that
                 Po
                 will
                 ascend
                 upwards
                 into
                 Reno
                 ,
                 since
                 that
                 these
                 are
                 the
                 same
                 persons
                 who
                 would
                 introduce
                 a
                 small
                 branch
                 of
                 the
                 said
                 Po
                 into
                 the
                 Chanel
                 of
                 Ferrara
                 ,
                 that
                 so
                 it
                 may
                 conveigh
                 to
                 the
                 Sea
                 ,
                 not
                 Reno
                 onely
                 ,
                 but
                 also
                 all
                 the
                 other
                 Brooks
                 of
                 which
                 we
                 complained
                 ;
                 and
                 because
                 that
                 withal
                 it
                 is
                 impossible
                 ,
                 that
                 a
                 River
                 so
                 capacious
                 as
                 Po
                 should
                 be
                 incommoded
                 by
                 a
                 Torrent
                 ,
                 that
                 ,
                 as
                 I
                 may
                 say
                 ,
                 hath
                 no
                 proportion
                 to
                 it
                 .
              
               
                 I
                 come
                 now
                 to
                 the
                 businesse
                 of
                 the
                 Ditches
                 and
                 Draines
                 ;
                 and
                 as
                 to
                 the
                 Conveyance
                 of
                 Burana
                 ,
                 it
                 hath
                 heretofore
                 been
                 debated
                 to
                 turn
                 it
                 into
                 Main-Po
                 ,
                 so
                 that
                 in
                 this
                 case
                 it
                 will
                 receive
                 no
                 harm
                 ,
                 and
                 though
                 it
                 were
                 not
                 removed
                 ,
                 yet
                 would
                 it
                 by
                 a
                 Trench
                 under
                 ground
                 pursue
                 the
                 course
                 that
                 it
                 now
                 holdeth
                 ,
                 and
                 also
                 would
                 be
                 able
                 to
                 dis-imbogue
                 again
                 into
                 the
                 said
                 new
                 Chanel
                 of
                 Reno
                 ,
                 which
                 conforming
                 to
                 the
                 superficies
                 of
                 the
                 Water
                 of
                 Po
                 ,
                 would
                 continue
                 at
                 a
                 lower
                 level
                 than
                 that
                 which
                 Panara
                 had
                 when
                 it
                 came
                 to
                 Ferrara
                 ,
                 into
                 which
                 Burana
                 did
                 neverthelesse
                 empty
                 it self
                 for
                 some
                 time
                 .
              
               
                 The
                 Conveyance
                 or
                 Drain
                 of
                 
                   Santa
                   Bianca
                
                 ,
                 and
                 the
                 little
                 Chanel
                 of
                 Cento
                 may
                 also
                 empty
                 themselves
                 by
                 two
                 subterranean
                 Trenches
                 ,
                 without
                 any
                 prejudice
                 where
                 they
                 run
                 at
                 present
                 ,
                 or
                 without
                 any
                 more
                 works
                 of
                 that
                 nature
                 ,
                 they
                 may
                 be
                 turned
                 into
                 the
                 said
                 new
                 Chanel
                 ,
                 although
                 with
                 somewhat
                 more
                 of
                 inconvenience
                 ;
                 and
                 withall
                 ,
                 the
                 Chanel
                 of
                 Ferrara
                 ,
                 left
                 dry
                 ,
                 would
                 be
                 a
                 sufficient
                 receptacle
                 for
                 any
                 other
                 Sewer
                 or
                 Drain
                 whatsoever
                 ,
                 that
                 should
                 remain
                 there
                 .
              
               
               
                 All
                 which
                 Operations
                 might
                 be
                 brought
                 to
                 perfection
                 with
                 150.
                 thousand
                 Crowns
                 ,
                 well
                 and
                 faithfully
                 laid
                 out
                 ;
                 which
                 summ
                 the
                 Bolognesi
                 will
                 not
                 be
                 unwilling
                 to
                 provide
                 ;
                 besides
                 that
                 those
                 Ferraresi
                 ought
                 to
                 contribute
                 to
                 it
                 ,
                 who
                 shall
                 partake
                 of
                 the
                 benefit
                 .
              
               
                 Let
                 me
                 be
                 permitted
                 in
                 this
                 place
                 to
                 propose
                 a
                 thing
                 which
                 I
                 have
                 thought
                 of
                 ,
                 and
                 which
                 peradventure
                 might
                 occasion
                 two
                 benefits
                 at
                 once
                 ,
                 although
                 it
                 be
                 not
                 wholly
                 new
                 .
                 It
                 was
                 in
                 the
                 time
                 of
                 
                   Pope
                   Paul
                
                 V.
                 propounded
                 by
                 one
                 Crescenzio
                 an
                 Ingineer
                 ,
                 to
                 cut
                 the
                 Main-Po
                 ,
                 above
                 
                   le
                   Papozze
                
                 ;
                 and
                 having
                 made
                 a
                 sufficient
                 evacuation
                 to
                 derive
                 the
                 water
                 thereof
                 into
                 the
                 Po
                 of
                 Adriano
                 ,
                 and
                 so
                 to
                 procure
                 it
                 to
                 be
                 Navigable
                 ,
                 which
                 was
                 not
                 at
                 that
                 time
                 effected
                 ,
                 either
                 by
                 reason
                 of
                 the
                 oppositions
                 of
                 those
                 ,
                 whose
                 possessions
                 were
                 to
                 be
                 cut
                 thorow
                 ,
                 or
                 by
                 reason
                 of
                 the
                 great
                 sum
                 of
                 money
                 that
                 was
                 necessary
                 for
                 the
                 effecting
                 of
                 it
                 :
                 But
                 in
                 viewing
                 those
                 Rivers
                 ,
                 we
                 have
                 observed
                 ,
                 that
                 the
                 sedge
                 cutting
                 might
                 easily
                 be
                 made
                 below
                 
                   le
                   Papozze
                
                 ,
                 in
                 digging
                 thorow
                 the
                 Bank
                 called
                 
                   Santa
                   Maria
                
                 ,
                 &
                 drawing
                 a
                 Trench
                 of
                 the
                 bigness
                 that
                 skilful
                 Artists
                 shall
                 judge
                 meet
                 unto
                 the
                 Po
                 *
                 of
                 Ariano
                 ,
                 below
                 the
                 Secche
                 of
                 the
                 said
                 S.
                 Maria
                 ;
                 which
                 as
                 being
                 a
                 work
                 of
                 not
                 above
                 160.
                 
                 Perches
                 in
                 length
                 ,
                 would
                 be
                 finished
                 with
                 onely
                 12000.
                 
                 Crowns
                 .
              
               
                 First
                 ;
                 it
                 is
                 to
                 be
                 believed
                 ,
                 that
                 the
                 waters
                 running
                 that
                 way
                 ,
                 would
                 not
                 fail
                 to
                 open
                 that
                 Mouth
                 into
                 the
                 Sea
                 ,
                 which
                 at
                 present
                 is
                 almost
                 choakt
                 up
                 by
                 the
                 Shelf
                 of
                 Sand
                 ,
                 which
                 the
                 new
                 Mouth
                 of
                 
                   Ponto
                   Virro
                
                 hath
                 brought
                 thither
                 ;
                 and
                 that
                 it
                 would
                 again
                 bring
                 into
                 use
                 the
                 Port
                 Goro
                 ,
                 and
                 its
                 Navigation
                 .
              
