Mechanick dyalling teaching any man, though of an ordinary capacity and unlearned in the mathematicks, to draw a true sun-dyal on any given plane, however scituated : only with the help of a straight ruler and a pair of compasses, and without any arithmetical calculation / by Joseph Moxon ...
         Moxon, Joseph, 1627-1691.
      
       
         
           1668
        
      
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         ESTC R20066
         12354007
         ocm 12354007
         60072
         
           
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         Images scanned from microfilm: (Early English books, 1641-1700 ; 643:12)
      
       
         
           
             Mechanick dyalling teaching any man, though of an ordinary capacity and unlearned in the mathematicks, to draw a true sun-dyal on any given plane, however scituated : only with the help of a straight ruler and a pair of compasses, and without any arithmetical calculation / by Joseph Moxon ...
             Moxon, Joseph, 1627-1691.
          
           49, [6] p. : ill.
           
             Printed for Joseph Moxon ...,
             London :
             1668.
          
           
             Advertisement: p. [1]-[6] at end.
             Reproduction of original in Huntington Library.
          
        
      
    
     
       
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         eng
      
       
         
           Sundials.
           Mathematical instruments.
        
      
    
     
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             Mechanick
             Dyalling
          
           :
           TEACHING
           Any
           Man
           ,
           though
           of
           an
           Ordinary
           Capacity
           and
           unlearned
           in
           the
           Mathematicks
           ,
           to
           draw
           a
           True
           SUN-DYAL
           On
           any
           Given
           Plane
           ,
           However
           scituated
           :
           Only
           with
           the
           help
           of
           a
           straight
           RVLER
           and
           a
           pair
           of
           COMPASSES
           ;
           And
           without
           any
           Arithmetical
           Calculation
           .
        
         
           By
           
             Joseph
             Moxon
          
           ,
           Hydrographer
           to
           the
           Kings
           most
           Excellent
           Majesty
           .
        
         
           LONDON
           .
           Printed
           for
           
             Joseph
             Moxon
          
           on
           Ludgate-hill
           ,
           at
           the
           Sign
           of
           Atlas
           .
           
             MDCLXVIII
          
        
      
    
     
       
         
         
         MECHANICK
         DYALLING
         .
      
       
         
           Description
           of
           Dyalling
           .
        
         
           DYalling
           originally
           is
           a
           
             Mathematical
             Science
          
           ,
           attained
           by
           the
           Philosophical
           contemplation
           of
           the
           motion
           of
           the
           Sun
           ,
           the
           motion
           of
           the
           Shaddow
           ,
           the
           Constitution
           of
           the
           Sphere
           ,
           the
           Scituation
           of
           Planes
           ,
           and
           the
           consideration
           of
           Lines
           .
        
      
       
         
           Explanation
           .
        
         
           THE
           motion
           of
           the
           Sun
           is
           regular
           ,
           it
           moving
           equal
           Space
           in
           equal
           Time
           ;
           But
           the
           motion
           of
           the
           Shaddow
           irregular
           in
           all
           parts
           of
           the
           Earth
           ,
           unless
           under
           the
           two
           Poles
           ,
           and
           that
           more
           or
           less
           according
           to
           the
           Constitution
           of
           the
           Sphere
           and
           scituation
           of
           the
           Plane
           .
           And
           therefore
           Scientifick
           Dyalists
           by
           the
           Geometrick
           considerations
           of
           Lines
           ,
           have
           found
           out
           Rules
           to
           mark
           out
           the
           irregular
           motion
           of
           the
           Shaddow
           in
           all
           Latitudes
           ,
           and
           on
           all
           Planes
           ,
           to
           comply
           with
           the
           regular
           motion
           of
           the
           Sun.
           And
           these
           Rules
           of
           adjusting
           the
           motion
           of
           the
           Shaddow
           to
           the
           motion
           of
           the
           Sun
           may
           be
           called
           
             Scientifick
             Dyalling
          
           .
        
         
         
           But
           though
           we
           may
           justly
           account
           Dyalling
           originally
           a
           Science
           ,
           yet
           such
           hath
           been
           the
           Generosity
           of
           many
           of
           its
           studious
           Contemplators
           ,
           that
           they
           have
           communicated
           their
           acquired
           Rules
           ;
           whereby
           it
           is
           now
           become
           to
           many
           of
           the
           Ingenious
           no
           more
           difficult
           than
           an
           Art
           ,
           and
           by
           many
           late
           Authors
           so
           intituled
           :
           Nay
           more
           ,
           by
           this
           small
           Treatise
           it
           will
           scarce
           be
           accounted
           more
           than
           a
           
             Manual
             Operation
          
           ;
           for
           ,
           though
           (
           hitherto
           )
           all
           the
           Authors
           I
           have
           met
           with
           seem
           to
           presuppose
           their
           Reader
           to
           understand
           Geometry
           ,
           and
           the
           
             projecting
             of
             the
             Sphere
          
           already
           ,
           or
           else
           endeavour
           in
           their
           Works
           to
           make
           him
           understand
           them
           ,
           as
           if
           they
           were
           absolutely
           necessary
           to
           be
           known
           by
           every
           one
           that
           would
           make
           a
           Dyal
           ,
           when
           as
           in
           truth
           (
           the
           contemplative
           pains
           of
           others
           aforesaid
           considered
           )
           they
           are
           not
           ;
           but
           indeed
           are
           only
           useful
           to
           those
           that
           would
           know
           the
           reason
           of
           Dyalling
           .
           Thus
           they
           do
           not
           only
           discourage
           young
           beginners
           ,
           but
           also
           disappoint
           many
           Gentlemen
           and
           others
           that
           would
           willingly
           either
           make
           them
           themselves
           ,
           or
           set
           their
           Workmen
           about
           them
           ,
           if
           they
           knew
           how
           to
           make
           them
           .
        
         
           This
           little
           Piece
           I
           have
           therefore
           composed
           for
           the
           help
           of
           those
           who
           understand
           neither
           the
           
             Projection
             of
             the
             Sphere
          
           ,
           or
           
             Geometrical
             Operations
          
           :
           Only
           ,
           if
           they
           know
           how
           to
           draw
           a
           straight
           Line
           between
           two
           Points
           by
           the
           side
           of
           a
           Ruler
           ,
           describe
           a
           Circle
           with
           a
           pair
           of
           Compasses
           ,
           erect
           a
           Perpendicular
           ,
           and
           draw
           one
           Line
           parallel
           to
           another
           ,
           they
           may
           know
           how
           to
           draw
           a
           Dyal
           for
           any
           given
           Plane
           ,
           however
           scituated
           in
           any
           Latitude
           .
        
         
           But
           perhaps
           these
           two
           last
           little
           Tricks
           are
           not
           known
           to
           all
           new
           beginners
           ,
           therefore
           I
           shall
           shew
           them
           .
           First
           ,
        
      
       
         
         
           How
           to
           erect
           a
           Perpendicular
           .
           For
           Example
           ,
           in
           Fig.
           1.
           
        
         
           Upon
           the
           Line
           AB
           you
           would
           erect
           a
           Perpendicular
           to
           the
           Point
           C
           :
           Place
           one
           Foot
           of
           your
           Compasses
           upon
           the
           point
           C
           ,
           and
           open
           the
           other
           to
           what
           distance
           you
           please
           ;
           For
           Example
           ,
           to
           the
           point
           A
           ,
           make
           there
           a
           mark
           ;
           then
           keeping
           the
           first
           Foot
           
           still
           in
           C
           ,
           turn
           the
           other
           Foot
           toward
           B
           ,
           and
           make
           there
           another
           mark
           ;
           then
           open
           your
           Compasses
           wider
           ,
           suppose
           to
           the
           length
           AB
           ,
           and
           placing
           one
           Foot
           in
           the
           point
           A
           ,
           with
           the
           other
           Foot
           describe
           a
           small
           Arch
           over
           the
           point
           C
           ,
           and
           removing
           the
           Foot
           of
           your
           Compasses
           to
           the
           point
           B
           ,
           with
           the
           other
           Foot
           describe
           another
           small
           Arch
           ,
           to
           cut
           the
           first
           Arch
           ,
           as
           at
           D.
           Then
           lay
           your
           straight
           Ruler
           to
           the
           point
           where
           the
           two
           small
           Arches
           cut
           each
           other
           ,
           and
           upon
           the
           point
           C
           ,
           and
           by
           the
           side
           of
           the
           Ruler
           draw
           the
           Line
           CD
           ,
           which
           shall
           be
           a
           Perpendicular
           to
           the
           Line
           AB
           .
        
      
       
         
           Another
           way
           with
           once
           opening
           the
           Compasses
           ,
           as
           by
           Fig.
           2.
           
        
         
           Draw
           the
           Line
           AB
           ,
           and
           place
           one
           Foot
           of
           your
           Compasses
           upon
           the
           point
           you
           would
           have
           the
           Perpendicular
           erected
           ,
           as
           at
           the
           point
           C
           ,
           and
           with
           the
           other
           foot
           describe
           the
           Semi-Circle
           A
           ab
           B
           ,
           then
           placing
           one
           Foot
           in
           B
           ,
           extend
           the
           other
           Foot
           to
           b
           ,
           
           in
           the
           Semi-Circle
           ;
           and
           keeping
           that
           Foot
           in
           b
           ,
           extend
           the
           other
           Foot
           to
           D
           ,
           and
           make
           there
           a
           small
           Arch
           :
           Then
           remove
           one
           Foot
           of
           your
           Compasses
           to
           A
           ,
           and
           extend
           the
           other
           Foot
           to
           a
           in
           the
           Semi-Circle
           ,
           and
           keeping
           that
           Foot
           in
           a
           ,
           extend
           the
           other
           to
           D
           ,
           and
           make
           there
           another
           small
           Arch
           ,
           to
           cut
           the
           first
           small
           Arch
           ;
           and
           laying
           a
           straight
           Ruler
           to
           the
           point
           where
           these
           two
           small
           Arches
           cut
           each
           other
           ,
           and
           upon
           the
           point
           C
           ,
           draw
           by
           the
           side
           of
           the
           Ruler
           the
           Line
           CD
           ,
           which
           shall
           be
           Perpendicular
           to
           the
           Line
           AB
           .
        
      
       
         
           To
           erect
           a
           Perpendicular
           upon
           the
           end
           of
           a
           Line
           ,
           as
           by
           Fig.
           3.
           
        
         
           On
           the
           point
           B
           ,
           at
           one
           end
           of
           the
           Line
           AB
           ,
           place
           one
           Foot
           of
           your
           Compasses
           in
           the
           point
           B
           ,
           and
           extend
           the
           other
           on
           the
           Line
           towards
           A
           ,
           as
           to
           b
           ,
           and
           with
           it
           describe
           the
           Arch
           ba
           C
           ;
           then
           placing
           one
           Foot
           in
           b
           ,
           extend
           the
           other
           to
           a
           in
           the
           Arch
           ,
           and
           make
           there
           a
           mark
           ;
           Divide
           with
           your
           Compasses
           the
           Arch
           ba
           into
           two
           equal
           parts
           ,
           and
           keeping
           the
           Feet
           of
           your
           Compasses
           at
           that
           distance
           ,
           measure
           in
           the
           Arch
           from
           a
           to
           C
           ,
           then
           draw
           a
           straight
           Line
           from
           the
           point
           C
           to
           the
           end
           of
           the
           Line
           B
           ,
           and
           that
           straight
           Line
           shall
           be
           Perpendicular
           to
           the
           end
           of
           the
           Line
           AB
           .
        
      
       
         
           To
           draw
           a
           Line
           Parallel
           to
           another
           Line
           ,
           as
           by
           Fig.
           4.
           
        
         
           Example
           .
           If
           you
           would
           draw
           a
           Line
           Parallel
           to
           the
           Line
           AB
           ,
           open
           your
           Compasses
           to
           the
           distance
           you
           intend
           the
           Lines
           shall
           stand
           off
           each
           other
           ,
           and
           placing
           one
           Foot
           successively
           near
           each
           end
           ,
           describe
           with
           the
           other
           Foot
           the
           small
           Arches
           CD
           ;
           lay
           a
           straight
           Ruler
           to
           the
           top
           of
           these
           Arches
           ,
           and
           draw
           a
           Line
           by
           the
           side
           of
           it
           ,
           and
           that
           Line
           shall
           be
           Parallel
           to
           the
           Line
           AB
           .
        
      
       
         
         
           Definitions
           .
        
         
           A
           
             Dyal
             Plane
          
           is
           that
           Flat
           whereon
           a
           Dyal
           is
           intended
           to
           be
           projected
           .
        
         
           Of
           
             Dyal
             Planes
          
           some
           be
           Direct
           ,
           other
           Decliners
           ,
           others
           Oblique
           .
        
         
           Of
           
             Direct
             Planes
          
           there
           are
           five
           sorts
           :
           
             
               1.
               
               The
               Horizontal
               whose
               Plane
               lies
               flat
               ,
               and
               is
               parallel
               to
               the
               Horizon
               ,
               beholding
               the
               Zenith
               .
            
             
               2.
               
               The
               
                 South
                 Erect
              
               ,
               whose
               Plane
               stands
               upright
               ,
               and
               directly
               beholds
               the
               South
               .
            
             
               3.
               
               The
               
                 North
                 Erect
              
               ,
               whose
               Plane
               stands
               upright
               ,
               and
               directly
               beholds
               the
               North.
               
            
             
               4.
               
               The
               
                 East
                 Erect
              
               ,
               whose
               Plane
               stands
               upright
               ,
               and
               directly
               beholds
               the
               East
               .
            
             
               5.
               
               The
               
                 West
                 Erect
              
               ,
               whose
               Plane
               stands
               upright
               ,
               and
               directly
               beholds
               the
               West
               .
            
          
        
         
           Of
           Decliners
           there
           are
           infinite
           :
           and
           yet
           may
           be
           reduced
           into
           these
           two
           Kinds
           :
           
             
               1.
               
               The
               
                 South
                 Erect
              
               Plane
               ,
               declining
               more
               or
               less
               towards
               the
               East
               or
               West
               .
            
             
               2.
               
               The
               
                 North
                 Erect
              
               Plane
               ,
               declining
               more
               or
               less
               towards
               the
               East
               or
               West
               .
            
          
        
         
           Of
           
             Oblique
             Planes
          
           some
           are
           Direct
           ,
           others
           Declining
           ;
           and
           are
           of
           four
           sorts
           :
           
             
               1.
               
               
                 Direct
                 Inclining
              
               Planes
               ,
               which
               lean
               towards
               you
               ,
               and
               lie
               directly
               in
               the
               
                 East
                 ,
                 West
                 ,
                 North
              
               ,
               or
               South
               quarters
               of
               Heaven
               .
            
             
               2.
               