               
                 And
                 haply
                 experience
                 might
                 teach
                 us
                 ,
                 that
                 the
                 superficies
                 of
                 Po
                 might
                 come
                 to
                 fall
                 by
                 this
                 asswagement
                 of
                 Water
                 ,
                 so
                 that
                 the
                 accession
                 of
                 Reno
                 would
                 questionless
                 make
                 no
                 rising
                 in
                 it
                 :
                 Whereupon
                 ,
                 if
                 it
                 should
                 so
                 fall
                 out
                 ,
                 those
                 Princes
                 would
                 have
                 no
                 reason
                 to
                 complain
                 ;
                 who
                 seem
                 to
                 question
                 ,
                 lest
                 by
                 this
                 new
                 accession
                 of
                 water
                 into
                 Po
                 ,
                 the
                 Sluices
                 might
                 be
                 endangered
                 .
                 Which
                 I
                 thought
                 not
                 fit
                 to
                 omit
                 to
                 represent
                 to
                 your
                 Lordship
                 ;
                 not
                 ,
                 that
                 I
                 propose
                 it
                 to
                 you
                 as
                 a
                 thing
                 absolutely
                 certain
                 ,
                 but
                 that
                 you
                 might
                 ,
                 if
                 you
                 so
                 pleased
                 ,
                 lay
                 it
                 before
                 persons
                 whose
                 judgements
                 are
                 approved
                 in
                 these
                 affairs
                 .
              
               
                 I
                 return
                 now
                 from
                 where
                 I
                 degrest
                 ,
                 and
                 affirm
                 it
                 as
                 indubitable
                 ,
                 that
                 Reno
                 neither
                 can
                 ,
                 nor
                 ought
                 to
                 continue
                 longer
                 where
                 it
                 at
                 this
                 day
                 is
                 ;
                 and
                 that
                 it
                 cannot
                 go
                 into
                 any
                 other
                 place
                 but
                 that
                 ,
                 whither
                 
                   Cardinal
                   Capponi
                
                 designed
                 to
                 carry
                 it
                 ,
                 and
                 which
                 at
                 present
                 pleaseth
                 me
                 better
                 than
                 any
                 other
                 ;
                 or
                 into
                 Volana
                 ,
                 whence
                 it
                 was
                 taken
                 away
                 ;
                 the
                 vigilance
                 of
                 Men
                 being
                 able
                 to
                 obviate
                 part
                 of
                 those
                 mischiefs
                 ,
                 which
                 it
                 may
                 do
                 there
                 .
              
               
                 But
                 from
                 its
                 Removal
                 ,
                 besides
                 the
                 alleviation
                 of
                 the
                 harm
                 
                 which
                 by
                 it self
                 is
                 caused
                 ,
                 there
                 would
                 also
                 result
                 the
                 diminution
                 of
                 that
                 which
                 is
                 occasioned
                 by
                 the
                 other
                 Brooks
                 ,
                 to
                 the
                 right
                 hand
                 of
                 the
                 Po
                 of
                 Argenta
                 ;
                 forasmuch
                 as
                 the
                 said
                 Po
                 wanting
                 all
                 the
                 water
                 of
                 Reno
                 ,
                 it
                 would
                 of
                 necessity
                 come
                 to
                 ebb
                 in
                 such
                 manner
                 ,
                 that
                 the
                 Valleys
                 would
                 have
                 a
                 greater
                 Fall
                 into
                 the
                 same
                 ,
                 and
                 consequently
                 it
                 would
                 take
                 in
                 ,
                 and
                 swallow
                 greater
                 abundance
                 of
                 water
                 ;
                 and
                 by
                 this
                 means
                 the
                 Ditches
                 and
                 Draines
                 of
                 the
                 Up-Lands
                 would
                 likewise
                 more
                 easily
                 Fall
                 into
                 them
                 ;
                 especially
                 if
                 the
                 scouring
                 of
                 Zenzalino
                 were
                 brought
                 to
                 perfection
                 ,
                 by
                 which
                 the
                 waters
                 of
                 Marrara
                 would
                 fall
                 into
                 Marmorta
                 :
                 And
                 if
                 also
                 that
                 of
                 Bastia
                 were
                 enlarged
                 ,
                 and
                 finished
                 ,
                 by
                 which
                 there
                 might
                 enter
                 as
                 much
                 water
                 into
                 the
                 said
                 Po
                 of
                 Argenta
                 ,
                 as
                 is
                 taken
                 from
                 it
                 by
                 the
                 removal
                 of
                 Reno
                 ;
                 although
                 that
                 by
                 that
                 meanes
                 the
                 water
                 of
                 the
                 Valleys
                 would
                 asswage
                 double
                 :
                 Nor
                 would
                 the
                 people
                 of
                 Argenta
                 ,
                 the
                 Isles
                 of
                 S.
                 Giorgio
                 ,
                 and
                 Comacchio
                 have
                 any
                 cause
                 to
                 complain
                 ;
                 for
                 that
                 there
                 would
                 not
                 be
                 given
                 to
                 them
                 more
                 water
                 than
                 was
                 taken
                 away
                 :
                 Nay
                 sometimes
                 whereas
                 they
                 had
                 Muddy
                 waters
                 ,
                 they
                 would
                 have
                 clear
                 ;
                 nor
                 need
                 they
                 to
                 fear
                 any
                 rising
                 :
                 And
                 furthermore
                 ,
                 by
                 this
                 means
                 a
                 very
                 great
                 quantity
                 of
                 ground
                 would
                 be
                 restored
                 to
                 culture
                 ;
                 For
                 the
                 effecting
                 of
                 all
                 which
                 ,
                 the
                 summ
                 of
                 50.
                 thousand
                 Crowns
                 would
                 go
                 very
                 far
                 ,
                 and
                 would
                 serve
                 the
                 turn
                 at
                 present
                 touching
                 those
                 Brooks
                 ,
                 carrying
                 them
                 a
                 little
                 farther
                 in
                 the
                 mean
                 time
                 ,
                 to
                 fill
                 up
                 the
                 greater
                 cavities
                 of
                 the
                 Valleys
                 ,
                 that
                 we
                 might
                 not
                 enter
                 upon
                 a
                 vaster
                 and
                 harder
                 work
                 ,
                 that
                 would
                 bring
                 with
                 it
                 the
                 difficulties
                 of
                 other
                 operations
                 ,
                 and
                 so
                 would
                 hinder
                 the
                 benefit
                 which
                 these
                 people
                 expect
                 from
                 the
                 paternal
                 charity
                 of
                 His
                 Holiness
                 .
              
            
          
        
         
      
    
     
       
         
         
           TO
           The
           Right
           Honourable
           ,
           MONSIGNORE
           D.
           Ferrante
           Cesarini
           .
        
         
           MY
           Treatise
           of
           the
           MENSURATION
           of
           RUNNING
           WATERS
           ,
           Right
           Honourable
           ,
           and
           most
           Noble
           Sir
           ,
           hath
           not
           a
           greater
           Prerogative
           than
           its
           having
           been
           the
           production
           of
           the
           command
           of
           Pope
           Vrban
           VIII
           .
           when
           His
           Holiness
           was
           pleased
           to
           enjoyn
           me
           to
           go
           with
           
             Monsignore
             Corsini
          
           ,
           in
           the
           Visitation
           that
           was
           imposed
           upon
           him
           in
           the
           year
           1625.
           of
           the
           Waters
           of
           
             Ferrara
             ,
             Bologna
             ,
             Romagna
          
           ,
           and
           Romagnola
           ;
           for
           that
           ,
           on
           that
           occasion
           applying
           my
           whole
           Study
           to
           my
           service
           and
           duty
           ,
           I
           published
           in
           that
           Treatise
           some
           particulars
           till
           then
           not
           rightly
           understood
           and
           considered
           (
           that
           I
           knew
           )
           by
           any
           one
           ;
           although
           they
           be
           in
           themselves
           most
           important
           ,
           and
           of
           extraordinary
           consequence
           .
           Yet
           I
           must
           render
           thanks
           to
           Your
           Lordship
           for
           the
           honour
           you
           have
           done
           to
           that
           my
           Tract
           ;
           but
           wish
           withal
           ,
           that
           your
           Esteem
           of
           it
           may
           not
           prejudice
           the
           universal
           Esteem
           that
           the
           World
           hath
           of
           Your
           Honours
           most
           refined
           judgement
           .
        