               
                 Direct
                 Reclining
              
               Planes
               ,
               which
               lean
               from
               you
               ,
               and
               lie
               directly
               in
               the
               
                 East
                 ,
                 West
                 ,
                 North
              
               ,
               or
               South
               quarters
               of
               Heaven
               .
            
             
               3.
               
               
                 Inclining
                 Declining
              
               Planes
               ,
               which
               lean
               towards
               you
               ,
               but
               lie
               not
               directly
               in
               the
               
                 East
                 ,
                 West
                 ,
                 North
              
               ,
               or
               
               South
               quarters
               of
               Heaven
               :
               But
               decline
               more
               or
               less
               from
               the
               North
               or
               South
               ,
               towards
               the
               East
               or
               West
               .
            
             
               4.
               
               
                 Reclining
                 Declining
              
               Planes
               ,
               which
               lean
               from
               you
               ,
               but
               lie
               not
               directly
               in
               the
               
                 East
                 ,
                 West
                 ,
                 North
              
               ,
               or
               South
               quarters
               of
               Heaven
               :
               But
               Decline
               more
               or
               less
               from
               the
               North
               or
               South
               ,
               towards
               the
               East
               or
               West
               .
            
          
        
         
           If
           the
           Scituation
           of
           the
           Plane
           be
           not
           given
           ,
           you
           must
           seek
           it
           :
           For
           ,
           there
           are
           several
           wayes
           how
           to
           know
           these
           several
           kinds
           of
           Planes
           used
           among
           Artists
           ;
           But
           the
           readiest
           and
           easiest
           is
           by
           an
           Instrument
           called
           a
           Declinatory
           ,
           fitted
           to
           the
           variation
           of
           your
           Place
           :
           And
           if
           it
           be
           truly
           made
           ,
           you
           may
           as
           safely
           rely
           upon
           it
           as
           any
           other
           .
        
      
       
         
           OPERATION
           I.
           The
           Description
           of
           the
           Clinatory
           .
        
         
           THE
           Clinatory
           is
           made
           of
           a
           square
           Board
           ,
           as
           ABCD
           ,
           of
           a
           good
           thickness
           ;
           ,
           and
           the
           larger
           the
           better
           ;
           between
           two
           of
           the
           side
           is
           described
           on
           the
           Center
           Aa
           Quadrant
           as
           EF
           devided
           into
           90
           equal
           parts
           or
           degrees
           ,
           which
           are
           figured
           with
           10
           ,
           20
           ,
           30
           ,
           to
           90
           ;
           and
           then
           back
           again
           with
           the
           Complements
           of
           the
           same
           numbers
           to
           90
           :
           between
           the
           Limb
           and
           the
           two
           Semi-diameters
           is
           made
           a
           round
           Box
           ,
           into
           which
           a
           Magnetical
           Needle
           is
           fitted
           ;
           and
           a
           Card
           of
           the
           Nautical
           Compass
           ,
           devided
           into
           four
           Nineties
           ,
           beginning
           their
           numbers
           at
           the
           East
           ,
           West
           ,
           North
           ,
           and
           South
           points
           of
           the
           Compass
           ,
           from
           which
           points
           the
           opposite
           sides
           of
           the
           Clinatory
           receives
           their
           Names
           of
           East
           ,
           West
           ,
           North
           and
           South
           .
        
         
           But
           ,
           Note
           ,
           that
           the
           North
           point
           of
           the
           Card
           must
           be
           placed
           so
           many
           degrees
           towards
           the
           East
           or
           West
           sides
           of
           the
           Clinatory
           as
           the
           Needle
           varies
           from
           the
           true
           
           North
           point
           of
           the
           world
           ,
           in
           the
           place
           where
           you
           make
           your
           Dyal
           ;
           which
           your
           Workman
           that
           makes
           your
           Clinatory
           will
           know
           how
           to
           fit
           .
        
         
           Upon
           the
           Center
           A
           ,
           whereon
           the
           Quadrant
           was
           described
           ,
           is
           fastened
           a
           Plumb-line
           ,
           having
           a
           Plumbet
           of
           Lead
           or
           Brass
           fastned
           to
           the
           end
           of
           it
           ,
           which
           Plumb-line
           is
           of
           such
           length
           that
           the
           Plumbet
           may
           fall
           just
           into
           the
           Grove
           GH
           ,
           below
           the
           Quadrant
           ,
           which
           is
           for
           that
           purpose
           made
           of
           such
           a
           depth
           that
           the
           Plumbet
           may
           ride
           freely
           within
           it
           ,
           without
           stopping
           at
           the
           sides
           of
           it
           .
           See
           the
           Figure
           annexed
           .
        
         
         
         
           With
           this
           Clinatory
           you
           may
           examine
           the
           scituation
           of
           Planes
           .
           As
           if
           your
           Plane
           be
           Horizontal
           ,
           it
           is
           direct
           :
           and
           then
           for
           the
           true
           scituating
           your
           Dyal
           you
           have
           only
           the
           true
           North
           and
           South
           Line
           to
           find
           :
           which
           is
           done
           only
           by
           setting
           the
           Clinatory
           flat
           down
           upon
           the
           Plane
           ,
           and
           turning
           it
           towards
           the
           right
           or
           left
           hand
           ,
           till
           you
           can
           bring
           the
           North
           point
           of
           the
           Needle
           to
           hang
           just
           over
           the
           Flower-de-luce
           ,
           for
           then
           if
           you
           draw
           a
           Line
           by
           either
           of
           the
           sides
           parallel
           to
           the
           Needle
           ,
           that
           Line
           shall
           be
           a
           North
           and
           South
           Line
           .
        
         
           If
           Your
           Plane
           either
           Recline
           or
           Incline
           ,
           Apply
           one
           of
           the
           sides
           of
           your
           Clinatory
           parallel
           to
           one
           of
           the
           Semi-diameters
           of
           the
           Quadrant
           to
           the
           Plane
           ,
           in
           such
           sort
           that
           the
           Plumb-line
           hanging
           at
           liberty
           ,
           may
           fall
           upon
           the
           Circumference
           of
           the
           Quadrant
           ,
           for
           then
           the
           number
           of
           degrees
           of
           the
           Quadrant
           comprehended
           between
           the
           side
           of
           the
           Quadrant
           parallel
           to
           the
           Plane
           ,
           and
           the
           Plumb-line
           shall
           be
           the
           number
           of
           degrees
           for
           Reclination
           ,
           if
           the
           Center
           of
           the
           Quadrant
           points
           upwards
           ;
           or
           Inclination
           ,
           if
           the
           Center
           points
           downwards
           .
        
         
           If
           your
           Reclining
           or
           Inclining
           Plane
           Decline
           ,
           Draw
           upon
           it
           a
           Line
           parallel
           to
           the
           Horizon
           ,
           which
           you
           may
           do
           by
           applying
           the
           back-side
           of
           the
           Clinatory
           ,
           and
           raising
           or
           depressing
           the
           Center
           of
           the
           Quadrant
           ,
           till
           the
           Plumb-line
           hang
           just
           upon
           one
           of
           the
           Semi-diameters
           ,
           for
           then
           you
           may
           by
           the
           upper
           side
           of
           the
           Clinatory
           draw
           an
           Horizontal
           Line
           if
           the
           Plane
           Incline
           ,
           or
           by
           the
           under
           side
           if
           it
           Recline
           .
           If
           it
           neither
           Incline
           or
           Recline
           ,
           you
           may
           draw
           a
           Horizontal
           Line
           both
           by
           the
           upper
           and
           under
           sides
           of
           the
           Clinatory
           .
           Having
           drawn
           the
           Horizontal
           Line
           ,
           apply
           the
           North
           side
           of
           the
           Clinatory
           to
           it
           ,
           and
           if
           the
           North
           end
           of
           the
           Needle
           points
           directly
           towards
           the
           Plane
           ,
           it
           is
           then
           a
           South
           Plane
           .
           If
           the
           North
           point
           of
           the
           Needle
           points
           directly
           from
           the
           Plane
           ,
           
           it
           is
           a
           North
           Plane
           :
           but
           if
           it
           points
           towards
           the
           East
           ,
           it
           is
           an
           East
           Plane
           :
           if
           towards
           the
           West
           ,
           a
           West
           Plane
           .
           If
           it
           do
           not
           point
           directly
           either
           East
           ,
           West
           ,
           North
           ,
           or
           South
           ,
           then
           so
           many
           degrees
           as
           the
           Needle
           declines
           from
           any
           of
           these
           four
           points
           to
           any
           of
           the
           other
           of
           these
           four
           points
           ,
           so
           many
           degrees
           is
           the
           Declination
           of
           the
           Plane
           .
        
         
           You
           may
           find
           a
           Meridian
           Line
           another
           way
           ;
           thus
           ,
           If
           the
           Sun
           shine
           just
           at
           Noon
           ,
           hold
           up
           a
           Plumb-line
           so
           as
           the
           shaddow
           of
           it
           may
           fall
           upon
           your
           Plane
           ,
           and
           that
           shaddow
           shall
           be
           a
           
             Meridian
             Line
          
           .
        
      
       
         
           OPERAT.
           II.
           To
           describe
           a
           Dyal
           upon
           a
           
             Horizontal
             Plane
          
           .
        
         
           FIrst
           draw
           a
           North
           and
           South
           Line
           (
           which
           is
           called
           a
           
             Meridian
             Line
          
           )
           through
           the
           middle
           of
           the
           Plane
           :
           Thus
           ,
           Set
           your
           Declinatory
           flat
           upon
           the
           Plane
           ,
           and
           turn
           it
           to
           and
           fro
           till
           the
           Needle
           hang
           precisely
           over
           the
           
             Meridian
             Line
          
           of
           the
           Declinatory
           ;
           then
           by
           the
           side
           of
           the
           Declinatory
           parallel
           to
           its
           
             Meridian
             Line
          
           ,
           draw
           a
           straight
           Line
           on
           the
           Plane
           ,
           and
           if
           that
           straight
           Line
           be
           in
           the
           middle
           of
           the
           Plane
           ,
           it
           shall
           be
           the
           
             Meridian
             Line
          
           ,
           without
           more
           ado
           :
           But
           if
           it
           be
           not
           in
           the
           middle
           of
           the
           Plane
           ,
           you
           must
           draw
           a
           Line
           parallel
           to
           it
           through
           the
           middle
           of
           the
           Plane
           for
           the
           
             Meridian
             Line
          
           ,
           or
           twelve
           a
           Clock
           line
           :
           And
           it
           shall
           be
           the
           
             Meridian
             Line
          
           ,
           and
           also
           be
           the
           
             Substilar
             Line
          
           ;
           then
           draw
           another
           straight
           Line
           through
           the
           middle
           of
           this
           Line
           ,
           to
           cut
           it
           at
           right
           Angles
           for
           the
           VI.
           a
           Clock
           Lines
           ;
           and
           where
           these
           two
           Lines
           cut
           one
           another
           make
           your
           Centre
           ,
           whereon
           describe
           a
           Circle
           on
           your
           Plane
           as
           large
           as
           you
           can
           ,
           which
           by
           the
           
             Meridian
             Line
          
           ,
           and
           the
           Line
           drawn
           at
           right
           .
           Angles
           
           with
           it
           will
           be
           devided
           into
           four
           Quadrants
           ;
           one
           of
           the
           Quadrants
           devide
           into
           90
           degrees
           thus
           ,
           Keeping
           your
           Compasses
           at
           the
           same
           width
           they
           were
           at
           when
           you
           described
           the
           Quadrant
           ,
           place
           one
           Foot
           in
           the
           twelve
           a
           Clock
           Line
           ,
           and
           extend
           the
           other
           in
           the
           Quadrant
           ,
           and
           make
           in
           the
           Quadrant
           a
           mark
           with
           it
           ;
           so
           shall
           you
           have
           the
           sixtieth
           degree
           marked
           out
           :
           then
           place
           one
           Foot
           of
           your
           Compasses
           in
           the
           six
           a
           Clock
           Line
           ,
           and
           extend
           the
           other
           in
           the
           Quadrant
           ,
           and
           make
           in
           the
           Quadrant
           another
           mark
           with
           it
           ;
           so
           shall
           that
           Quadrant
           be
           divided
           into
           three
           equal
           parts
           ;
           each
           of
           these
           three
           equal
           parts
           contains
           30
           degrees
           :
           Then
           with
           your
           Compasses
           devide
           one
           of
           these
           three
           equal
           parts
           into
           three
           parts
           ,
           and
           transfer
           that
           distance
           to
           the
           other
           two
           third
           parts
           of
           the
           Quadrant
           ,
           so
           shall
           the
           whole
           Quadrant
           be
           devided
           into
           nine
           equal
           parts
           .
           Then
           devide
           one
           of
           these
           nine
           equal
           parts
           into
           two
           equal
           parts
           ,
           and
           transfer
           that
           distance
           to
           the
           other
           eight
           equal
           parts
           ,
           so
           shall
           the
           Quadrant
           be
           devided
           into
           eighteen
           equal
           parts
           .
           Then
           devide
           one
           of
           these
           eighteen
           equal
           parts
           into
           five
           equal
           parts
           ,
           and
           transfer
           that
           distance
           to
           the
           other
           seventeen
           equal
           parts
           ,
           so
           shall
           the
           whole
           Quadrant
           be
           devided
           into
           90
           equal
           parts
           .
           Each
           of
           these
           90
           equal
           parts
           are
           called
           Degrees
           .
        
         
           Note
           ,
           That
           you
           may
           in
           small
           Quadrants
           devide
           truer
           and
           with
           less
           trouble
           with
           Steel
           Deviders
           ,
           (
           which
           open
           or
           close
           with
           a
           Screw
           for
           that
           purpose
           ,
           )
           than
           you
           can
           with
           Compasses
           .
        