         
           As
           to
           that
           Point
           which
           I
           touch
           upon
           in
           the
           Conclusion
           ,
           namely
           ,
           That
           the
           consideration
           of
           the
           Velocity
           of
           Running
           Water
           supplyeth
           the
           consideration
           of
           the
           *
           Length
           omitted
           in
           the
           common
           way
           of
           measuring
           Running
           Waters
           ;
           Your
           Lordship
           having
           commanded
           me
           that
           in
           favour
           of
           Practise
           ,
           and
           for
           the
           perfect
           discovery
           of
           the
           disorder
           that
           commonly
           happeneth
           now
           adayes
           in
           the
           distribution
           of
           the
           Waters
           of
           Fountains
           ,
           I
           should
           demonstrate
           that
           the
           knowledge
           of
           the
           Velocity
           serveth
           for
           the
           finding
           of
           the
           Length
           :
           I
           have
           thought
           fit
           to
           satisfie
           your
           Command
           by
           relating
           a
           Fable
           ;
           which
           ,
           if
           I
           do
           not
           deceive
           my self
           ,
           will
           make
           out
           to
           us
           the
           truth
           thereof
           ;
           insomuch
           that
           the
           rest
           of
           my
           Treatise
           shall
           thereby
           also
           become
           more
           manifest
           and
           intelligible
           ,
           even
           to
           
           those
           who
           finde
           therein
           some
           kinde
           of
           obscurity
           .
        
         
           In
           the
           dayes
           of
           yore
           ,
           before
           that
           the
           admirable
           Art
           of
           Weaving
           was
           in
           use
           ,
           there
           was
           found
           in
           Persia
           a
           vast
           and
           unvaluable
           Treasure
           ,
           which
           consisted
           in
           an
           huge
           multitude
           of
           pieces
           of
           Ermesin
           ,
           or
           Damask
           ,
           I
           know
           not
           whether
           ;
           which
           ,
           as
           I
           take
           it
           ,
           amounted
           to
           near
           two
           thousand
           pieces
           ;
           which
           were
           of
           such
           a
           nature
           ,
           that
           though
           their
           Breadth
           and
           Thickness
           were
           finite
           and
           determinate
           ,
           as
           they
           use
           to
           be
           at
           this
           day
           ;
           yet
           nevertheless
           ,
           their
           Length
           was
           in
           a
           certain
           sense
           infinite
           ,
           for
           that
           those
           two
           thousand
           pieces
           ,
           day
           and
           night
           without
           ceasing
           ,
           issued
           out
           with
           their
           ends
           at
           such
           a
           rate
           ,
           that
           of
           each
           piece
           there
           issued
           100.
           
           Ells
           a
           day
           ,
           from
           a
           deep
           and
           dark
           Cave
           ,
           consecrated
           by
           the
           Superstition
           of
           those
           people
           ,
           to
           the
           fabulous
           Arachne
           .
           In
           those
           innocent
           and
           early
           times
           (
           I
           take
           it
           to
           have
           been
           ,
           in
           that
           so
           much
           applauded
           and
           desired
           Golden
           age
           )
           it
           was
           left
           to
           the
           liberty
           of
           any
           one
           ,
           to
           cut
           off
           of
           those
           pieces
           what
           quantity
           they
           pleased
           without
           any
           difficulty
           :
           But
           that
           felicity
           decaying
           and
           degenerating
           ,
           which
           was
           altogether
           ignorant
           of
           Meum
           and
           Tuum
           ;
           terms
           certainly
           most
           pernicious
           ,
           the
           Original
           of
           all
           evils
           ,
           and
           cause
           of
           all
           discords
           ;
           there
           were
           by
           those
           people
           strong
           and
           vigilant
           Guards
           placed
           upon
           the
           Cave
           ,
           who
           resolved
           to
           make
           merchandize
           of
           the
           Stuffes
           ;
           and
           in
           this
           manner
           they
           began
           to
           set
           a
           price
           upon
           that
           inestimable
           Treasure
           ,
           selling
           the
           propriety
           in
           those
           pieces
           to
           divers
           Merchants
           ;
           to
           some
           they
           sold
           a
           right
           in
           one
           ,
           to
           some
           in
           two
           ,
           and
           to
           some
           in
           more
           .
           But
           that
           which
           was
           the
           worst
           of
           all
           ,
           There
           was
           found
           out
           by
           the
           insatiable
           avarice
           of
           these
           men
           crafty
           inventions
           to
           deceive
           the
           Merchants
           also
           ;
           who
           came
           to
           buy
           the
           aforesaid
           commodity
           ,
           and
           to
           make
           themselves
           Masters
           ,
           some
           of
           one
           some
           of
           two
           ,
           and
           some
           of
           more
           ends
           of
           those
           pieces
           of
           stuff
           ;
           and
           in
           particular
           ,
           there
           were
           cetain
           ingenuous
           Machines
           placed
           in
           the
           more
           secret
           places
           of
           the
           Cave
           ,
           with
           which
           at
           the
           pleasure
           of
           the
           Guards
           ,
           they
           did
           retard
           the
           velocity
           of
           those
           Stuffs
           ,
           in
           their
           issuing
           out
           of
           the
           Cave
           ;
           insomuch
           ,
           that
           he
           who
           ought
           to
           have
           had
           100.
           
           Ells
           of
           Stuff
           in
           a
           day
           ,
           had
           not
           above
           50
           ,
           and
           he
           who
           should
           have
           had
           400
           ,
           enjoyed
           the
           benefit
           of
           50.
           onely
           ;
           and
           so
           all
           the
           rest
           were
           defrauded
           of
           their
           Rights
           ,
           the
           surplusage
           being
           sold
           ,
           appropriated
           ,
           and
           shared
           at
           the
           will
           of
           the
           corrupt
           Officers
           :
           So
           that
           the
           business
           was
           without
           all
           order
           or
           justice
           ,
           insomuch
           that
           the
           Goddess
           Arachne
           being
           displeased
           at
           those
           people
           ,
           deprived
           every
           one
           of
           their
           benefit
           ,
           and
           with
           a
           dreadful
           Earthquake
           for
           ever
           closing
           the
           mouth
           of
           the
           Cave
           ,
           in
           punishment
           of
           so
           much
           impiety
           and
           malice
           :
           Nor
           did
           it
           avail
           them
           to
           excuse
           themselves
           ,
           by
           saying
           that
           they
           allowed
           the
           Buyer
           the
           Breadth
           and
           Thickness
           bargained
           for
           ;
           and
           that
           of
           the
           Length
           ,
           which
           was
           infinite
           ,
           
           there
           could
           no
           account
           be
           kept
           :
           For
           the
           wise
           and
           prudent
           Priest
           of
           the
           Sacred
           Grotto
           answered
           ,
           That
           the
           deceit
           lay
           in
           the
           length
           ,
           which
           they
           were
           defrauded
           of
           ,
           in
           that
           the
           velocity
           of
           the
           stuffe
           was
           retarded
           ,
           as
           it
           issued
           out
           of
           the
           Cave
           :
           and
           although
           the
           total
           length
           of
           the
           Piece
           was
           infinite
           ,
           for
           that
           it
           never
           ceased
           coming
           forth
           ,
           and
           so
           was
           not
           to
           be
           computed
           ;
           yet
           nevertheless
           its
           length
           considered
           ,
           part
           by
           part
           ,
           as
           it
           came
           out
           of
           the
           Cave
           ,
           and
           was
           bargained
           for
           ,
           continued
           still
           finite
           ,
           and
           might
           be
           one
           while
           greater
           ,
           and
           another
           while
           lesser
           ,
           according
           as
           the
           Piece
           was
           constituted
           in
           greater
           or
           lesser
           velocity
           ;
           and
           he
           added
           withall
           ,
           that
           exact
           Justice
           required
           ,
           that
           when
           they
           sold
           a
           piece
           of
           stuff
           ,
           and
           the
           propriety
           or
           dominion
           therein
           ,
           they
           ought
           not
           only
           to
           have
           ascertained
           the
           breadth
           and
           thicknesse
           of
           the
           Piece
           ,
           but
           also
           to
           have
           determined
           the
           length
           ,
           determining
           its
           velocity
           .
        