         
           In
           this
           Quadrant
           (
           thus
           devided
           )
           count
           from
           the
           Substilar
           or
           
             Meridian
             Line
          
           the
           Elevation
           of
           the
           Pole
           ,
           that
           is
           ,
           the
           number
           of
           Degrees
           that
           the
           Pole
           of
           the
           World
           is
           elevated
           above
           the
           Horizon
           of
           your
           Place
           ,
           and
           draw
           a
           Line
           from
           the
           Center
           through
           that
           number
           of
           Degrees
           for
           the
           
             Stilar
             Line
          
           .
           Then
           on
           the
           
             Substilar
             Line
          
           
           choose
           a
           point
           (
           where
           you
           please
           )
           and
           through
           that
           point
           draw
           a
           Line
           at
           right
           Angles
           to
           the
           
             Substilar
             Line
          
           as
           long
           as
           you
           can
           ,
           for
           the
           Line
           of
           Contingence
           ,
           and
           from
           that
           point
           in
           the
           
             Substilar
             Line
          
           measure
           the
           nearest
           distance
           any
           part
           of
           the
           
             Stilar
             Line
          
           hath
           to
           that
           point
           ;
           and
           keeping
           one
           Foot
           of
           your
           Compasses
           still
           in
           that
           point
           ,
           set
           off
           that
           distance
           in
           the
           
             Substilar
             Line
          
           ,
           and
           at
           that
           distance
           describe
           against
           the
           Line
           of
           Contingence
           a
           Semi-Circle
           ,
           which
           devide
           from
           either
           side
           the
           Meridian
           or
           
             Substilar
             Line
          
           into
           six
           equal
           parts
           thus
           ;
           Draw
           a
           Line
           through
           the
           Center
           of
           this
           Semi-Circle
           parallel
           to
           the
           
             Line
             of
             Contingence
          
           ,
           which
           shall
           be
           the
           
             Diametral
             Line
          
           ,
           and
           shall
           devide
           this
           Semi
           Circle-into
           two
           Quadrants
           ;
           one
           on
           one
           side
           the
           
             Substilar
             Line
          
           ,
           and
           the
           other
           Quadrant
           on
           the
           other
           side
           the
           
             Substilar
             Line
          
           :
           Then
           keeping
           your
           Compasses
           at
           the
           same
           distance
           they
           were
           at
           when
           you
           described
           the
           Semi-Circle
           ,
           place
           one
           Foot
           first
           on
           one
           side
           the
           
             Diametral
             Line
          
           at
           the
           Intersection
           of
           it
           and
           the
           Semi-Circle
           ,
           and
           then
           on
           the
           other
           side
           ,
           at
           the
           Intersection
           of
           it
           and
           the
           Semi-Circle
           ,
           and
           extend
           the
           other
           in
           the
           Semi-Circle
           ,
           and
           make
           marks
           in
           the
           Semi-Circle
           on
           either
           side
           the
           
             Substilar
             Line
          
           :
           Then
           place
           one
           Foot
           of
           your
           Compasses
           at
           the
           Intersection
           of
           the
           Semi-Circle
           and
           the
           
             Substilar
             Line
          
           ,
           and
           turn
           the
           other
           Foot
           about
           on
           either
           side
           the
           Semi-Circle
           and
           make
           marks
           in
           the
           Semi-Circle
           ,
           so
           shall
           the
           Semi-Circle
           be
           devided
           into
           six
           equal
           parts
           :
           Devide
           one
           of
           these
           equal
           parts
           into
           two
           equal
           parts
           ,
           and
           transfer
           that
           distance
           to
           the
           other
           five
           equal
           parts
           ,
           so
           shall
           the
           whole
           Semi-Circle
           be
           devided
           into
           twelve
           equal
           parts
           .
           These
           twelve
           Devisions
           are
           to
           describe
           the
           twelve
           Hours
           of
           the
           Day
           ,
           between
           six
           a
           Clock
           in
           the
           Morning
           ,
           and
           six
           a
           Clock
           at
           Night
           .
        
         
           If
           you
           will
           have
           half
           Hours
           you
           may
           devide
           each
           of
           
           these
           twelve
           into
           two
           equal
           parts
           ,
           as
           before
           :
           If
           you
           will
           have
           Quarters
           you
           may
           devide
           each
           of
           these
           twenty
           four
           into
           two
           equal
           parts
           more
           ,
           as
           before
           .
        
         
           For
           thus
           proportioning
           the
           Devisions
           in
           the
           Semi-Circle
           ,
           you
           may
           proportion
           the
           Devisions
           and
           Sub-devisions
           of
           Hours
           upon
           the
           
             Dyal
             Plane
          
           ;
           for
           a
           straight
           Ruler
           laid
           upon
           each
           of
           these
           Devisions
           ,
           and
           on
           the
           Center
           of
           this
           Semi-Circle
           ,
           shall
           shew
           on
           the
           
             Line
             of
             Contingence
          
           the
           several
           Distances
           of
           all
           the
           Hours
           and
           parts
           of
           Hours
           on
           the
           
             Dyal
             Plane
          
           :
           And
           straight
           Lines
           drawn
           from
           the
           Center
           of
           the
           
             Dyal
             Plane
          
           ,
           through
           the
           several
           Devisions
           on
           the
           
             Line
             of
             Contingence
          
           shall
           be
           the
           several
           Hour
           Lines
           and
           parts
           on
           the
           
             Dyal
             Plane
          
           .
        
         
           But
           an
           
             Horizontal
             Dyal
          
           in
           our
           Latitude
           will
           admit
           of
           four
           Hours
           more
           ,
           viz.
           V
           ,
           IV
           ,
           in
           the
           Morning
           ,
           and
           VII
           ,
           VIII
           ,
           in
           the
           Evening
           .
           Therefore
           in
           the
           Circle
           described
           on
           the
           Center
           of
           the
           
             Dyal
             Plane
          
           transfer
           the
           distance
           between
           VI
           and
           V
           ,
           and
           VI
           and
           IV
           ,
           on
           the
           other
           side
           the
           six
           a
           Clock
           Line
           ;
           And
           transfer
           the
           Distances
           between
           VI
           and
           VII
           ,
           and
           VI
           and
           VIII
           on
           the
           other
           side
           the
           opposite
           six
           a
           Clock
           Hour
           Line
           ,
           and
           from
           the
           Center
           of
           the
           
             Dyal
             Plane
          
           draw
           Lines
           through
           those
           transferred
           Distances
           for
           the
           Hour
           Lines
           before
           and
           after
           VI.
           
        
         
           Then
           mark
           your
           Hour
           Lines
           with
           their
           respective
           numbers
           .
           The
           
             Substiler
             Line
          
           in
           this
           Dyal
           (
           as
           aforesaid
           )
           is
           XII
           ,
           from
           thence
           towards
           the
           right
           hand
           mark
           every
           successive
           Hour
           Line
           with
           I
           ,
           II
           ,
           III
           ,
           &c.
           and
           from
           XII
           towards
           the
           left
           hand
           with
           XI
           ,
           X
           ,
           IX
           ,
           &c.
           
        
         
           The
           Stile
           must
           be
           erected
           perpendicularly
           over
           the
           
             Substilar
             Line
          
           ,
           so
           as
           to
           make
           an
           Angle
           with
           the
           
             Dyal
             Plane
          
           equal
           to
           the
           Elevation
           of
           the
           Pole
           of
           your
           Place
           .
        
         
           
           
             Example
             .
          
           
             You
             would
             draw
             a
             Dyal
             upon
             a
             
               Horizontal
               Plane
            
             here
             at
             London
             ;
             First
             draw
             the
             Meridian
             (
             or
             North
             and
             South
             Line
             )
             as
             XII
             B
             ,
             and
             cross
             it
             in
             the
             middle
             with
             another
             Line
             at
             right
             Angles
             ,
             as
             VI
             ,
             VI
             ,
             which
             is
             an
             East
             and
             West
             Line
             ;
             where
             these
             two
             Lines
             cut
             each
             other
             as
             at
             A
             ,
             make
             the
             Center
             ,
             whereon
             describe
             the
             Semi-Circle
             B
             ,
             VI.
             VI
             ;
             but
             one
             of
             the
             Quadrants
             ,
             viz.
             the
             Quadrant
             from
             XII
             to
             VI
             ,
             towards
             the
             right
             hand
             you
             must
             devide
             into
             90
             equal
             parts
             (
             as
             you
             were
             taught
             in
             Fol.
             12.
             )
             and
             at
             51
             ½
             degrees
             (
             which
             is
             Londons
             Latitude
             )
             make
             a
             mark
             ,
             and
             laying
             a
             straight
             Ruler
             to
             the
             Center
             of
             the
             Plane
             ,
             and
             to
             this
             mark
             draw
             a
             Line
             by
             the
             side
             of
             it
             for
             the
             
               Stiler
               Line
            
             .
             Then
             on
             the
             
               Substilar
               Line
            
             chuse
             a
             point
             as
             at
             C
             ,
             and
             through
             that
             point
             draw
             a
             Line
             as
             long
             as
             you
             can
             perpendicular
             to
             the
             East
             and
             West
             Line
             VI
             ,
             VI
             ,
             as
             EF
             ,
             (
             which
             is
             called
             the
             
               Contingent
               Line
            
             ,
             )
             where
             this
             
               Contingent
               Line
            
             cuts
             the
             
               Substilar
               Line
            
             place
             one
             Foot
             of
             your
             Compasses
             ,
             and
             from
             thence
             measure
             the
             shortest
             distance
             between
             the
             point
             C
             and
             the
             
               Stilar
               Line
            
             .
             And
             keeping
             one
             Foot
             of
             your
             Compasses
             still
             in
             the
             point
             C
             ,
             set
             off
             the
             shortest
             distance
             between
             the
             point
             C
             and
             the
             
               Stilar
               Line
            
             on
             the
             
               Substilar
               Line
            
             ,
             as
             at
             D
             ;
             which
             point
             D
             shall
             be
             a
             Center
             ,
             whereon
             with
             your
             Compasses
             at
             the
             same
             width
             you
             must
             describe
             a
             Semi-Circle
             to
             represent
             a
             Semi-Circle
             of
             the
             Equinoctial
             .
             This
             Semi-Circle
             devide
             into
             six
             equal
             parts
             (
             as
             you
             were
             taught
             Fol.
             13.
             )
             to
             each
             of
             which
             equal
             parts
             ,
             and
             to
             the
             Center
             of
             the
             Equinoctial
             Semi-Circle
             lay
             a
             straight
             Ruler
             ,
             and
             where
             the
             straight
             Ruler
             cuts
             the
             
               Line
               of
               Contingence
            
             make
             marks
             in
             the
             
               Line
               of
               Contingence
            
             .
             Then
             lay
             the
             straight
             Ruler
             to
             the
             Semi-Circle
             
             of
             the
             
               Dyal
               Plane
            
             ,
             and
             to
             each
             of
             the
             marks
             in
             the
             
               Line
               of
               Contingence
            
             ,
             and
             by
             the
             side
             of
             it
             draw
             twelve
             straight
             Lines
             for
             the
             twelve
             Fore
             and
             Afternoon
             Hour
             Lines
             ,
             viz.
             from
             VI
             in
             the
             Morning
             to
             VI
             in
             the
             Evening
             .
             Then
             in
             the
             Quadrant
             VI
             B
             ,
             measure
             the
             distance
             between
             the
             VI
             a
             Clock
             Hour
             Line
             ,
             and
             the
             V
             a
             Clock
             Hour
             Line
             ,
             and
             transfer
             the
             same
             distances
             from
             the
             VI
             a
             Clock
             Line
             to
             VII
             ,
             and
             V
             on
             both
             sides
             the
             VI
             a
             Clock
             Hour
             Lines
             ,
             and
             through
             those
             distances
             draw
             from
             the
             Center
             of
             the
             Plane
             the
             VII
             and
             V
             a
             Clock
             Hour
             Lines
             ,
             and
             measure
             the
             distance
             between
             the
             VI
             a
             Clock
             Hour
             Line
             and
             the
             IV
             a
             Clock
             Hour
             Line
             ,
             and
             transfer
             the
             same
             distance
             from
             the
             VI
             a
             Clock
             Line
             to
             VIII
             and
             IV
             ,
             and
             through
             those
             distances
             draw
             from
             the
             Center
             of
             the
             Plane
             the
             VIII
             a
             Clock
             and
             IV
             a
             Clock
             Hour
             Lines
             .
          
           
           
           
             If
             you
             will
             have
             the
             half
             Hours
             and
             quarter
             Hours
             ,
             or
             any
             other
             devision
             of
             hours
             ,
             you
             must
             devide
             each
             six
             devisions
             of
             the
             Equinoctial
             into
             so
             many
             parts
             as
             you
             intend
             ,
             and
             by
             a
             straight
             Ruler
             laid
             to
             the
             Center
             of
             the
             Equinoctial
             ,
             and
             those
             devisions
             in
             the
             Equinoctial
             Circle
             make
             marks
             in
             the
             
               Line
               of
               Contingence
            
             ,
             as
             you
             did
             before
             for
             the
             whole
             Hour
             Lines
             ;
             and
             Lines
             drawn
             from
             the
             Center
             of
             the
             Plane
             through
             those
             marks
             shall
             be
             the
             sub-devisions
             of
             the
             Hours
             :
             But
             you
             must
             remember
             to
             make
             all
             sub-devisions
             short
             Lines
             ,
             and
             near
             the
             verge
             of
             the
             
               Dyal
               Plane
            
             ,
             that
             you
             may
             the
             easier
             distinguish
             between
             the
             whole
             Hours
             and
             the
             parts
             of
             Hours
             ;
             as
             you
             may
             see
             in
             the
             Figure
             .
          
           
             Having
             drawn
             the
             Hour
             Lines
             ,
             set
             the
             number
             of
             each
             Hour
             Line
             under
             it
             ,
             as
             you
             see
             in
             the
             Figure
             .
          
           
             Last
             of
             all
             sit
             a
             Triangular
             Iron
             ,
             whose
             angular
             point
             being
             laid
             to
             the
             Center
             of
             the
             
               Dyal
               Plane
            
             ,
             one
             side
             must
             agree
             with
             the
             
               Substilar
               Line
            
             ,
             and
             its
             other
             side
             with
             the
             
               Stilar
               Line
            
             ;
             so
             is
             the
             Stile
             made
             .
             And
             this
             Stile
             you
             must
             erect
             perpendicularly
             over
             the
             
               Substilar
               Line
            
             on
             the
             
               Dyal
               Plane
            
             ,
             and
             there
             fix
             it
             .
             Then
             is
             your
             Dyal
             finished
             .
          
        
      
       
         
           OPERAT.
           III.
           To
           describe
           an
           
             Erect
             Direct
             South
             Dyal
          
           .
        
         
           YOU
           may
           know
           an
           
             Erect
             Direct
             South
             Plane
          
           by
           applying
           the
           North
           side
           of
           the
           Declinatory
           to
           it
           ;
           For
           then
           if
           the
           North
           end
           of
           the
           Needle
           hang
           directly
           over
           the
           North
           point
           of
           the
           Card
           in
           the
           bottom
           of
           the
           Box
           ,
           it
           is
           a
           
             South
             Plane
          
           ;
           but
           if
           it
           hang
           not
           directly
           over
           the
           North
           point
           of
           the
           Card
           ,
           it
           is
           not
           a
           
             Direct
             South
             Plane
          
           ,
           but
           Declines
           either
           East
           or
           West
           ,
           and
           that
           
           contrary
           to
           the
           pointing
           of
           the
           Needle
           Easterly
           or
           Westerly
           from
           the
           North
           point
           of
           the
           Card
           :
           for
           if
           the
           North
           point
           of
           the
           Needle
           points
           Easterly
           ,
           the
           
             Plane
             Declines
          
           from
           the
           South
           towards
           the
           West
           :
           if
           it
           point
           Westerly
           ,
           the
           
             Plane
             Declines
          
           from
           the
           South
           towards
           the
           East
           .
        
         
           You
           may
           know
           if
           the
           Plane
           be
           truly
           Erect
           or
           upright
           ,
           by
           applying
           one
           of
           the
           sides
           AB
           or
           AD
           to
           it
           ;
           for
           then
           by
           holding
           the
           Center
           A
           upwards
           ,
           so
           as
           the
           Plumb-line
           play
           free
           in
           the
           Grove
           ,
           if
           the
           Line
           falls
           upon
           0
           ,
           or
           90
           ,
           the
           Plane
           is
           upright
           ;
           but
           if
           it
           hang
           upon
           any
           of
           the
           intermediate
           Degrees
           ,
           it
           is
           not
           upright
           ,
           but
           Inclines
           or
           Reclines
           .
        
         
           If
           you
           find
           it
           Incline
           ,
           apply
           the
           side
           AB
           to
           it
           ,
           and
           see
           what
           number
           of
           Degrees
           the
           Plumb-line
           falls
           on
           ,
           for
           that
           number
           of
           Degrees
           counted
           from
           the
           side
           AB
           ,
           is
           the
           number
           of
           Degrees
           of
           Inclination
           .
        
         
           If
           you
           find
           the
           
             Plane
             Reclines
          
           ,
           apply
           the
           side
           AD
           to
           it
           ,
           and
           see
           what
           number
           of
           Degrees
           the
           Plumb-line
           falls
           on
           ,
           for
           that
           number
           of
           Degrees
           counted
           from
           the
           side
           AD
           is
           the
           number
           of
           Degrees
           of
           Reclination
           .
        
         
           These
           Rules
           being
           well
           understood
           ,
           may
           serve
           you
           to
           find
           the
           scituation
           of
           all
           other
           sorts
           of
           Planes
           .
        
         
           But
           for
           the
           making
           a
           Dyal
           on
           this
           Plane
           ,
           you
           must
           first
           draw
           a
           
             Meridian
             Line
          
           through
           the
           middle
           of
           the
           Plane
           ,
           by
           applying
           a
           Plumb-line
           to
           the
           middle
           of
           it
           ,
           till
           the
           Plumbet
           hang
           quietly
           before
           it
           :
           for
           then
           if
           the
           Plumb-line
           be
           black't
           (
           for
           a
           white
           Ground
           ,
           or
           chalked
           for
           a
           dark
           Ground
           )
           and
           strained
           as
           Carpenters
           do
           their
           Lines
           ,
           you
           may
           with
           one
           stroak
           of
           the
           string
           on
           the
           Plane
           describe
           the
           
             Meridian
             Line
          
           ,
           as
           A
           XII
           :
           This
           Meridian
           is
           also
           the
           
             Substilar
             Line
          
           .
        
         
         
           Then
           on
           the
           top
           of
           this
           
             Meridian
             Line
          
           ,
           as
           at
           A
           ,
           draw
           another
           Line
           athwart
           it
           to
           cut
           it
           at
           right
           Angles
           ,
           as
           VI
           ,
           VI
           ,
           for
           an
           East
           and
           West
           Line
           .
           At
           the
           meeting
           of
           these
           two
           Lines
           on
           the
           top
           ,
           make
           your
           Center
           ,
           whereon
           describe
           a
           Semi-Circle
           on
           your
           Plane
           ,
           as
           large
           as
           you
           can
           ,
           which
           by
           the
           
             Meridian
             Line
          
           and
           the
           East
           and
           West
           Line
           will
           be
           devided
           into
           two
           Quadrants
           .
           One
           of
           these
           Quadrants
           devide
           into
           90
           Degrees
           (
           as
           you
           were
           taught
           Fol.
           12.
           )
           and
           from
           the
           
             Substilar
             Line
          
           count
           the
           Complement
           of
           the
           
             Poles
             Elevation
          
           ,
           which
           (
           here
           at
           London
           where
           the
           Pole
           is
           elevated
           51
           ½
           Degrees
           ,
           its
           Complement
           to
           90
           )
           is
           38
           ½
           Degrees
           ,
           and
           make
           there
           a
           mark
           ,
           as
           at
           E.
           Then
           on
           the
           
             Substilar
             Line
          
           chuse
           a
           point
           (
           where
           you
           please
           )
           as
           at
           F
           ,
           for
           the
           
             Line
             of
             Contingence
          
           to
           pass
           through
           :
           which
           
             Line
             of
             Contingence
          
           draw
           as
           long
           as
           you
           can
           ,
           so
           as
           it
           may
           cut
           the
           
             Substilar
             Line
          
           at
           right
           Angles
           ,
           and
           from
           the
           point
           F
           in
           the
           
             Substilar
             Line
          
           measure
           the
           shortest
           distance
           between
           it
           and
           the
           
             Stilar
             Line
          
           ,
           and
           keeping
           one
           Foot
           of
           your
           Compasses
           still
           in
           the
           point
           F
           ,
           transfer
           that
           distance
           into
           the
           
             Substilar
             Line
          
           ,
           as
           at
           G
           ;
           then
           on
           the
           point
           G
           describe
           a
           Semi-Circle
           of
           the
           Equinoctial
           against
           the
           
             Line
             of
             Contingence
          
           ,
           which
           Semi-Circle
           devide
           into
           
           twelve
           equal
           parts
           ,
           (
           as
           you
           were
           taught
           by
           the
           Example
           in
           the
           
             Horizontal
             Dyal
          
           ,
           Fol.
           13.
           )
           and
           by
           a
           straight
           Ruler
           laid
           to
           each
           of
           these
           Devisions
           ,
           and
           to
           the
           Center
           of
           the
           Semi-Circle
           make
           marks
           in
           the
           
             Line
             of
             Contingence
          
           by
           the
           side
           of
           the
           Ruler
           :
           For
           straight
           Lines
           drawn
           from
           the
           Center
           of
           the
           
             Dyal
             Plane
          
           through
           these
           marks
           in
           the
           
             Contingent
             Line
          
           shall
           be
           the
           12
           Hour
           Lines
           before
           and
           after
           Noon
           .
        
         
           Then
           mark
           your
           Hour
           Lines
           with
           their
           respective
           Numbers
           :
           The
           Substilar
           or
           
             Meridian
             Line
          
           is
           XII
           ,
           from
           thence
           towards
           the
           right
           hand
           with
           I
           ,
           II
           ,
           III
           ,
           &c.
           and
           from
           thence
           towards
           the
           left
           hand
           with
           XI
           ,
           X
           ,
           IX
           ,
           &c.
           
        
         
           The
           Stile
           must
           be
           erected
           perpendicularly
           over
           the
           
             Substilar
             Line
          
           ,
           so
           as
           to
           make
           an
           Angle
           with
           the
           
             Dyal
             Plane
          
           equal
           to
           the
           Complement
           of
           the
           
             Poles
             Elevation
             ,
             viz.
          
           38
           ½
           Degrees
           .
        
      
       
         
           OPERAT.
           IV.
           To
           make
           an
           Erect
           Direct
           North
           Dyal
           .
        
         
           THE
           
             Erect
             Direct
             North
             Dyal
          
           ,
           Stile
           and
           all
           ,
           is
           made
           by
           the
           same
           Rules
           ,
           changing
           upwards
           for
           downwards
           ,
           and
           the
           left
           side
           for
           the
           right
           ,
           the
           
             Erect
             Direct
             South
             Dyal
          
           is
           made
           :
           for
           if
           the
           
             Erect
             Direct
             South
             Dyal
          
           be
           drawn
           on
           any
           transparent
           Plane
           ,
           as
           on
           Glass
           ,
           Horn
           ,
           or
           an
           oyled
           Paper
           ,
           and
           the
           
             Horizontal
             Line
          
           VI
           ,
           VI
           ,
           turned
           downwards
           ,
           and
           the
           Line
           VII
           mark't
           with
           V
           ,
           the
           Line
           VIII
           with
           IIII
           ,
           the
           Line
           V
           with
           VII
           ,
           and
           the
           Line
           IIII
           with
           VIII
           ,
           then
           have
           you
           of
           it
           a
           
             North
             Erect
             Direct
             Dyal
          
           .
        
         
           All
           the
           other
           Hour
           Lines
           in
           this
           Dyal
           are
           useless
           ,
           because
           the
           Sun
           in
           our
           Latitude
           shines
           on
           a
           North
           Face
           the
           longest
           Day
           only
           before
           VI
           in
           the
           Morning
           ,
           and
           after
           VI
           at
           Night
           .
        
      
       
         
         
           OPERAT.
           V.
           To
           describe
           an
           Erect
           direct
           East
           Dyal
           .
        
         
           HAng
           a
           Plumb-line
           a
           little
           above
           the
           place
           on
           the
           Wall
           where
           you
           intend
           to
           make
           your
           Dyal
           ,
           and
           wait
           till
           it
           hang
           quietly
           before
           the
           Wall
           :
           Then
           if
           the
           Line
           be
           rubbed
           with
           Chalk
           (
           like
           a
           Carpenters
           Line
           )
           you
           may
           by
           holding
           the
           Plumbet
           end
           close
           to
           the
           Wall
           ,
           and
           straining
           it
           pretty
           stiff
           ,
           strike
           with
           it
           a
           straight
           Line
           ,
           as
           Carpenters
           do
           :
           This
           Line
           shall
           be
           a
           perpendicular
           ,
           as
           AB
           .
           Then
           chuse
           a
           convenient
           point
           in
           this
           Perpendicular
           ,
           as
           at
           C
           ,
           for
           a
           Center
           ,
           whereon
           describe
           an
           occult
           Arch
           ,
           as
           DE
           ;
           This
           Arch
           must
           contain
           the
           number
           of
           Degrees
           of
           the
           Elevation
           of
           the
           Equinoctial
           ,
           counted
           between
           D
           and
           E
           ,
           which
           in
           our
           Latitude
           is
           38
           ½
           ,
           or
           (
           which
           is
           all
           one
           )
           the
           Complement
           of
           the
           
             Poles
             Elevation
          
           .
           Therefore
           in
           a
           Quadrant
           of
           the
           same
           Radius
           with
           the
           occult
           Arch
           measure
           38
           ½
           Degrees
           ,
           and
           set
           them
           off
           in
           the
           Plane
           from
           E
           to
           D
           :
           Then
           from
           D
           to
           the
           Center
           C
           in
           the
           Perpendicular
           draw
           the
           prick't
           Line
           DC
           ;
           this
           prick't
           Line
           shall
           represent
           the
           
             Axis
             of
             the
             World.
          
           Then
           cross
           this
           Line
           at
           right
           Angles
           with
           the
           Line
           CF
           ,
           and
           draw
           it
           from
           C
           to
           F
           ,
           so
           long
           as
           possibly
           you
           can
           :
           This
           Line
           shall
           be
           the
           
             Contingent
             Line
          
           .
           Then
           chuse
           a
           point
           in
           this
           
             Contingent
             Line
          
           ,
           as
           at
           VI
           ,
           draw
           a
           Line
           through
           that
           point
           at
           right
           Angles
           for
           the
           
             Substilar
             Line
          
           ,
           as
           G
           VI
           H
           for
           the
           
             Substilar
             Line
          
           ;
           then
           open
           your
           Compasses
           to
           a
           convenient
           width
           ,
           (
           as
           to
           VIG
           )
           and
           pitching
           one
           Foot
           in
           the
           point
           G
           ,
           with
           the
           other
           Foot
           describe
           a
           Semi-Circle
           of
           the
           Equinoctial
           against
           the
           
             Line
             of
             Contingence
          
           ,
           which
           Semi-Circle
           devide
           from
           VI
           both
           wayes
           into
           six
           equal
           parts
           ,
           as
           you
           were
           taught
           by
           the
           Example
           in
           the
           
             Horizontal
             
             Dyal
          
           :
           and
           laying
           a
           straight
           Ruler
           on
           the
           Center
           of
           this
           Semi-Circle
           of
           the
           Equinoctial
           ,
           and
           to
           each
           of
           those
           equal
           parts
           mark
           on
           the
           
             Contingent
             Line
          
           where
           the
           Ruler
           cuts
           it
           ,
           for
           those
           marks
           shall
           be
           the
           several
           points
           from
           whence
           Lines
           drawn
           parallel
           to
           the
           Line
           CD
           shall
           be
           the
           respective
           Hour
           Lines
           .
        
         
         
           The
           reason
           why
           the
           
             Contingent
             Line
          
           is
           drawn
           from
           VI.
           to
           F
           ,
           so
           much
           longer
           than
           from
           VI
           to
           C
           is
           ;
           because
           the
           Hour
           Lines
           from
           VI
           towards
           XII
           are
           more
           in
           number
           towards
           Noon
           ,
           than
           they
           are
           from
           VI
           backward
           towards
           IIII
           :
           for
           this
           Dyal
           will
           only
           shew
           the
           Hours
           
           from
           a
           little
           before
           IV
           in
           the
           Morning
           to
           almost
           Noon
           :
           For
           just
           at
           Noon
           the
           Shaddow
           goes
           off
           the
           Plane
           ;
           as
           you
           may
           see
           if
           you
           apply
           a
           straight
           Ruler
           to
           the
           Center
           of
           the
           Equinoctial
           Semi-Circle
           G
           ,
           and
           lay
           it
           to
           the
           point
           12
           in
           the
           Semi-Circle
           ;
           for
           the
           straight
           Ruler
           will
           then
           never
           cut
           the
           
             Line
             of
             Contingence
          
           ,
           because
           the
           
             Line
             of
             Contingence
          
           is
           parallel
           to
           the
           Line
           G
           XII
           on
           the
           Equinoctial
           Circle
           ,
           and
           Lines
           parallel
           ,
           though
           continued
           to
           never
           so
           great
           a
           length
           never
           meet
           .
        
         
           To
           these
           
             Hour
             Lines
          
           ,
           set
           Figures
           as
           may
           be
           seen
           in
           the
           Scheme
           .
        
         
           The
           Stile
           IK
           of
           this
           Dyal
           as
           well
           as
           of
           all
           others
           must
           stand
           parallel
           to
           the
           
             Axis
             of
             the
             World
          
           ;
           and
           also
           parallel
           to
           the
           Face
           of
           the
           Plane
           ,
           and
           parallel
           to
           all
           the
           
             Hour
             Lines
          
           ,
           and
           stand
           directly
           over
           the
           Substilar
           or
           VI
           a
           Clock
           Hour-Line
           ,
           and
           that
           so
           high
           as
           is
           the
           distance
           of
           the
           Center
           of
           the
           Equinoctial
           Semi-Circle
           from
           the
           
             Contingent
             Line
          
           .
        
      
       
         
           OPERAT.
           VI.
           To
           describe
           a
           Dyal
           on
           an
           
             Erect
             Direct
             West
             Plane
          
           .
        
         
           AN
           
             Erect
             Direct
             West
             Dyal
          
           ,
           is
           the
           same
           in
           all
           respects
           with
           an
           
             Erect
             Direct
             East
             Dyal
          
           :
           Only
           as
           the
           
             East
             Dyal
          
           shews
           the
           Forenoon
           Hours
           ,
           so
           the
           West
           shews
           the
           Afternoon
           Hours
           .
        