         
           The
           same
           disorder
           and
           confusion
           ,
           that
           was
           represented
           in
           the
           Fable
           ,
           doth
           come
           to
           passe
           in
           the
           History
           of
           the
           Distribution
           of
           the
           Waters
           of
           Conduits
           and
           Fountains
           ,
           seeing
           that
           they
           are
           sold
           and
           bought
           ,
           having
           regard
           only
           to
           the
           two
           Dimensions
           ,
           I
           mean
           of
           Breadth
           and
           Height
           of
           the
           Mouth
           that
           dischargeth
           the
           Water
           ;
           and
           to
           remedy
           such
           an
           inconvenience
           ,
           it
           is
           necessary
           to
           determine
           the
           length
           in
           the
           velocity
           ;
           for
           never
           shall
           we
           be
           able
           to
           make
           a
           guesse
           at
           the
           quantity
           of
           the
           Body
           of
           Running
           VVater
           ,
           with
           the
           two
           Dimensions
           only
           of
           Breadth
           and
           Height
           ,
           without
           Length
           .
        
         
           And
           to
           the
           end
           ,
           that
           the
           whole
           business
           may
           be
           reduced
           to
           a
           most
           easie
           practice
           ,
           by
           which
           the
           waters
           of
           Aqueducts
           may
           be
           bought
           and
           sold
           justly
           ,
           and
           with
           measures
           alwayes
           exact
           and
           constant
           .
        
         
           First
           ,
           the
           quantity
           of
           the
           Water
           ought
           diligently
           to
           be
           examined
           ,
           which
           the
           whole
           principal
           *
           Pipe
           dischargeth
           in
           a
           time
           certain
           ,
           as
           for
           instance
           ,
           in
           an
           hour
           ,
           in
           half
           an
           hour
           ,
           or
           in
           a
           lesse
           interval
           of
           time
           ,
           (
           for
           knowing
           which
           I
           have
           a
           most
           exact
           and
           easie
           Rule
           )
           and
           finding
           that
           the
           whole
           principal
           pipe
           dischargeth
           
             v.
             g.
          
           a
           thousand
           Tuns
           of
           Water
           in
           the
           space
           of
           one
           or
           more
           hours
           ,
           in
           selling
           of
           this
           water
           ,
           it
           ought
           not
           to
           be
           uttered
           by
           the
           ordinary
           and
           false
           measure
           ,
           but
           the
           distribution
           is
           to
           be
           made
           with
           agreement
           to
           give
           and
           maintain
           to
           the
           buyer
           ten
           or
           twenty
           ,
           or
           a
           greater
           number
           of
           Tuns
           ,
           as
           the
           bargain
           shall
           be
           made
           ,
           in
           the
           space
           of
           an
           hour
           ,
           or
           of
           some
           other
           set
           and
           determinate
           time
           .
           And
           here
           I
           adde
           ,
           that
           if
           I
           were
           to
           undertake
           to
           make
           such
           an
           adjustment
           ,
           I
           would
           make
           use
           of
           a
           way
           to
           divide
           and
           measure
           the
           time
           with
           such
           accuratenesse
           ,
           that
           the
           space
           of
           an
           hour
           should
           be
           divided
           into
           four
           ,
           six
           ,
           or
           eight
           thousand
           parts
           
           without
           the
           least
           errour
           ;
           which
           Rule
           was
           taught
           me
           by
           my
           Master
           
             Sign
             .
             Galilaeo
             Galilaei
          
           ,
           Chief
           Philosopher
           to
           the
           most
           Serene
           
             Grand
             Duke
          
           of
           Tuscany
           .
           And
           this
           way
           will
           serve
           easily
           and
           admirably
           to
           our
           purpose
           and
           occasion
           ;
           so
           that
           we
           shall
           thereby
           be
           able
           to
           know
           how
           many
           Quarts
           of
           Water
           an
           Aqueduct
           will
           discharge
           in
           a
           given
           time
           of
           hours
           ,
           moneths
           ,
           or
           years
           .
           And
           in
           this
           manner
           we
           may
           constitute
           a
           Cock
           that
           shall
           discharge
           a
           certain
           and
           determinate
           quantity
           of
           water
           in
           a
           time
           given
           .
        
         
           And
           because
           daily
           experience
           shews
           us
           ,
           that
           the
           Springs
           of
           Aqueducts
           do
           not
           maintain
           them
           alwayes
           equally
           high
           ,
           and
           full
           of
           Water
           ,
           but
           that
           sometimes
           they
           increase
           ,
           and
           sometimes
           decrease
           ,
           which
           accident
           might
           possibly
           procure
           some
           difficulty
           in
           our
           distribution
           :
           Therefore
           ,
           to
           the
           end
           that
           all
           manner
           of
           scruple
           may
           be
           removed
           ,
           I
           conceive
           that
           it
           would
           be
           convenient
           to
           provide
           a
           Cistern
           ,
           according
           to
           the
           occasion
           ,
           into
           which
           there
           might
           alwayes
           fall
           one
           certain
           quantity
           of
           water
           ,
           which
           should
           not
           be
           greater
           than
           that
           which
           the
           principal
           pipe
           dischargeth
           in
           times
           of
           drought
           ,
           when
           the
           Springs
           are
           bare
           of
           water
           ,
           that
           so
           in
           this
           Cistern
           the
           water
           might
           alwayes
           keep
           at
           one
           constant
           height
           .
           Then
           to
           the
           Cistern
           so
           prepared
           we
           are
           to
           fasten
           the
           Cocks
           of
           particular
           persons
           to
           whom
           the
           Water
           is
           sold
           by
           the
           Reverend
           Apostolique
           Chamber
           ,
           according
           to
           what
           hath
           been
           observed
           before
           ;
           and
           that
           quantity
           of
           Water
           which
           remaineth
           over
           and
           above
           ,
           is
           to
           be
           discharged
           into
           another
           Cistern
           ,
           in
           which
           the
           Cocks
           of
           the
           Waters
           for
           publick
           services
           ,
           and
           of
           those
           which
           people
           buy
           upon
           particular
           occasions
           are
           to
           be
           placed
           .
           And
           when
           the
           businesse
           shall
           have
           been
           brought
           to
           this
           passe
           ,
           there
           will
           likewise
           a
           remedy
           be
           found
           to
           the
           so
           many
           disorders
           that
           continually
           happen
           ;
           of
           which
           ,
           for
           brevity
           sake
           ,
           I
           will
           instance
           in
           but
           four
           only
           ,
           which
           concern
           both
           publique
           and
           private
           benefit
           ,
           as
           being
           ,
           in
           my
           judgment
           ,
           the
           most
           enormous
           and
           intolerable
           .
        
         
           The
           first
           inconvenience
           it
           ,
           that
           in
           the
           common
           way
           of
           measuring
           ,
           dispensing
           ,
           and
           selling
           the
           Waters
           of
           Aqueducts
           ,
           it
           is
           not
           understood
           ,
           neither
           by
           the
           Buyer
           nor
           Seller
           ,
           what
           the
           quantity
           truly
           is
           that
           is
           bought
           and
           sold
           ;
           nor
           could
           I
           ever
           meet
           with
           any
           either
           Engineer
           or
           Architect
           ,
           or
           Artist
           ,
           or
           other
           that
           was
           able
           to
           decypher
           to
           me
           ,
           what
           one
           ,
           or
           two
           ,
           or
           ten
           inches
           of
           water
           was
           .
           But
           by
           our
           above
           declared
           Rule
           ,
           for
           dispensing
           the
           Waters
           of
           Aqueducts
           we
           may
           very
           easily
           know
           the
           true
           quantity
           of
           Water
           that
           is
           bought
           or
           sold
           ,
           as
           that
           it
           is
           so
           many
           Tuns
           an
           hour
           ,
           so
           many
           a
           day
           ,
           so
           many
           in
           a
           year
           ,
           &c.
           