         
           Thus
           if
           you
           should
           draw
           the
           
             East
             Dyal
          
           on
           any
           transparent
           Plane
           ,
           as
           on
           Glass
           ,
           Horn
           ,
           or
           oyled
           Paper
           ,
           on
           the
           one
           side
           will
           appear
           an
           
             East
             Dyal
          
           ,
           on
           the
           other
           side
           a
           West
           :
           Only
           the
           numbers
           to
           the
           
             Hour
             Lines
          
           (
           as
           was
           said
           before
           in
           the
           
             North
             Dyal
          
           )
           must
           be
           changed
           ;
           for
           that
           which
           in
           the
           
             East
             Dyal
          
           is
           XI
           ,
           in
           the
           West
           must
           be
           I
           ;
           that
           which
           in
           the
           
             East
             Dyal
          
           is
           X
           ,
           in
           the
           West
           
           must
           be
           II
           ;
           that
           which
           in
           the
           
             East
             Dyal
          
           is
           IX
           ,
           in
           the
           West
           must
           be
           III
           ,
           &c.
           
           The
           Stile
           is
           the
           same
           .
        
      
       
         
           OPERAT.
           VII
           .
           To
           describe
           a
           Dyal
           on
           an
           
             Erect
             North
          
           ,
           or
           
             Erect
             South
             Plane
             Declining
          
           Eastwards
           or
           Westwards
           .
        
         
           THese
           four
           Dyals
           ,
           viz.
           the
           
             Erect
             North
             Declining
             Eastwards
          
           ,
           the
           
             Erect
             North
             Declining
             Westwards
          
           ,
           the
           
             Erect
             South
             Declining
             Eastwards
          
           ,
           and
           the
           
             Erect
             South
             Declining
             Westwards
          
           ,
           are
           all
           projected
           by
           the
           same
           Rules
           ;
           and
           therefore
           are
           in
           effect
           but
           one
           Dyal
           differently
           placed
           ,
           as
           you
           shall
           see
           hereafter
           .
        
         
           First
           draw
           on
           your
           Plane
           a
           straight
           Line
           to
           represent
           the
           Horizon
           of
           your
           place
           ,
           and
           mark
           one
           end
           of
           it
           W
           for
           West
           ,
           and
           the
           other
           end
           E
           for
           East
           .
           Chuse
           a
           point
           in
           this
           Horizontal
           Line
           for
           a
           Center
           ,
           as
           at
           A
           ,
           whereon
           you
           may
           describe
           a
           Circle
           to
           comprehend
           all
           these
           four
           Dyals
           :
           Draw
           a
           Line
           as
           MAM
           perpendicular
           to
           the
           
             Horizontal
             Line
          
           WE
           ,
           through
           the
           Center
           A
           for
           a
           
             Meridian
             Line
          
           ,
           and
           on
           that
           Center
           describe
           a
           Circle
           ,
           which
           by
           the
           two
           Lines
           WAE
           ,
           and
           MAM
           will
           be
           devided
           into
           four
           Quadrants
           ,
           which
           will
           comprehend
           the
           four
           Dyals
           aforesaid
           :
           for
           if
           it
           be
           a
           
             North
             declining
             West
          
           you
           are
           to
           draw
           ,
           the
           upper
           Quadrant
           to
           the
           left
           hand
           serves
           your
           purpose
           :
           If
           a
           
             South
             Declining
             West
          
           ,
           the
           same
           Lines
           continued
           through
           the
           Center
           A
           into
           the
           lower
           Quadrant
           to
           the
           right
           Hand
           serves
           your
           turn
           ;
           if
           a
           
             North
             Declining
             East
          
           ,
           the
           upper
           Quadrant
           to
           the
           right
           Hand
           serves
           your
           turn
           ;
           or
           if
           a
           
             South
             Declining
             East
          
           ,
           the
           same
           Lines
           continued
           through
           the
           Center
           A
           into
           the
           lower
           Quadrant
           to
           the
           left
           hand
           serves
           your
           turn
           ;
           and
           you
           must
           draw
           the
           
             Declination
             ,
             Complement
             of
             the
             Poles
             Altitude
             ,
             Substile
             ,
             Stile
          
           
           and
           
             Hour
             Lines
          
           in
           it
           ;
           but
           the
           
             Hour
             Lines
          
           must
           be
           differently
           marked
           as
           you
           shall
           see
           hereafter
           .
           I
           shall
           onely
           give
           you
           an
           Example
           of
           one
           of
           these
           
             Dyals
             ;
             viz.
          
           A
           
             South
             Declining
             East
          
           .
        
         
         
           We
           will
           suppose
           you
           are
           to
           draw
           a
           Dyal
           that
           declines
           from
           the
           South
           50
           Degrees
           towards
           the
           East
           ;
           here
           being
           but
           one
           Dyal
           ,
           you
           need
           describe
           but
           one
           Quadrant
           of
           a
           Circle
           .
           Set
           off
           in
           the
           lower
           Quadrant
           WAM
           50
           degrees
           from
           the
           
             Meridian
             Line
          
           M
           towards
           W
           ,
           and
           from
           the
           Center
           A
           draw
           a
           straight
           Line
           through
           that
           mark
           in
           the
           Quadrant
           as
           DA
           ,
           which
           may
           be
           called
           the
           
             Line
             of
             Declination
          
           ;
           then
           set
           off
           from
           the
           
             Meridian
             Line
          
           the
           Complement
           of
           the
           
             Poles
             Elevation
          
           ,
           which
           in
           our
           Latitude
           is
           38
           ½
           degrees
           ,
           and
           there
           draw
           another
           Line
           from
           the
           Center
           as
           AP
           ,
           which
           we
           will
           
           call
           the
           
             Polar
             Line
          
           .
           Then
           take
           in
           the
           
             Horizontal
             Line
          
           a
           convenient
           portion
           of
           the
           Quadrant
           ,
           as
           AB
           ,
           and
           from
           the
           point
           B
           draw
           a
           Line
           parallel
           to
           the
           
             Meridian
             Line
          
           AM
           ,
           and
           continue
           that
           Line
           till
           it
           intersect
           the
           
             Polar
             Line
          
           ,
           as
           at
           P
           ,
           from
           which
           Point
           P
           draw
           a
           Line
           parallel
           to
           WA
           ,
           as
           PC
           :
           Then
           measure
           the
           distance
           of
           AB
           in
           the
           
             Horizontal
             Line
          
           ,
           and
           set
           off
           that
           distance
           in
           the
           Line
           of
           Declination
           ,
           as
           from
           A
           to
           D
           ,
           and
           from
           that
           point
           of
           distance
           draw
           a
           Line
           parallel
           to
           the
           Meridian
           AM
           through
           the
           
             Horizontal
             Line
          
           at
           R
           ,
           and
           through
           the
           Point
           D
           ,
           and
           continue
           it
           through
           the
           Line
           PC
           ,
           as
           at
           S
           ;
           then
           laying
           a
           straight
           Ruler
           to
           the
           Center
           A
           ,
           and
           the
           Intersection
           of
           the
           Line
           PC
           ,
           at
           S
           draw
           the
           Line
           AS
           for
           the
           Substile
           :
           Then
           upon
           the
           Point
           S
           erect
           a
           Line
           perpendicularly
           as
           ST
           ;
           Then
           measure
           the
           distance
           between
           R
           and
           D
           ,
           and
           set
           that
           distance
           off
           from
           S
           to
           T
           ,
           and
           from
           the
           Center
           to
           the
           point
           T
           draw
           the
           Line
           AT
           for
           the
           Stile
           or
           Gnomon
           ;
           and
           the
           Triangle
           SAT
           made
           of
           Iron
           or
           Brass
           and
           erected
           perpendicularly
           over
           the
           Substile
           SA
           shall
           by
           its
           upper
           side
           TA
           cast
           a
           shaddow
           upon
           the
           Hour
           of
           the
           day
           .
           But
           you
           will
           say
           the
           
             Hour
             Lines
          
           must
           be
           drawn
           first
           :
           It
           is
           true
           ;
           Therefore
           to
           draw
           them
           you
           must
           chuse
           a
           point
           in
           the
           
             Substile
             Line
          
           where
           you
           think
           good
           ,
           and
           through
           it
           draw
           the
           Line
           FF
           as
           long
           as
           you
           can
           for
           the
           the
           
             Line
             of
             Contingence
          
           :
           then
           with
           your
           Compasses
           take
           the
           shortest
           distance
           between
           this
           point
           and
           the
           Stile
           ,
           and
           transfer
           that
           distance
           below
           the
           
             Line
             of
             Contingence
          
           on
           the
           Substile
           as
           at
           Ae
           ,
           and
           with
           your
           Compasses
           at
           that
           distance
           describe
           on
           the
           Center
           Ae
           a
           Circle
           to
           represent
           the
           Equinoctial
           ;
           Then
           (
           as
           you
           were
           taught
           in
           the
           Example
           of
           the
           
             Horizontal
             Dyal
          
           )
           devide
           the
           Semi-Circle
           of
           the
           Equinoctial
           into
           twelve
           equal
           parts
           ,
           beginning
           at
           the
           point
           in
           the
           
             Equinoctial
             Circle
          
           ,
           where
           a
           
           straight
           Line
           drawn
           from
           the
           Center
           of
           it
           to
           the
           Intersection
           of
           the
           Line
           of
           Contingence
           with
           the
           Meridian
           Line
           cuts
           the
           Equinoctial
           Line
           ,
           as
           here
           at
           the
           Point
           G
           ;
           Then
           lay
           a
           straight
           Ruler
           to
           the
           Center
           of
           the
           
             Equinoctial
             Circle
          
           ,
           and
           to
           every
           one
           of
           the
           Devisions
           in
           the
           Semi-Circle
           ,
           and
           mark
           where
           the
           straight
           Ruler
           cuts
           the
           
             Contingent
             Line
          
           ;
           for
           straight
           Lines
           drawn
           from
           the
           Center
           A
           of
           the
           Dyal
           to
           those
           several
           marks
           on
           the
           
             Contingent
             Line
          
           shall
           be
           the
           
             Hour
             Lines
          
           ;
           and
           must
           be
           numbred
           from
           the
           Noon
           Line
           or
           Meridian
           A
           M
           backwards
           ,
           as
           XII
           ,
           XI
           ,
           X
           ,
           IX
           .
           &c.
           towards
           the
           left
           hand
           .
           So
           is
           your
           Dyal
           finished
           .
        
         
           This
           Dyal
           drawn
           on
           any
           transparent
           matter
           as
           Horn
           ,
           Glass
           ,
           or
           an
           oyled
           Paper
           ,
           shall
           on
           the
           other
           side
           the
           transparent
           matter
           become
           a
           
             South
             Declining
             West
             ,
             (
             Stile
          
           and
           all
           )
           but
           then
           the
           I
           a
           Clock
           Hour
           Line
           must
           be
           marked
           II
           ,
           the
           XII
           XII
           ,
           the
           XI
           a
           Clock
           Hour
           Line
           I
           ,
           X
           ,
           II
           ,
           IX
           ,
           III
           ,
           &c.
           
        
         
           If
           you
           project
           it
           anew
           ,
           you
           must
           describe
           the
           Quadrant
           MW
           on
           the
           other
           side
           the
           
             Meridian
             Line
          
           ,
           on
           the
           Center
           A
           from
           M
           to
           E
           ,
           and
           then
           count
           ,
           (
           as
           before
           )
           the
           
             Declination
             ,
             Altitude
          
           of
           the
           
             Pole
             ,
             Substile
          
           ,
           and
           Stile
           in
           the
           Quadrant
           ,
           beginning
           at
           M
           towards
           E
           ,
           and
           work
           in
           all
           respects
           as
           with
           the
           
             South
             Declining
             East
          
           ;
           only
           number
           this
           
             South
             Declining
             West
          
           as
           in
           the
           foregoing
           Paragraph
           .
        
         
           If
           you
           project
           a
           
             North
             Declining
             East
          
           ,
           you
           must
           describe
           the
           Quadrant
           above
           the
           
             Horizontal
             Line
          
           from
           M
           upwards
           ,
           towards
           E
           on
           your
           right
           hand
           ,
           and
           count
           (
           as
           before
           )
           the
           
             Declination
             ,
             Altitude
             ,
             Complement
          
           of
           the
           
             Pole
             ,
             Substile
          
           ,
           and
           Stile
           from
           the
           
             Meridian
             Line
          
           ,
           and
           work
           as
           with
           the
           
             South
             Declining
             East
          
           :
           It
           must
           be
           numbred
           from
           the
           Meridian
           Line
           M
           towards
           the
           right
           hand
           with
           XI
           ,
           X
           ,
           IX
           ,
           VIII
           ,
           &c.
           
        
         
         
           If
           this
           Dyal
           were
           drawn
           on
           transparent
           matter
           ,
           the
           other
           ▪
           side
           would
           shew
           a
           
             North
             Declining
             West
          
           :
           But
           if
           you
           will
           project
           it
           anew
           ,
           you
           must
           describe
           the
           Quadrant
           above
           the
           
             Horizontal
             Line
          
           ,
           from
           M
           upwards
           towards
           W
           ,
           and
           count
           from
           the
           Meridian
           Line
           AM
           the
           
             Declination
             ,
             Complement
             ,
             Altitude
             of
             the
             Pole
             ,
             Substile
          
           and
           Stile
           ,
           and
           work
           with
           them
           (
           in
           all
           respects
           )
           as
           with
           the
           
             South
             Declining
             East
          
           ;
           but
           then
           the
           XI
           a
           Clock
           Hour
           Line
           must
           be
           marked
           I
           ,
           the
           X
           ,
           II
           ;
           the
           IX
           ,
           III
           ,
           &c.
           
        
      
       
         
           OPERAT.
           VIII
           .
           To
           draw
           a
           Dyal
           on
           an
           East
           or
           
             West
             Plane
             Reclining
          
           ,
           or
           Inclining
           .
        
         
           DRaw
           a
           straight
           Line
           parallel
           to
           the
           Horizon
           ,
           to
           represent
           a
           Meridian
           ,
           or
           XII
           a
           Clock
           Line
           ,
           and
           mark
           one
           end
           N
           ,
           the
           other
           S
           ;
           Chuse
           a
           point
           in
           this
           Line
           ,
           as
           at
           A
           for
           a
           Center
           :
           then
           if
           your
           Plane
           be
           an
           East
           or
           a
           
             West
             Incliner
          
           ,
           let
           fall
           a
           Perpendicular
           upon
           this
           Center
           ,
           (
           that
           is
           ,
           the
           Perpendicular
           must
           stand
           above
           the
           
             Meridian
             Line
          
           NS
           .
           )
           as
           AE
           ,
           and
           upon
           the
           Center
           A
           describe
           a
           Semi-Circle
           above
           the
           
             Meridian
             Line
          
           NS
           ;
           )
           But
           if
           your
           Plane
           be
           an
           
             East
             Incliner
          
           ,
           or
           a
           
             West
             Recliner
          
           ,
           let
           fall
           a
           Perpendicular
           from
           the
           Center
           A
           under
           the
           
             Meridian
             Line
          
           ,
           and
           upon
           the
           Center
           A
           describe
           a
           Semi-Circle
           under
           the
           
             Meridian
             Line
          
           .
           If
           your
           Plane
           be
           a
           
             West
             Incliner
          
           ,
           work
           (
           as
           shall
           be
           taught
           )
           in
           the
           Quadrant
           on
           the
           left
           hand
           above
           the
           
             Meridian
             Line
          
           .
           If
           an
           
             East
             Recliner
          
           ,
           in
           the
           Quadrant
           on
           the
           right
           hand
           above
           the
           
             Meridian
             Line
          
           .
           If
           it
           be
           a
           
             West
             Recliner
          
           ,
           work
           in
           the
           Quadrant
           on
           the
           left
           hand
           under
           the
           Meridian
           .
           If
           an
           
             East
             Incliner
          
           ,
           in
           the
           Quadrant
           under
           the
           Meridian
           Line
           the
           right
           hand
           .
        
         
           
           
             For
             Example
             ,
             An
             East
             Dyal
             Reclining
             45
             Degrees
             .
          
           
             You
             would
             draw
             a
             Dyal
             on
             an
             
               East
               Plane
               Reclining
            
             45
             Degrees
             :
             Therefore
             in
             the
             Quadrant
             on
             the
             right
             hand
             above
             the
             
               Meridian
               Line
            
             ,
             set
             off
             from
             the
             Perpendicular
             AE
             45
             Degrees
             on
             the
             Quadrant
             ,
             for
             the
             Reclination
             of
             the
             Plane
             ;
             and
             set
             off
             also
             in
             the
             Quadrant
             38
             ½
             Degrees
             from
             the
             Perpendicular
             for
             the
             
               Complement
               of
               the
               Poles
               Elevation
            
             ,
             and
             at
             these
             settings
             off
             make
             marks
             in
             the
             Quadrant
             :
             Then
             lay
             a
             straight
             Ruler
             to
             the
             Center
             A
             ,
             and
             to
             the
             marks
             in
             the
             Quadrant
             ,
             and
             draw
             straight
             Lines
             through
             them
             from
             the
             Center
             .
             Then
             chuse
             in
             the
             
               Meridian
               Line
            
             NS
             a
             convenient
             point
             ,
             as
             at
             B
             ,
             and
             through
             that
             point
             draw
             a
             Line
             parallel
             to
             the
             Perpendicular
             AE
             ,
             which
             will
             intersect
             the
             Line
             drawn
             for
             the
             Complement
             of
             the
             
               Poles
               Elevation
            
             AP
             in
             P
             ;
             from
             which
             point
             P
             ,
             draw
             a
             Line
             parallel
             to
             the
             Meridian
             Line
             NS
             ,
             to
             cut
             the
             Perpendicular
             AE
             in
             C
             ,
             and
             also
             the
             Line
             of
             Obliquity
             AO
             in
             O.
             Then
             measure
             the
             length
             AO
             ,
             and
             set
             off
             that
             length
             in
             the
             Perpendicular
             ACE
             from
             A
             to
             E
             ,
             and
             draw
             the
             Line
             EG
             parallel
             to
             the
             
               Meridian
               Line
            
             NS
             ,
             which
             will
             cut
             the
             Line
             BP
             prolonged
             in
             G.
             Measure
             also
             the
             length
             of
             CO
             ,
             and
             set
             that
             length
             off
             from
             A
             to
             Q
             on
             the
             Line
             of
             Obliquity
             AO
             ,
             and
             draw
             the
             Line
             QR
             parallel
             to
             the
             Perpendicular
             ACE
             .
             Then
             measure
             the
             distance
             of
             AR
             ,
             and
             upon
             the
             Line
             GPB
             set
             it
             off
             from
             G
             to
             S
             ;
             and
             laying
             a
             straight
             Ruler
             to
             the
             point
             S
             and
             the
             Center
             A
             ,
             draw
             by
             the
             side
             of
             it
             the
             Line
             AS
             ;
             for
             the
             
               Substile
               Line
            
             .
             Then
             measure
             the
             length
             of
             QR
             ,
             and
             from
             S
             raise
             a
             Perpendicular
             ,
             and
             in
             that
             Perpendicular
             set
             that
             length
             off
             from
             S
             to
             T
             ;
             and
             laying
             a
             straight
             Ruler
             to
             the
             Center
             A
             and
             the
             point
             T
             ,
             draw
             the
             Line
             
             AT
             for
             the
             
               Stilar
               Line
            
             ,
             which
             
               Stilar
               Line
            
             being
             perpendicularly
             erected
             over
             the
             
               Substilar
               Line
            
             AS
             ,
             will
             stand
             parallel
             to
             the
             
               Axis
               of
               the
               World
            
             ,
             and
             cast
             its
             shaddow
             on
             the
             Hour
             of
             the
             Day
             .
          
           
           
             To
             draw
             the
             Hour
             Lines
             on
             this
             Plane
             ,
             you
             must
             (
             as
             you
             have
             several
             times
             before
             been
             directed
             )
             chuse
             a
             point
             in
             the
             
               Substilar
               Line
            
             ,
             and
             through
             that
             point
             draw
             at
             right
             Angles
             with
             the
             
               Substilar
               Line
            
             the
             
               Line
               of
               Contingence
            
             so
             long
             as
             you
             can
             :
             Then
             measure
             the
             shortest
             distance
             between
             that
             Point
             and
             the
             
               Stilar
               Line
            
             ,
             and
             transfer
             that
             distance
             below
             the
             
               Line
               of
               Contingence
            
             in
             the
             
               Substilar
               Line
            
             ,
             as
             at
             Ae
             ,
             and
             with
             your
             Compasses
             
             at
             that
             distance
             describe
             against
             the
             
               Line
               of
               Contingence
            
             the
             
               Equinoctial
               Circle
            
             ;
             Then
             divide
             the
             Semi-Circle
             of
             the
             Equinoctial
             next
             the
             Line
             of
             Contingence
             into
             twelve
             equal
             parts
             ,
             (
             as
             you
             have
             formerly
             been
             taught
             )
             beginning
             at
             the
             Point
             in
             the
             
               Equinoctial
               Circle
            
             ,
             where
             a
             straight
             Line
             drawn
             from
             the
             Center
             of
             it
             to
             the
             Intersection
             of
             the
             
               Line
               of
               Contingence
            
             with
             the
             Meridian
             Line
             NS
             cuts
             the
             
               Equinoctial
               Circle
            
             ,
             as
             here
             at
             the
             point
             D
             :
             Then
             lay
             a
             straight
             Ruler
             to
             the
             Center
             of
             the
             Equinoctial
             Circle
             ,
             and
             to
             every
             one
             of
             the
             Devisions
             in
             the
             Equinoctial
             Semi-Circle
             ,
             and
             mark
             where
             the
             straight
             Ruler
             cuts
             the
             
               Contingent
               Line
            
             :
             for
             straight
             Lines
             drawn
             from
             the
             Center
             A
             of
             the
             Dyal
             through
             these
             several
             marks
             in
             the
             
               Contingent
               Line
            
             shall
             be
             the
             Hour
             Lines
             ,
             and
             must
             be
             numbred
             from
             the
             Meridian
             or
             Noon-Line
             NS
             which
             is
             the
             XII
             a
             Clock
             Line
             upwards
             ,
             with
             XI
             ,
             X
             ,
             IX
             ,
             VIII
             ,
             &c.
             
             The
             Center
             of
             this
             Dyal
             must
             stand
             downward
             .
          
           
             If
             this
             Dyal
             were
             turned
             with
             its
             Center
             upwards
             ,
             it
             would
             shew
             a
             
               West
               Inclining
            
             45
             degrees
             ,
             only
             the
             numbers
             to
             the
             Hour
             Lines
             must
             be
             changed
             ;
             for
             to
             XI
             you
             must
             set
             I
             ,
             to
             X
             ,
             II
             ;
             to
             IX
             ,
             III
             ,
             &c.
             and
             the
             Substile
             over
             which
             the
             Stile
             must
             stand
             ,
             must
             be
             placed
             in
             the
             Semi-Circle
             (
             at
             first
             described
             )
             as
             much
             to
             the
             right
             hand
             the
             Perpendicular
             AE
             ,
             as
             it
             doth
             on
             the
             left
             hand
             .
          
           
             If
             this
             Dyal
             were
             drawn
             on
             Glass
             ,
             Horn
             ,
             or
             an
             oyled
             Paper
             ,
             and
             you
             turn
             the
             Meridian
             Line
             NS
             upwards
             ,
             the
             backside
             shall
             be
             an
             
               East
               Inclining
            
             45
             degrees
             ,
             and
             the
             Hour
             Lines
             must
             be
             numbred
             as
             they
             are
             on
             the
             
               East
               Reclining
            
             :
             But
             the
             Substile
             over
             which
             the
             Stile
             must
             stand
             ,
             must
             be
             placed
             ,
             in
             the
             Semi-Circle
             (
             at
             first
             described
             )
             as
             much
             to
             the
             left
             hand
             the
             Perpendicular
             AE
             ,
             as
             it
             is
             on
             the
             oyled
             Paper
             to
             the
             right
             hand
             .
          
           
           
             If
             you
             turn
             the
             Meridian
             Line
             NS
             downwards
             ,
             the
             backside
             shall
             be
             a
             
               West
               Recliner
            
             45
             degrees
             ,
             and
             the
             Hour
             Lines
             must
             be
             numbred
             from
             the
             XII
             a
             Clock
             Line
             upwards
             ,
             with
             I
             ,
             II
             ,
             III
             ,
             &c.
             
          
           
             You
             must
             note
             that
             all
             the
             Hour
             Lines
             of
             the
             Day
             will
             not
             be
             described
             in
             this
             single
             Quadrant
             ,
             nor
             does
             the
             Quadrant
             at
             all
             relate
             to
             the
             Hour
             Lines
             ;
             but
             is
             described
             onely
             for
             setting
             off
             the
             
               Complement
               of
               the
               Poles
               Elevation
            
             and
             Reclination
             of
             the
             Plane
             ,
             that
             by
             working
             (
             as
             hath
             been
             shewn
             )
             you
             may
             find
             the
             place
             of
             the
             
               Substilar
               Line
            
             ,
             and
             the
             Angle
             the
             Stile
             makes
             with
             it
             :
             For
             having
             the
             
               Substilar
               Line
            
             ,
             you
             know
             how
             to
             draw
             the
             
               Line
               of
               Contingence
            
             ,
             and
             to
             describe
             the
             
               Equinoctial
               Circle
            
             ,
             by
             which
             all
             the
             Hours
             are
             described
             on
             the
             Plane
             .
          
        
         
           
             To
             draw
             a
             Dyal
             on
             a
             
               Direct
               South
            
             or
             
               North
               Plane
               Inclining
            
             or
             Reclining
             .
          
           
             
               Direct
               Reclining
               or
               Inclining
            
             Dyals
             are
             the
             same
             with
             
               Erect
               Direct
            
             Dyals
             that
             are
             made
             for
             the
             Latitude
             of
             some
             other
             Places
             ;
             the
             Latitude
             of
             which
             Places
             are
             either
             more
             than
             the
             Latitude
             of
             your
             Place
             ,
             if
             the
             
               Plane
               Recline
            
             ;
             or
             less
             ,
             if
             the
             
               Plane
               Incline
            
             :
             and
             that
             in
             such
             a
             proportion
             as
             the
             Arch
             of
             Reclination
             or
             Inclination
             is
             .
          
           
             Thus
             a
             
               Direct
               South
            
             Dyal
             Reclining
             10
             degrees
             in
             
             London's
             Latitude
             ,
             (
             viz.
             51
             ½
             degrees
             )
             is
             an
             
               Erect
               Direct
               South
            
             Dyal
             made
             for
             the
             Latitude
             of
             61
             ½
             degrees
             .
             And
             a
             
               Direct
               South
            
             Dyal
             Inclining
             10
             in
             the
             Latitude
             of
             51
             ½
             is
             an
             
               Erect
               Direct
               South
            
             Dyal
             in
             the
             Latitude
             of
             41
             ½
             degrees
             :
             and
             is
             to
             be
             made
             according
             to
             the
             Direction
             given
             in
             Operat
             .
             III.
             
          
        
      
       
         
         
           OPERAT.
           IX
           .
           To
           draw
           a
           Dyal
           on
           a
           South
           or
           
             North
             Inclining
             Declining
          
           ,
           or
           
             Reclining
             Declining
             Plane
          
           .
        
         
           THese
           four
           sorts
           of
           Dyals
           viz.
           the
           
             South
             Inclining
             Declining
          
           ,
           and
           
             South
             Reclining
             Declining
          
           ,
           and
           
             North
             Inclining
             Declining
          
           ,
           and
           
             South
             Reclining
             Declining
          
           ,
           are
           all
           projected
           by
           the
           same
           Rules
           ;
           and
           therefore
           are
           in
           effect
           but
           one
           Dyal
           differently
           placed
           ,
           as
           you
           shall
           see
           hereafter
           .
        