        
         
           The
           second
           disorder
           that
           happeneth
           ,
           at
           present
           ,
           in
           the
           distribution
           
           of
           Aqueducts
           is
           ,
           that
           as
           the
           businesse
           is
           now
           governed
           ,
           it
           lieth
           in
           the
           power
           of
           a
           ●ordid
           Mason
           to
           take
           unjustly
           from
           one
           ,
           and
           give
           undeservedly
           to
           another
           more
           or
           lesse
           Water
           than
           belongeth
           to
           them
           of
           right
           :
           And
           I
           have
           seen
           it
           done
           ,
           of
           my
           own
           experience
           .
           But
           in
           our
           way
           of
           measuring
           and
           distributing
           Waters
           ,
           there
           can
           no
           fraud
           be
           committed
           ;
           and
           putting
           the
           case
           that
           they
           should
           be
           committed
           ,
           it
           s
           an
           easie
           matter
           to
           know
           it
           ,
           and
           amend
           it
           ,
           by
           repairing
           to
           the
           Tribunal
           appointed
           .
        
         
           Thirdly
           ,
           it
           happens
           very
           often
           ,
           (
           and
           we
           have
           examples
           thereof
           both
           antient
           and
           modern
           )
           that
           in
           dispensing
           the
           Water
           after
           the
           common
           and
           vulgar
           way
           ;
           there
           is
           sometimes
           more
           Water
           dispended
           than
           there
           is
           in
           the
           Register
           ,
           in
           which
           there
           will
           be
           registred
           ,
           as
           they
           say
           ,
           two
           hundred
           inches
           (
           for
           example
           )
           and
           there
           will
           be
           dispensed
           two
           hundred
           and
           fifty
           inches
           ,
           or
           more
           .
           Which
           passage
           happened
           in
           the
           time
           of
           Nerva
           the
           Emperour
           ,
           as
           
             Giulio
             Frontino
          
           writes
           ,
           in
           his
           2.
           
           Book
           ,
           
             De
             Aquaductibus
             Vrbis
             Romae
          
           ,
           where
           he
           observeth
           that
           they
           had
           
             in
             Commentariis
          
           12755.
           
           Quinaries
           of
           Water
           ;
           and
           found
           that
           they
           dispensed
           14018.
           
           Quinaries
           .
           And
           the
           like
           Errour
           hath
           continued
           ,
           and
           is
           in
           use
           also
           modernly
           until
           our
           times
           .
           But
           if
           our
           Rule
           shall
           be
           observed
           ,
           we
           shall
           incur
           no
           such
           disorder
           ,
           nay
           there
           will
           alwayes
           be
           given
           to
           every
           one
           his
           share
           ,
           according
           to
           the
           holy
           end
           of
           exact
           justice
           ,
           which
           
             dat
             unicuique
             quod
             suum
             est
          
           .
           As
           on
           the
           contrary
           ,
           it
           is
           manifest
           ,
           that
           His
           Divine
           Majesty
           hateth
           and
           abominateth
           
             Pondus
             &
             pondus
             ,
             Mensura
             &
             mensura
             ,
          
           as
           the
           Holy
           Ghost
           speaketh
           by
           the
           mouth
           of
           Solomon
           in
           the
           
             Proverbs
             ,
             Chap.
          
           20.
           
           
             Pondus
             &
             Pondus
             ,
             Mensura
             &
             Mensura
             ,
             utrumque
             abominabile
             est
             apud
             Deum
             .
          
           And
           therefore
           who
           is
           it
           that
           seeth
           not
           that
           the
           way
           of
           dividing
           and
           measuring
           of
           VVaters
           ,
           commonly
           used
           ,
           is
           expresly
           against
           the
           Law
           of
           God.
           Since
           that
           thereby
           the
           same
           measure
           is
           made
           sometimes
           greater
           ,
           and
           sometimes
           lesser
           ;
           A
           disorder
           so
           enormous
           and
           execrable
           ,
           that
           I
           shall
           take
           the
           boldness
           to
           say
           ,
           that
           for
           this
           sole
           respect
           it
           ought
           to
           be
           condemned
           and
           prohibited
           likewise
           by
           human
           Law
           ,
           which
           should
           Enact
           that
           in
           this
           business
           there
           should
           be
           imployed
           either
           this
           our
           Rule
           ,
           or
           some
           other
           that
           is
           more
           exquisite
           and
           practicable
           ,
           whereby
           the
           measure
           might
           keep
           one
           constant
           and
           determinate
           tenor
           ,
           as
           we
           make
           it
           ,
           and
           not
           ,
           as
           it
           is
           now
           ,
           to
           make
           
             Pondus
             &
             Pondus
             ,
             Mensura
             &
             Mensura
             .
          
        
         
           And
           this
           is
           all
           that
           I
           had
           to
           offer
           to
           Your
           most
           Illustrious
           Lordship
           ,
           in
           obedience
           to
           your
           commands
           ,
           reserving
           to
           my self
           the
           giving
           of
           a
           more
           exact
           account
           of
           this
           my
           invention
           ,
           when
           the
           occasion
           shall
           offer
           ,
           of
           reducing
           to
           practice
           so
           holy
           ,
           just
           ,
           and
           
           necessary
           a
           reformation
           of
           the
           Measure
           of
           Running
           Waters
           and
           of
           Aqueducts
           in
           particular
           :
           which
           Rule
           may
           also
           be
           of
           great
           benefit
           in
           the
           division
           of
           the
           greater
           Waters
           to
           over-flow
           Grounds
           ,
           and
           for
           other
           uses
           :
           I
           humbly
           bow
           ,
        
         
           
             Your
             Most
             Devoted
             ,
             and
             Most
             Obliged
             Servant
             ,
             
               D.
               Benedetto
               Castelli
            
             ,
             Abb.
             Casin
             .
          
        
         
           FINIS
           .
        
      
       
         
         
           A
           TABLE
           Of
           the
           most
           observable
           matters
           in
           this
           Treatise
           of
           the
           MENSURATION
           of
           RUNNING
           WATERS
           .
        
         
           
             A
          
           
             
               A
               Batements
            
             of
             a
             River
             in
             different
             and
             unequal
             Diversions
             ,
             is
             alwaies
             equal
             ,
             which
             is
             proved
             with
             100.
             
             Syphons
             .
             Page
             75
          
           
             Arno
             River
             when
             it
             riseth
             upon
             a
             Land-Flood
             near
             the
             Sea
             one
             third
             of
             a
             Brace
             ,
             it
             riseth
             about
             Pisa
             6.
             or
             7.
             
             Braces
             .
             82
          
        
         
           
             B
          
           
             Banks
             near
             to
             the
             Sea
             lower
             ,
             than
             far
             from
             thence
             .
             Corollary
             XIV
             .
             16
          
           
             Brent
             River
             diverted
             from
             the
             Lake
             of
             Venice
             ,
             and
             its
             effects
             .
             64
          
           
             Brent
             supposed
             insufficient
             to
             remedy
             the
             inconveniences
             of
             the
             Lake
             ,
             and
             the
             falsity
             of
             that
             supposition
             .
             67
          
           
             Brent
             ,
             and
             its
             benefits
             in
             the
             Lake
             .
             70
          
           
             Its
             Deposition
             of
             Sand
             in
             the
             Lake
             ,
             how
             great
             it
             is
             .
             78
             ,
             79
          
           
             Bridges
             over
             Rivers
             ,
             and
             how
             they
             are
             to
             be
             made
             .
             Appendix
             VIII
             .
             20
          
           
             Burana
             River
             ,
             its
             rising
             ,
             and
             falling
             in
             Panaro
             .
             110
          
        
         
           
             C
          
           
             Castelli
             applyed
             himself
             to
             this
             Study
             by
             Order
             of
             Urban
             VIII
             .
             2
          
           
             
               Chanel
               of
               Navigation
            
             in
             the
             Valleys
             of
             Bologna
             ,
             and
             its
             inconveniences
             .
             99
          
           
             Carried
             into
             the
             Po
             of
             Ferrara
             ,
             and
             its
             benefits
             ibid.
             
          
           
             Ciampoli
             a
             lover
             of
             those
             Observations
             of
             Waters
             .
             3
          
        
         
           
             D
          
           
             Difficulty
             of
             this
             business
             of
             Measuring
             Waters
             .
             2
          
           
             Disorders
             that
             happen
             in
             the
             distribution
             of
             the
             Waters
             of
             Aqueducts
             ,
             and
             their
             remedies
             .
             113
          
           
             Distribution
             of
             the
             Waters
             of
             Fountains
             ,
             and
             Aqueducts
             .
             Appendix
             X.
             22
          
           
             Distribution
             of
             Water
             to
             over-flow
             Grounds
             .
             Appendix
             XI
             .
             23
             ,
             69
             ,
             70
          
           
             Diversion
             of
             Reno
             and
             other
             Brooks
             of
             Romagna
             ,
             advised
             by
             
               P.
               Spernazzati
            
             to
             what
             end
             it
             was
             .
             100
          
           
             Drains
             and
             Ditches
             ,
             the
             benefit
             they
             receive
             by
             cutting
             away
             the
             Weeds
             and
             Reeds
             .
             Appendix
             IX
             .
             21
          
           
             Drains
             and
             Sewers
             obstructed
             ,
             in
             the
             Diversion
             of
             Reno
             into
             
               Main
               Po
            
             ,
             and
             a
             remedy
             for
             the
             same
             .
             110
          
        
         
           
             E
          
           
             Engineers
             unvers'd
             in
             the
             matters
             of
             Waters
             .
             2
          
           
             Erour
             found
             in
             the
             common
             way
             of
             Measuring
             Running
             Waters
             :
             68
             ,
             69
          
           
             Errour
             in
             deriving
             the
             Water
             of
             
               Acqua
               Paola
            
             .
             Appendix
             II.
             17
             ,
             18
          
           
             
             Errour
             of
             Bartolotti
             .
             86
             ,
             87
          
           
             Errours
             of
             Engineers
             in
             the
             Derivation
             of
             Chanels
             .
             Corollary
             ,
             XII
             .
             12
          
           
             Errour
             of
             Engineers
             in
             Measuring
             of
             Reno
             in
             Po.
             Appendix
             III.
             ibid.
             
          
           
             Errour
             of
             other
             Engineers
             ;
             contrary
             to
             the
             precedent
             .
             Appendix
             IV.
             Ibid.
             
          
           
             Errour
             of
             
               Giovanni
               Fontana
            
             in
             Measuring
             Waters
             .
             Corollary
             XI
             .
             9
          
           
             Errour
             of
             
               Giulio
               Frontino
            
             in
             Measuring
             the
             Waters
             of
             Aqueducts
             .
             Appendix
             I.
             17
          
           
             Errours
             committed
             in
             cutting
             the
             Bank
             at
             Bondeno
             ,
             in
             the
             swellings
             of
             Po
             :
             Corollary
             XIII
             .
             81
          
        
         
           
             F
          
           
             Fenns
             Pontine
             ,
             Drained
             by
             Pope
             
               Sixtus
               Quintus
            
             ,
             with
             vast
             expence
             .
             92
          
           
             The
             ruine
             and
             miscarriage
             thereof
             .
             93
          
           
             Tardity
             of
             the
             principal
             Chanel
             that
             Drains
             them
             ,
             cause
             of
             the
             Drowning
             .
             ibid.
             
          
           
             They
             are
             obstructed
             by
             the
             Fishing-Wears
             ,
             which
             swell
             the
             River
             .
             94
          
           
             Waters
             of
             
               Fiume
               Sisto
            
             ,
             which
             flow
             in
             great
             abundance
             into
             the
             Evacuator
             of
             the
             said
             Fenns
             .
             94
             ,
             95
          
           
             Remedies
             to
             the
             disorders
             of
             those
             Fenns
             .
             95
             ,
             96
          
           
             
               Fontana
               Giovanni
            
             ,
             his
             errours
             in
             Measuring
             Waters
             .
             Corollary
             XI
             .
             9
          
           
             
               Fiume
               Morto
            
             ,
             whether
             it
             ought
             to
             fall
             into
             the
             Sea
             ,
             or
             into
             Serchio
             ,
             79
          
           
             Let
             into
             Serchio
             and
             its
             inconveniences
             .
             79
             ,
             80
          
           
             The
             dangerous
             rising
             of
             its
             Waters
             :
             when
             to
             be
             expected
             .
             81
          
           
             Its
             inconveniences
             when
             it
             is
             higher
             in
             level
             than
             Serchio
             ,
             and
             why
             it
             riseth
             most
             On
             the
             Sea-coasts
             ,
             at
             such
             time
             as
             the
             Winds
             make
             the
             Sea
             to
             swell
             .
             83
          
        
         
           
             G
          
           
             
               Galilaeo
               Galilaei
            
             ,
             honourably
             mentioned
             .
             Page
             2
             ,
             28
          
           
             His
             Rule
             for
             measuring
             the
             time
             .
             49
          
        
         
           
             H
          
           
             Height
             ,
             vide
             Quick
          
           
             Heights
             different
             ,
             made
             by
             the
             same
             stream
             of
             a
             Brook
             or
             Torrent
             ,
             according
             to
             the
             divers
             Velocities
             in
             the
             entrance
             of
             the
             River
             .
             Corollary
             I.
             6
          
           
             Heights
             different
             ,
             made
             by
             the
             Torrent
             in
             the
             River
             ,
             according
             to
             the
             different
             heights
             of
             the
             River
             .
             Corollary
             II.
             ibid.
             
          
        
         
           
             K
          
           
             Knowledge
             of
             Motion
             how
             much
             i●
             importeth
             .
             1
          
        
         
           
             L
          
           
             Lake
             of
             Perugia
             ,
             and
             ,
             be
             Observation
             made
             on
             it
             .
             Appendix
             XII
             .
             42
          
           
             Lake
             of
             Thrasimenus
             and
             Considerations
             upon
             it
             ,
             a
             Letter
             written
             to
             
               Sig.
               Galilaeo
               Galilaei
            
             .
             28
          
           
             Lake
             of
             Venice
             ,
             and
             Considerations
             upon
             it
             .
             63
             ,
             73
          
           
             Low
             Waters
             which
             let
             the
             bottom
             of
             it
             be
             discovered
             .
             64
          
           
             The
             stoppage
             and
             choaking
             of
             the
             Ports
             ,
             a
             main
             cause
             of
             the
             disorders
             of
             the
             Lake
             ,
             and
             the
             grand
             remedy
             to
             those
             disorders
             what
             it
             is
             .
             66
          
           
             Lakes
             and
             Meers
             along
             the
             Sea-coasts
             ,
             and
             the
             causes
             thereof
             .
             65
          
           
             Length
             of
             Waters
             ,
             how
             it
             is
             to
             be
             Measured
             .
             70
          
        
         
           
             M
          
           
             Measure
             and
             Distributions
             of
             Waters
             .
             Appendix
             V.
             18
          
           
             
             Measure
             of
             Rivers
             that
             fall
             into
             others
             difficult
             .
             Coroll
             .
             X
             :
             9
          
           
             Measure
             of
             the
             Running
             Water
             of
             a
             Chanel
             of
             an
             height
             known
             by
             a
             Regulator
             of
             a
             Measure
             given
             ,
             in
             a
             time
             assigned
             .
             Proposition
             I.
             Problem
             I.
             50
          
           
             Measure
             of
             the
             Water
             of
             any
             River
             ,
             of
             any
             greatness
             ,
             in
             a
             time
             given
             .
             Proposition
             V.
             Problem
             III.
             60
          
           
             Measure
             that
             shewes
             how
             much
             Water
             a
             River
             dischargeth
             in
             a
             time
             given
             .
             48
          
           
             Mole-holes
             ,
          
           
             Motion
             the
             principal
             subject
             of
             Philosophy
             .
             1
          
           
             Mud.
             Vide
             Sand.
             