         
           First
           draw
           on
           your
           Plane
           a
           straight
           Line
           parallel
           to
           the
           Horizon
           ,
           and
           mark
           one
           end
           W
           for
           West
           ,
           and
           the
           other
           E
           for
           East
           .
           On
           
             South
             Incliners
          
           and
           Recliners
           ,
           E
           on
           the
           right
           hand
           ,
           and
           W
           on
           the
           left
           :
           on
           
             North
             Incliners
          
           and
           Recliners
           E
           on
           the
           left
           hand
           and
           W
           on
           the
           right
           .
           Chuse
           a
           point
           in
           this
           Horizontal
           Line
           for
           a
           Center
           ,
           as
           at
           A
           ;
           Through
           this
           point
           A
           draw
           a
           Line
           Perpendicular
           to
           the
           Horizon
           ,
           and
           on
           this
           point
           (
           as
           on
           a
           Center
           )
           describe
           a
           Semi-Circle
           ,
           one
           Quadrant
           above
           ,
           and
           another
           below
           the
           Horizontal
           Line
           .
           (
           though
           for
           this
           Example
           I
           describe
           but
           one
           .
           )
           Then
           if
           the
           Plane
           respect
           the
           South
           ,
           set
           off
           in
           the
           lower
           Quadrant
           from
           the
           Perpendicular
           the
           Declination
           ,
           the
           Inclination
           ,
           or
           the
           Reclination
           ,
           and
           the
           Complement
           of
           the
           Altitude
           of
           the
           Pole
           ;
           and
           through
           these
           several
           settings
           off
           in
           the
           Quadrant
           ,
           draw
           straight
           Lines
           from
           the
           Center
           A
           ;
           then
           take
           in
           the
           Horizontal
           Line
           towards
           the
           Semi-Circle
           ,
           a
           convenient
           distance
           from
           the
           Center
           A
           ,
           as
           B
           ,
           and
           through
           the
           point
           B
           draw
           a
           straight
           Line
           parallel
           to
           the
           Perpendicular
           ,
           and
           prolong
           it
           through
           the
           Polar
           Line
           ,
           as
           BP
           :
           Through
           the
           point
           P
           ,
           draw
           a
           Line
           parallel
           to
           the
           Horizontal
           Line
           ,
           as
           PC
           ;
           this
           Line
           will
           cut
           the
           Line
           of
           Obliquity
           in
           the
           point
           O
           :
           Then
           measure
           the
           distance
           of
           AO
           ,
           and
           set
           
           off
           that
           distance
           on
           the
           Perpendicular
           from
           A
           to
           F
           ,
           and
           through
           the
           point
           F
           draw
           a
           straight
           Line
           parallel
           to
           the
           Horizontal
           Line
           ,
           as
           FG
           ,
           for
           the
           Horizontal
           Intersection
           .
           Then
           measure
           the
           distance
           of
           CO
           ,
           and
           set
           off
           that
           distance
           on
           the
           Perpendicular
           from
           A
           to
           I
           ;
           from
           the
           point
           I
           ,
           draw
           the
           Line
           ID
           parallel
           to
           the
           Horizontal
           Line
           ,
           to
           cut
           the
           Line
           of
           Declination
           in
           the
           point
           D.
           Then
           measure
           the
           distance
           of
           AB
           ,
           and
           set
           off
           that
           distance
           in
           the
           Line
           of
           Declination
           from
           A
           to
           E
           ;
           and
           from
           the
           point
           E
           draw
           a
           straight
           Line
           parallel
           to
           the
           Horizontal
           Line
           WE
           ,
           to
           cut
           the
           Perpendicular
           in
           the
           point
           K.
           Measure
           the
           distance
           of
           EK
           ,
           and
           set
           off
           that
           distance
           on
           the
           other
           side
           the
           Perpendicular
           in
           the
           Horizontal
           Intersection
           ,
           from
           F
           to
           H
           ,
           and
           from
           the
           point
           H
           draw
           HN
           parallel
           to
           the
           Perpendicular
           to
           cut
           the
           Horizontal
           Line
           in
           the
           point
           N.
           
        
         
         
           Then
           to
           find
           the
           Meridian
           Line
           ,
           Substile
           and
           Stile
           ,
           do
           thus
           .
           If
           your
           Plane
           be
           a
           
             Southern
             Incliner
          
           ,
           or
           a
           
             Northern
             Recliner
          
           ,
           measure
           the
           distance
           of
           LD
           ,
           and
           set
           off
           
           that
           distance
           in
           the
           Horizontal
           Intersection
           from
           F
           to
           M
           ,
           and
           through
           the
           point
           M
           draw
           the
           Line
           AM
           for
           the
           Meridian
           Line
           .
           Then
           add
           the
           distance
           of
           AL
           to
           AK
           ,
           thus
           :
           measure
           the
           distance
           of
           AL
           ,
           and
           place
           one
           Foot
           of
           your
           Compasses
           in
           the
           point
           K
           in
           the
           Perpendicular
           Line
           ,
           and
           extend
           the
           other
           to
           X
           ,
           and
           measuring
           the
           distance
           of
           AX
           ,
           set
           it
           off
           in
           the
           Line
           of
           Obliquity
           from
           A
           to
           Q
           ;
           and
           from
           the
           point
           Q
           draw
           the
           Line
           QR
           parallel
           to
           the
           Perpendicular
           ,
           and
           cutting
           the
           Horizontal
           Line
           in
           the
           point
           R.
           Then
           measure
           the
           distance
           of
           AR
           ,
           and
           set
           off
           that
           distance
           from
           H
           in
           the
           Horizontal
           Intersection
           to
           S
           on
           the
           Line
           HN
           ,
           and
           to
           the
           point
           S
           draw
           the
           Line
           AS
           for
           the
           Substile
           .
           Then
           measure
           the
           distance
           of
           QR
           ,
           and
           set
           off
           that
           distance
           perpendicularly
           from
           the
           point
           S
           to
           T
           ;
           and
           lastly
           ,
           from
           the
           point
           A
           ,
           draw
           the
           straight
           Line
           AT
           for
           the
           Stilar
           Line
           ,
           which
           Stilar
           Line
           being
           perpendicularly
           erected
           over
           the
           Substilar
           Line
           AS
           ,
           will
           stand
           parallel
           to
           the
           
             Axis
             of
             the
             World
          
           ,
           and
           cast
           its
           shadow
           on
           the
           Hour
           of
           the
           Day
           .
        
         
           But
           if
           the
           Plane
           be
           a
           
             Southern
             Recliner
          
           ,
           or
           
             Northern
             Incliner
          
           ,
           measure
           (
           as
           before
           )
           the
           distance
           of
           LD
           ,
           and
           (
           as
           before
           you
           were
           directed
           )
           to
           set
           it
           off
           from
           F
           in
           the
           Horizontal
           Intersection
           on
           the
           right
           hand
           the
           perpendicular
           Line
           ;
           So
           now
           ,
           set
           that
           distance
           from
           F
           to
           m
           in
           the
           Horizontal
           Intersection
           on
           the
           left
           hand
           in
           the
           Perpendicular
           Line
           ,
           and
           draw
           the
           Line
           A
           m
           for
           the
           Meridian
           Line
           .
           Then
           as
           before
           you
           were
           directed
           to
           add
           AL
           to
           AK
           :
           So
           now
           ,
           substract
           the
           distance
           of
           AL
           from
           AK
           ,
           and
           the
           remainder
           will
           be
           LK
           :
           Set
           therefore
           the
           distance
           of
           IK
           from
           A
           to
           q
           in
           the
           same
           Line
           of
           Obliquity
           ,
           and
           from
           the
           point
           q
           ,
           draw
           the
           Line
           qr
           parallel
           to
           the
           perpendicular
           .
           Measure
           then
           the
           distance
           of
           A
           r
           ,
           and
           set
           off
           that
           distance
           in
           the
           Line
           HN
           ,
           from
           H
           to
           s
           for
           the
           Substilar
           
           Line
           :
           Then
           erect
           on
           the
           point
           s
           a
           Perpendicular
           ,
           and
           on
           that
           Perpendicular
           set
           off
           from
           s
           to
           t
           the
           distance
           of
           qr
           :
           And
           lastly
           ,
           from
           A
           draw
           the
           Line
           A
           t
           for
           the
           
             Stilar
             Line
          
           .
        
         
           If
           K
           falls
           upon
           L
           the
           Plane
           is
           parallel
           to
           the
           Axis
           of
           the
           World
           ,
           and
           the
           Dyal
           drawn
           upon
           it
           will
           have
           no
           Center
           :
           But
           s
           will
           fall
           upon
           H
           ,
           and
           AH
           (
           or
           A
           s
           )
           will
           be
           the
           Substile
           .
        
         
           I
           shall
           give
           you
           two
           Examples
           of
           these
           Rules
           :
           One
           of
           a
           Dyal
           with
           a
           Center
           ,
           and
           the
           other
           of
           a
           Dyal
           without
           a
           Center
           .
           And
           first
           ,
        
      
       
         
           OPERAT.
           X.
           How
           to
           draw
           a
           Dyal
           with
           a
           Center
           ,
           
             Declining
             20
          
           Degrees
           ,
           and
           
             Inclining
             30
          
           Degrees
           .
        
         
           
        
         
           HAving
           by
           the
           foregoing
           Precepts
           of
           the
           last
           Operat
           .
           found
           the
           
             Substile
             ,
             Stile
          
           ,
           and
           Meridian
           ,
           you
           must
           (
           as
           
           you
           have
           often
           been
           directed
           )
           chuse
           a
           point
           in
           the
           Substilar
           Line
           ,
           through
           which
           ,
           at
           right
           Angles
           to
           the
           Substilar
           Line
           draw
           the
           Line
           of
           Contingence
           as
           long
           as
           you
           can
           :
           Then
           measure
           the
           shortest
           distance
           between
           the
           point
           of
           Intersection
           and
           the
           Stilar
           Line
           ,
           and
           transfer
           that
           distance
           on
           one
           side
           the
           Line
           of
           Contingence
           upon
           the
           
             Substilar
             Line
          
           ,
           and
           so
           describe
           the
           Equinoctial
           Semi-Circle
           against
           the
           Line
           of
           Contingence
           :
           Then
           lay
           a
           straight
           Ruler
           to
           the
           Center
           of
           the
           Equinoctial
           Circle
           ,
           as
           at
           Ae
           ,
           and
           to
           the
           point
           where
           the
           Line
           of
           Contingence
           cuts
           the
           Meridian
           Line
           ,
           as
           at
           Z
           ,
           and
           mark
           where
           the
           straight
           Ruler
           cuts
           the
           
             Equinoctial
             Circle
          
           ,
           and
           from
           that
           mark
           begin
           to
           devide
           the
           Semi-Circle
           into
           twelve
           equal
           parts
           ,
           and
           by
           a
           straight
           Ruler
           laid
           to
           those
           devisions
           and
           the
           Center
           of
           the
           Equinoctial
           ,
           make
           marks
           in
           the
           Line
           of
           Contingence
           .
           Then
           shall
           straight
           Lines
           drawn
           from
           the
           Center
           A
           of
           the
           Dyal
           through
           every
           one
           of
           those
           marks
           in
           the
           
             Contingent
             Line
          
           be
           the
           Hour
           Lines
           of
           the
           Dyal
           ,
           and
           must
           be
           numbred
           from
           the
           XII
           a
           Clock
           Line
           towards
           the
           right
           Hand
           with
           I
           ,
           II
           ,
           III
           ,
           IV
           ,
           &c.
           
           And
           the
           other
           way
           with
           XI
           ,
           X
           ,
           IX
           ,
           &c.
           
        
      
       
         
           OPERAT.
           XI
           .
           How
           to
           draw
           a
           Dyal
           without
           a
           Center
           ,
           on
           a
           
             South
             Plane
             ;
             Declining
             East
             30
          
           Degrees
           ,
           
             Reclining
             34
          
           Degrees
           32
           Minutes
           .
        
         
           HAving
           by
           the
           Precepts
           of
           Operat
           .
           IX
           found
           the
           Substile
           ,
           you
           must
           find
           the
           Meridian
           Line
           otherwise
           than
           you
           were
           there
           taught
           :
           For
           ,
           having
           drawn
           the
           Lines
           of
           
             Latitude
             ,
             Declination
          
           and
           Reclination
           ,
           and
           found
           the
           Substile
           ,
           measure
           the
           distance
           of
           BP
           ,
           and
           set
           it
           off
           on
           the
           Line
           of
           Declination
           from
           A
           to
           K
           ,
           and
           draw
           from
           the
           
           Perpendicular
           AF
           the
           Line
           KQ
           parallel
           to
           AB
           :
           Then
           measure
           the
           length
           of
           KQ
           ,
           and
           set
           it
           off
           on
           the
           
             Polar
             Line
          
           AP
           ,
           from
           A
           to
           V
           ;
           then
           take
           the
           nearest
           distance
           between
           the
           point
           V
           and
           the
           Line
           AB
           ,
           and
           set
           it
           off
           on
           the
           Line
           QK
           from
           Q
           to
           M
           ;
           through
           which
           point
           M
           ,
           draw
           a
           Line
           from
           the
           Center
           A
           :
           Then
           measure
           with
           your
           Compasses
           in
           the
           Semi-Circle
           WNE
           (
           which
           in
           this
           Dyal
           may
           represent
           the
           Equinoctial
           )
           the
           distance
           of
           the
           Arch
           N
           m
           ,
           and
           set
           off
           that
           distance
           from
           the
           Intersection
           of
           the
           Substile
           with
           the
           Semi-Circle
           at
           S
           to
           T
           in
           the
           Semi-Circle
           ,
           which
           point
           T
           shall
           be
           the
           point
           in
           the
           Equinoctial
           that
           you
           must
           begin
           to
           devide
           the
           Hours
           at
           ,
           for
           the
           finding
           their
           distances
           on
           the
           
             Line
             of
             Contingence
          
           .
        
         
         
           Then
           consider
           (
           according
           to
           the
           bigness
           of
           your
           Plane
           )
           what
           heighth
           your
           Stile
           shall
           stand
           above
           the
           Substile
           ,
           and
           there
           make
           a
           mark
           in
           the
           Substile
           :
           For
           the
           distance
           between
           the
           Center
           A
           and
           that
           mark
           must
           
           be
           the
           heighth
           of
           the
           Stile
           perpendicularly
           erected
           over
           the
           Substile
           ,
           as
           at
           I.
           Draw
           through
           this
           point
           I
           a
           Line
           of
           Contingence
           ,
           as
           long
           as
           you
           can
           to
           cut
           the
           Substile
           at
           right
           Angles
           ,
           and
           then
           laying
           a
           Ruler
           to
           the
           Center
           A
           ,
           and
           successively
           to
           each
           Devision
           of
           the
           Equinoctial
           make
           marks
           in
           the
           Line
           of
           Contingence
           ,
           and
           through
           those
           marks
           draw
           straight
           Lines
           parallel
           to
           the
           Substile
           ,
           which
           shall
           be
           the
           
             Hour
             Lines
          
           ;
           and
           must
           be
           numbred
           from
           the
           left
           hand
           towards
           the
           right
           ,
           beginning
           at
           the
           XII
           a
           Clock
           Line
           with
           I
           ,
           II
           ,
           III
           ,
           &c.
           and
           from
           the
           right
           hand
           towards
           the
           left
           on
           the
           XII
           a
           Clock
           Line
           with
           XI
           ,
           X
           ,
           IX
           ,
           &c.
           
        
         
           The
           Stile
           to
           this
           Dyal
           may
           be
           either
           a
           straight
           Pin
           of
           the
           length
           of
           AI
           ,
           or
           else
           a
           Square
           of
           the
           same
           heighth
           ,
           erected
           perpendicularly
           upon
           the
           point
           I
           ,
           in
           the
           Substile
           Line
           .
        
      
       
         
           OPERAT.
           XII
           .
           To
           make
           a
           Dyal
           on
           the
           Ceeling
           of
           a
           Room
           ,
           where
           the
           
             Direct
             Beams
          
           of
           the
           Sun
           never
           come
           .
        