          
        
         
           
             N
          
           
             Navigation
             from
             Bologna
             to
             Ferrara
             ,
             is
             become
             impossible
             ,
             till
             such
             time
             as
             Reno
             be
             diverted
             .
             101
          
           
             Navigation
             in
             the
             Lake
             of
             Venice
             endangered
             ,
             and
             how
             restored
             .
             65
             ,
             70
          
        
         
           
             P
          
           
             Perpendicularity
             of
             the
             Banks
             of
             the
             River
             ,
             to
             the
             upper
             superficies
             of
             it
             .
             37
          
           
             Perpendicularity
             of
             the
             Banks
             to
             the
             bottom
             .
             37
          
           
             Perugia
             .
             Vide
             Lake
             .
          
           
             Pontine
             .
             Vide
             Fenns
             .
          
           
             Ports
             of
             
               Venice
               ,
               Malamocco
               ,
               Bondolo
            
             ,
             and
             Chiozza
             ,
             choaked
             up
             for
             want
             of
             Water
             in
             the
             Lake
             .
             65
          
           
             Proportions
             of
             unequal
             Sections
             of
             equal
             Velocity
             ,
             and
             of
             equal
             Sections
             of
             unequal
             Velocity
             .
             Axiome
             IV.
             and
             V.
             38
          
           
             Proportions
             of
             equal
             and
             unequal
             quantities
             of
             Water
             ,
             which
             pass
             by
             the
             Sections
             of
             different
             Rivers
             .
             Proposition
             II.
             39
          
           
             Proportions
             of
             unequal
             Sections
             that
             in
             equal
             times
             discharge
             equal
             quantities
             of
             Water
             .
             Proposition
             III.
             41
          
           
             Proportion
             wherewith
             one
             River
             falling
             into
             another
             ,
             varieth
             in
             height
             .
             Proposition
             IV.
             44
          
           
             Proportion
             of
             the
             Water
             discharged
             by
             a
             River
             in
             the
             time
             of
             Flood
             ,
             to
             the
             Water
             discharged
             in
             an
             equal
             time
             by
             the
             said
             River
             ,
             before
             or
             after
             the
             Flood
             .
             Proposition
             V.
             44
          
           
             Proportion
             of
             the
             Heights
             made
             by
             two
             equal
             Brooks
             or
             Streams
             falling
             into
             the
             same
             River
             .
             Proposition
             VI.
             45
          
           
             Proportion
             of
             the
             Water
             which
             a
             River
             dischargeth
             encreasing
             in
             Quick-height
             by
             the
             addition
             of
             new
             Water
             ,
             to
             that
             which
             it
             dischargeth
             after
             the
             encrease
             is
             made
             .
             Proposition
             IV.
             Theor.
             II.
             54
          
           
             Proportion
             of
             a
             River
             when
             high
             ,
             to
             it self
             when
             low
             .
             Coroll
             .
             I.
             55
          
        
         
           
             Q
          
           
             Quantity
             of
             Running
             Waters
             is
             never
             certain
             ,
             if
             with
             the
             Vulgar
             way
             of
             Measuring
             them
             ,
             their
             Velocities
             be
             not
             considered
             .
             32
          
           
             Quantities
             of
             Waters
             which
             are
             discharged
             by
             a
             River
             ,
             answer
             in
             equality
             to
             the
             Velocities
             and
             times
             in
             which
             they
             are
             discharged
             .
             Axiome
             I
             ,
             II
             ,
             III.
             38
          
           
             Quick-Height
             of
             a
             River
             ,
             what
             it
             is
             .
             Definition
             V.
             48
          
        
         
           
             R
          
           
             Reason
             of
             the
             Proverb
             ,
             
               Take
               heed
               of
               the
               still
               Waters
               .
            
             Coroll
             .
             VI.
             7
          
           
             Reasons
             of
             
               Monsignore
               Corsini
            
             against
             the
             diversion
             of
             Reno
             into
             the
             Po
             of
             Volano
             .
             105
          
           
             Reasons
             of
             
               Cardinal
               Capponi
            
             and
             
               Monsig
               .
               Corsini
            
             ,
             for
             the
             turning
             of
             Reno
             into
             Main
             Po.
             106
          
           
             
             Two
             objections
             on
             the
             contrary
             ,
             and
             answers
             to
             them
             .
             104
             &
             105
          
           
             What
             ought
             to
             be
             the
             proportion
             of
             the
             Heights
             of
             Reno
             is
             Reno
             ,
             and
             of
             Reno
             in
             Po.
             110
          
           
             Regulator
             what
             it
             is
             .
             Definition
             IV.
             48
          
           
             Relation
             of
             the
             Waters
             of
             Bologna
             and
             Ferrara
             ,
             by
             
               Monsignore
               Corsini
            
             .
             100
          
           
             Reno
             in
             the
             Valleys
             ,
             and
             its
             bad
             effects
             .
             100
             ,
             101
          
           
             Two
             wayes
             to
             divert
             it
             .
             103
          
           
             The
             facility
             and
             utility
             of
             those
             wayes
             .
             Ibid.
             
          
           
             The
             difficulties
             objected
             .
             104
          
           
             Reply
             to
             Bartolotti
             touching
             the
             dangers
             of
             turning
             
               Fiume
               Morto
            
             into
             Serchio
             .
             83
          
           
             Retardment
             of
             the
             course
             of
             a
             River
             caused
             by
             its
             Banks
             .
             Appendix
             VII
             .
             19
          
           
             Risings
             made
             by
             Flood-Gates
             but
             small
             .
             Appendix
             XIII
             .
             26
          
           
             Rivers
             that
             are
             shallow
             swell
             much
             upon
             small
             showers
             ,
             such
             as
             are
             deep
             rise
             but
             little
             upon
             great
             Floods
             .
             Corollary
             III.
             6
          
           
             Rivers
             the
             higher
             they
             are
             ,
             the
             swifter
             .
             Ibid.
             
          
           
             Rivers
             the
             higher
             they
             are
             ,
             thelesse
             they
             encrease
             upon
             Floods
             .
             49
          
           
             Rivers
             when
             they
             are
             to
             have
             equal
             and
             when
             like
             Velocity
             .
             Ibid.
             
          
           
             Rivers
             in
             falling
             into
             the
             Sea
             ,
             form
             a
             Shelf
             of
             Sand
             called
             Cavallo
             .
             65
          
           
             Five
             Rivers
             to
             be
             diverted
             from
             the
             Lake
             of
             Venice
             ,
             and
             the
             inconveniences
             that
             would
             ensue
             thereupon
             .
             74
             ,
             75
          
           
             A
             River
             of
             Quick-height
             ,
             and
             Velocity
             in
             its
             Regulator
             being
             given
             ,
             if
             the
             Height
             be
             redoubled
             by
             new
             Water
             ,
             it
             redoubleth
             also
             in
             Velocity
             .
             Proposition
             II.
             Theorem
             I.
             51
          
           
             Keepeth
             the
             proportion
             of
             the
             heights
             ,
             to
             the
             Velocities
             .
             Corollary
             52
          
        
         
           
             S
          
           
             Sand
             and
             Mud
             that
             entereth
             into
             the
             Lake
             of
             Venice
             ,
             and
             the
             way
             to
             examine
             it
             .
             76
          
           
             Seas
             agitated
             and
             driven
             by
             the
             Winds
             stop
             up
             the
             Ports
             .
             64
             ,
             65
          
           
             Sections
             of
             a
             River
             what
             they
             are
             .
             Definition
             I.
             37
          
           
             Sections
             equally
             swift
             what
             they
             are
             .
             Definition
             II.
             Ibid.
             
          
           
             Sections
             of
             River
             being
             given
             ,
             to
             conceive
             others
             equal
             to
             them
             ,
             of
             different
             breadth
             ,
             height
             and
             Velocity
             .
             Petition
             .
             38
          
           
             Sections
             of
             the
             same
             River
             ,
             and
             their
             Proportions
             to
             their
             Velocities
             .
             Coroll
             .
             I.
             42
          
           
             Sections
             of
             a
             River
             discharge
             in
             any
             whatsoever
             place
             of
             the
             said
             River
             ,
             equal
             quantities
             of
             Water
             in
             equal
             times
             .
             Proposition
             I.
             39
          
           
             Sile
             River
             what
             mischiefes
             it
             threatneth
             ,
             diverted
             from
             the
             Lake
             .
             74
          
           
             Spirtings
             of
             Waters
             grow
             bigger
             the
             higher
             they
             go
             .
             Coroll
             .
             XVI
             .
             16
          
           
             Streams
             of
             Rivers
             how
             they
             encrease
             and
             vary
             .
             Coroll
             .
             I.
             6
          
           
             Streams
             retarded
             ,
             and
             the
             effects
             thereof
             .
             Coroll
             .
             IX
             .
             8
          
        
         
           
             T
          
           
             Table
             of
             the
             Heights
             ,
             Additions
             ,
             and
             Quantities
             of
             Waters
             ,
             and
             its
             use
             .
             56
          
           
             Thrasimenus
             .
             Vide
             Lake
             .
          
           
             Time
             how
             it
             s
             measured
             in
             these
             Operations
             of
             the
             Waters
             .
             49
          
           
             Torrents
             encrease
             at
             the
             encreasing
             of
             a
             River
             ,
             though
             they
             carry
             no
             more
             Water
             than
             before
             :
             Coroll
             .
             IV.
             6
          
           
             Torrents
             when
             they
             depose
             and
             carry
             away
             the
             Sand.
             Coroll
             .
             V.
             7
          
           
             Torrents
             and
             their
             effects
             in
             a
             River
             .
             6
             ,
             7
          
           
             Torrents
             that
             fall
             into
             the
             Valleys
             ,
             or
             into
             Po
             of
             Volano
             ,
             and
             their
             mischiefs
             prevented
             ,
             by
             the
             diverting
             of
             Reno
             into
             
               Main
               Po.
            
             100
          
           
             Tyber
             and
             the
             causes
             of
             its
             inundations
             ,
             Coroll
             .
             VIII
             .
             8
          
        
         
           
           
             V
          
           
             Valleys
             of
             Bologna
             and
             Ferrara
             ,
             their
             inundations
             and
             disorders
             ,
             whence
             they
             proceed
             .
             97
          
           
             Velocity
             of
             the
             Water
             shewn
             by
             several
             Examples
             .
             3
          
           
             Its
             proportion
             to
             the
             Measure
             .
             5
          
           
             Velocities
             equal
             ,
             what
             they
             are
             .
             47
          
           
             Velocities
             like
             ,
             what
             they
             are
             .
             47
             ,
             48
          
           
             Velocities
             of
             Water
             known
             ,
             how
             they
             help
             us
             in
             finding
             the
             Lengths
             .
             113
          
           
             A
             Fable
             to
             explain
             the
             truth
             thereof
             .
             Ibid.
             
          
           
             Venice
             .
             Vide
             Lake
             .
          
           
             Vse
             of
             the
             Regulator
             in
             measuring
             great
             Rivers
             .
             Consideration
             I.
             60
          
        
         
           
             W
          
           
             Waters
             falling
             ,
             why
             they
             disgross
             .
             Coroll
             .
             XVI
             .
             16
          
           
             Waters
             ,
             how
             the
             Length
             of
             them
             is
             Measured
             .
             70
          
           
             Waters
             that
             are
             imployed
             to
             flow
             Grounds
             ,
             how
             they
             are
             to
             be
             distributed
             .
             19
             ,
             53
             ,
             54
          
           
             Waters
             to
             be
             carryed
             in
             Pipes
             ,
             to
             serve
             Aquaducts
             and
             Conduits
             ,
             how
             they
             are
             to
             be
             Measured
             .
             115
             ,
             116
          
           
             Way
             to
             know
             the
             rising
             of
             Lakes
             by
             Raines
             .
             28
          
           
             Way
             of
             the
             Vulgar
             to
             Measure
             the
             VVaters
             of
             Rivers
             .
             68
          
           
             Wind
             Gun
             ,
             and
             Portable
             Fountain
             of
             
               Vincenzo
               Vincenti
            
             of
             Urbin
             .
             11
          
           
             Windes
             contrary
             ,
             retard
             ,
             and
             make
             Rivers
             encrease
             .
             Coroll
             .
             VII
             .
             8
          
        
         
           The
           END
           of
           the
           TABLE
           of
           the
           Second
           Part
           of
           the
           First
           TOME
           ,
        
      
       
         Notes, typically marginal, from the original text
         
           Notes for div A31214-e200
           
             a
             Nella
             continuatione
             dell
             Nuntio
             ●iderio
             .
          
           
             b
             Lettera
             al
             P.
             Abbate
             D.
             B.
             Castelli
             D'Arcetro
             ;
             li.
             3.
             
             Decemb.
             16●9
             .
          
           
             c
             De
             Motu
             Aquarum
             .
             Lib.
             2.
             
             Prop.
             37.
             p.
             191.
             
          
        
         
           Notes for div A31214-e2430
           
             *
             *
             And
             as
             is
             at
             large
             demonstrated
             by
             that
             most
             excellent
             and
             Honourable
             personage
             Mr.
             Boile
             in
             the
             industrious
             experiment
             of
             his
             Pneumatical
             Engine
             .
          
           
             *
             *
             Artesia
             .
          
           
             *
             *
             Commentarius
             beareth
             many
             senses
             ,
             but
             in
             this
             place
             signifieth
             a
             certain
             Register
             of
             the
             quantities
             of
             the
             Waters
             in
             the
             several
             publique
             Aquiducts
             of
             Rome
             ;
             which
             word
             I
             find
             frequently
             used
             in
             the
             Law-books
             of
             antient
             Civilians
             :
             And
             by
             errogation
             we
             are
             to
             understand
             the
             distribution
             or
             delivering
             out
             of
             those
             stores
             of
             Water
             .
          
           
             *
             *
             A
             Coyn
             of
             Pope
             Julius
             worth
             six
             pence
             .
          
        
         
           Notes for div A31214-e6940
           
             *
             *
             Or
             Sluice
             .
          
           
             *
             *
             In
             Pregadi
             ,
             a
             particular
             Council
             ,
             the
             Senators
             of
             which
             have
             great
             Authority
             .
          
           
             *
             *
             A
             Venice
             Brace
             is
             11
             /
             1●
             of
             our
             yard
             .
          
           
             *
             *
             A
             River
             of
             that
             name
             .
          
           
             *
             *
             
               I.
               Savii
               dell
               '
               Acque
            
             ,
             a
             particular
             Council
             that
             take
             care
             of
             the
             Lakes
             and
             other
             Aquatick
             affairs
             .
          
           
             *
             *
             He
             here
             intends
             the
             Demonstrations
             following
             ,
             at
             the
             end
             of
             the
             first
             Book
             
          
           
             *
             *
             Deeper
             .
          
           
             *
             *
             Lib.
             1.
             
          
           
             *
             *
             The
             Countrey
             or
             Province
             lying
             round
             the
             City
             ,
             heretofore
             called
             
               Lati
               〈◊〉
            
          
           
             *
             *
             Or
             Lordship
             .
          
           
             *
             *
             The
             Popes
             Exchequer
             .
          
           
             *
             *
             Polesine
             is
             a
             plat
             of
             Ground
             almost
             surrounded
             with
             Bogs
             or
             waters
             ,
             like
             an
             Island
             
          
           
             *
             *
             People
             of
             Ferrara
             .
          
           
             *
             *
             In
             Chanels
             made
             by
             hand
             .
          
           
             *
             *
             The
             inch
             of
             these
             places
             is
             somewhat
             bigger
             than
             ours
             .
          
           
             *
             *
             Of
             Adriano
             .
          
        
         
           Notes for div A31214-e16870
           
             *
             Larghezza
             ,
             but
             misprinted
             .