         
           FInd
           some
           convenient
           place
           in
           the
           Transum
           of
           a
           Window
           to
           place
           a
           small
           round
           piece
           of
           Looking-Glass
           ,
           about
           the
           bigness
           of
           a
           Groat
           ,
           or
           less
           ,
           so
           as
           it
           may
           lie
           exactly
           Horizontal
           .
           The
           point
           in
           the
           middle
           of
           this
           Glass
           we
           will
           mark
           A
           ,
           and
           for
           distinction
           sake
           call
           it
           Nodus
           .
           Through
           this
           Nodus
           you
           must
           draw
           a
           Meridian
           Line
           on
           the
           Floor
           ,
           Thus
           ,
           Hang
           a
           Plumb-line
           in
           the
           Window
           exactly
           over
           Nodus
           ,
           and
           the
           Shadow
           that
           the
           Plumb-line
           casts
           on
           the
           Floor
           just
           at
           Noon
           will
           be
           a
           Meridian
           Line
           ;
           or
           you
           may
           find
           a
           Meridian
           Line
           otherwise
           by
           the
           Clinatory
           .
           Having
           drawn
           the
           Meridan
           Line
           on
           the
           Floor
           ,
           find
           a
           Meridian
           Line
           on
           the
           Ceeling
           ,
           
           thus
           ,
           Hold
           a
           Plumb-line
           to
           the
           Ceeling
           ,
           over
           that
           end
           of
           the
           Meridian
           Line
           next
           the
           Window
           ;
           If
           the
           Plumbet
           hang
           not
           exactly
           on
           the
           Meridian
           Line
           on
           the
           Floor
           ,
           remove
           your
           hand
           on
           the
           Ceeling
           one
           way
           or
           other
           ,
           as
           you
           see
           cause
           ,
           till
           it
           do
           hang
           quietly
           just
           over
           it
           ,
           and
           at
           the
           point
           where
           the
           Plumb-line
           touches
           the
           Ceeling
           make
           a
           mark
           ,
           as
           at
           B
           ;
           that
           mark
           B
           shall
           be
           directly
           over
           the
           Meridian
           Line
           on
           the
           Floor
           :
           then
           remove
           your
           Plumb-line
           to
           the
           other
           end
           of
           the
           Meridian
           Line
           on
           the
           Floor
           ,
           and
           find
           a
           point
           on
           the
           Ceeling
           directly
           over
           it
           ,
           as
           you
           did
           the
           former
           point
           ,
           as
           at
           C
           ,
           and
           through
           these
           two
           points
           B
           and
           C
           on
           the
           Ceeling
           ,
           strain
           and
           strike
           a
           Line
           blackt
           with
           Smal-Coal
           or
           any
           other
           Colour
           (
           as
           Carpenters
           do
           )
           and
           that
           Line
           BC
           on
           the
           Ceeling
           shall
           be
           the
           Meridian
           Line
           ,
           as
           well
           as
           that
           on
           the
           Floor
           :
           Then
           fasten
           a
           string
           just
           on
           the
           Nodus
           ,
           and
           remove
           that
           string
           ,
           forwards
           or
           backwards
           ,
           in
           the
           Meridian
           Line
           on
           the
           Ceeling
           ,
           till
           it
           have
           the
           same
           Elevation
           in
           the
           Quadrant
           on
           the
           Clinatory
           above
           the
           Horizon
           that
           the
           Equinoctial
           hath
           in
           your
           Habitation
           ,
           and
           through
           the
           point
           where
           the
           string
           touches
           the
           Meridian
           Line
           in
           the
           Ceeling
           shall
           a
           line
           be
           drawn
           at
           right
           Angles
           with
           the
           Meridian
           ,
           to
           represent
           the
           Equinoctial
           Line
           .
        
         
           Thus
           in
           our
           Latitude
           the
           Elevation
           of
           the
           Equator
           being
           38
           ½
           degrees
           ;
           I
           remove
           the
           string
           fastned
           to
           the
           Nodus
           forwards
           or
           backwards
           in
           the
           Meridian
           Line
           of
           the
           Ceeling
           ,
           till
           the
           Plumb-line
           of
           the
           Quadrant
           on
           the
           Clinatory
           ,
           when
           one
           of
           the
           sides
           are
           applied
           to
           the
           string
           ,
           falls
           upon
           38
           ½
           degrees
           :
           and
           then
           I
           find
           it
           touch
           the
           Meridian
           Line
           at
           D
           in
           the
           Ceeling
           :
           therefore
           at
           DI
           make
           a
           mark
           ,
           and
           through
           this
           mark
           strike
           the
           line
           DE
           (
           as
           before
           I
           did
           in
           the
           Meridian
           Line
           )
           to
           cut
           the
           Meridian
           Line
           at
           right
           Angles
           :
           This
           Line
           shall
           be
           the
           Equinoctial
           Line
           ,
           and
           serve
           to
           denote
           the
           Hour
           Distances
           ,
           as
           the
           
           Contingent
           Line
           does
           on
           other
           Dyals
           ,
           as
           you
           have
           often
           seen·
        
         
           Then
           I
           place
           the
           Center
           of
           the
           Quadrant
           on
           the
           Clinatory
           upon
           Nodus
           ,
           so
           as
           the
           Arch
           of
           the
           Quadrant
           may
           be
           on
           the
           East
           side
           the
           Meridian
           Line
           ,
           and
           underprop
           it
           so
           ,
           that
           the
           flat
           side
           of
           the
           Quadrant
           may
           lie
           parallel
           to
           the
           string
           ,
           when
           it
           is
           strained
           between
           the
           Nodus
           and
           the
           Equinoctial
           ,
           and
           also
           so
           as
           the
           string
           may
           lie
           on
           the
           Semi-diameter
           of
           the
           Quadrant
           ,
           when
           it
           is
           held
           up
           to
           the
           Meridian
           Line
           on
           the
           Ceeling
           .
           Then
           removing
           the
           string
           the
           space
           of
           15
           degrees
           in
           the
           Quadrant
           ,
           and
           extending
           it
           to
           the
           Equator
           on
           the
           Ceeling
           ,
           where
           the
           string
           touches
           the
           Equator
           ,
           there
           shall
           be
           a
           point
           through
           which
           the
           I
           a
           Clock
           Hour
           line
           shall
           be
           drawn
           :
           and
           removing
           the
           string
           yet
           15
           degrees
           further
           to
           the
           Eastwards
           in
           the
           Semi-Circle
           of
           Position
           ,
           and
           extending
           it
           also
           to
           the
           Equator
           ,
           where
           it
           touches
           the
           Equator
           ,
           there
           shall
           be
           a
           point
           through
           which
           the
           II
           a
           Clock
           Hour
           Line
           shall
           be
           drawn
           .
           Removing
           the
           string
           yet
           15
           degrees
           f●rther
           ,
           to
           the
           Eastwards
           in
           the
           Semi-Circle
           of
           Position
           ,
           and
           extending
           it
           to
           the
           Equator
           ,
           there
           shall
           be
           a
           point
           through
           which
           the
           III
           a
           Clock
           Hour
           Line
           shall
           be
           drawn
           :
           The
           like
           for
           all
           the
           other
           After-noon
           Hour
           Lines
           .
           So
           oft
           as
           the
           string
           is
           removed
           through
           15
           degrees
           on
           the
           Quadrant
           ,
           so
           oft
           shall
           it
           point
           out
           the
           After-Noon
           distances
           in
           the
           
             Meridian
             Line
          
           on
           the
           Ceeling
           .
        
         
           Having
           thus
           found
           out
           the
           points
           in
           the
           Equator
           through
           which
           the
           After-noon
           Hour
           Lines
           are
           to
           be
           drawn
           ,
           I
           may
           find
           the
           Fore-noon
           Hour
           distances
           also
           the
           same
           way
           ,
           viz.
           by
           removing
           the
           Arch
           of
           the
           Quadrant
           to
           the
           West
           side
           the
           Meridian
           ,
           as
           before
           it
           was
           placed
           on
           the
           East
           ,
           and
           bringing
           the
           string
           to
           the
           several
           15
           degrees
           on
           the
           West
           side
           the
           Quadrant
           ;
           or
           else
           I
           need
           only
           measure
           the
           distances
           of
           each
           Hours
           distance
           
           found
           in
           the
           Equator
           from
           the
           Meridian
           Line
           on
           the
           Ceeling
           ;
           for
           the
           same
           number
           of
           Hours
           from
           XII
           ,
           have
           the
           same
           distance
           in
           the
           Equinoctial
           Line
           on
           the
           other
           side
           the
           Meridian
           ,
           both
           before
           and
           after-noon
           :
           The
           XI
           a
           Clock
           Hour
           distance
           is
           the
           same
           from
           the
           Meridian
           Line
           ,
           with
           the
           I
           a
           Clock
           distance
           on
           the
           other
           side
           the
           Meridian
           ;
           the
           X
           a
           Clock
           distance
           ,
           the
           same
           with
           the
           II
           a
           Clock
           distance
           ;
           the
           IX
           with
           the
           III
           ,
           &c.
           
           And
           thus
           the
           distances
           of
           all
           the
           Hour
           lines
           are
           found
           out
           on
           the
           Equator
           .
        
         
         
         
           Now
           if
           the
           Center
           of
           this
           Dyal
           lay
           within
           doors
           ,
           you
           might
           draw
           lines
           from
           the
           Center
           through
           these
           pricks
           in
           the
           Equator
           ,
           and
           those
           Lines
           should
           be
           the
           Hour
           lines
           ,
           as
           in
           other
           Dyals
           :
           But
           the
           Center
           of
           this
           Dyal
           lies
           without
           doors
           in
           the
           Air
           ,
           and
           therefore
           not
           convenient
           for
           this
           purpose
           :
           So
           that
           for
           drawing
           the
           Hour
           Lines
           ,
           you
           must
           consider
           what
           Angle
           every
           Hour
           Line
           in
           an
           
             Horizontal
             Dyal
          
           makes
           with
           the
           Meridian
           ;
           that
           is
           ,
           at
           what
           distance
           in
           Degrees
           and
           Minutes
           the
           Hour
           Lines
           of
           an
           
             Horizontal
             Dyal
          
           cut
           the
           Meridian
           ;
           which
           you
           may
           examine
           ,
           as
           by
           Operat
           .
           II.
           For
           an
           Angle
           equal
           to
           the
           Complement
           of
           the
           same
           Angle
           ,
           must
           each
           respective
           Hour
           Line
           with
           the
           Equator
           on
           the
           Ceeling
           have
           .
        
         
           Thus
           upon
           the
           point
           markt
           for
           each
           Hour
           distance
           in
           the
           Equinoctial
           Line
           on
           the
           Ceeling
           ,
           I
           describe
           the
           Arches
           I
           ,
           II
           ,
           III
           ,
           IV
           ,
           as
           in
           the
           Figure
           ,
           and
           finding
           the
           distance
           from
           the
           Meridian
           of
           the
           Hour
           Lines
           of
           an
           
             Horizontal
             Dyal
          
           to
           be
           according
           to
           the
           Operat
           .
           II.
           Thus
           ,
           
             
               The
               1
               a
               clock
               Hour
               line
               11.40
               whose
               Complement
               to
               90
               is
               78.20
            
             
               The
               2
               a
               clock
               Hour
               line
               24.15
               whose
               Complement
               to
               90
               is
               65.45
            
             
               The
               3
               a
               clock
               Hour
               line
               38.14
               whose
               Complement
               to
               90
               is
               51.56
            
             
               The
               4
               a
               clock
               Hour
               line
               53.36
               whose
               Complement
               to
               90
               is
               36.24
            
          
        
         
           I
           measure
           in
           a
           Quadrant
           of
           the
           same
           Radius
           with
           those
           Arches
           already
           drawn
           from
           the
           
             Equinoctial
             Line
          
           
             
               for
               the
               1
               a
               Clock
               Hour
               78.20
            
             
               for
               the
               2
               a
               Clock
               Hour
               65.45
            
             
               for
               the
               3
               a
               Clock
               Hour
               51.56
            
             
               for
               the
               4
               a
               Clock
               Hour
               36.24
            
          
           and
           transfer
           these
           distances
           to
           the
           Arches
           drawn
           on
           the
           Ceeling
           :
           For
           then
           straight
           Lines
           drawn
           through
           the
           
           mark
           in
           the
           Arch
           ,
           and
           through
           the
           mark
           in
           the
           Equator
           ,
           and
           prolonged
           both
           ways
           to
           a
           convenient
           length
           ,
           shall
           be
           the
           several
           Hour
           Lines
           (
           aforesaid
           ;
           )
           And
           when
           the
           Sun
           shines
           upon
           the
           Glass
           at
           Nodus
           ,
           its
           Beams
           shall
           reflect
           upon
           the
           Hour
           of
           the
           Day
           .
        
      
       
         
           Some
           helps
           to
           a
           young
           Dyalist
           for
           his
           more
           orderly
           and
           quick
           making
           of
           Dyals
           .
        
         
           IT
           may
           prove
           somewhat
           difficult
           to
           those
           that
           are
           unpractised
           in
           Mathematical
           Projections
           ,
           to
           devide
           a
           Circle
           into
           360
           Degrees
           (
           or
           which
           is
           all
           one
           )
           a
           Semi-Circle
           into
           180
           ,
           or
           a
           Quadrant
           into
           90
           degrees
           ;
           and
           though
           I
           have
           taught
           you
           in
           the
           projecting
           the
           
             Horizontal
             Dyal
          
           the
           original
           way
           of
           doing
           this
           ,
           yet
           you
           may
           do
           it
           a
           speedier
           way
           by
           a
           Line
           of
           Chords
           ,
           which
           if
           you
           will
           be
           curious
           in
           your
           Practise
           ,
           you
           may
           make
           your self
           ;
           or
           if
           you
           account
           it
           not
           worth
           your
           while
           ,
           you
           may
           buy
           it
           already
           made
           on
           Box
           or
           Brass
           of
           most
           Mathematical
           Instrument-Makers
           .
           This
           Instrument
           is
           by
           them
           called
           a
           
             Plain
             Scale
          
           ,
           which
           does
           not
           only
           accommodate
           you
           with
           the
           devisions
           of
           a
           Quadrant
           ,
           but
           also
           serves
           for
           a
           Ruler
           to
           draw
           straight
           Lines
           with
           :
           the
           manner
           of
           making
           it
           is
           as
           follows
           .
        
         
           Describe
           upon
           a
           smooth
           flat
           even-grain'd
           Board
           a
           quarter
           of
           an
           whole
           Circle
           ,
           as
           BC
           ,
           whose
           Radius
           AB
           or
           AC
           may
           be
           four
           inches
           ,
           if
           you
           intend
           to
           make
           large
           Dyals
           ,
           or
           two
           inches
           if
           small
           ;
           but
           if
           you
           will
           ,
           you
           may
           have
           several
           Lines
           of
           Chords
           on
           your
           Scale
           or
           Rule
           .
           Devide
           this
           Quadrant
           into
           90
           equal
           parts
           as
           you
           were
           taught
           in
           the
           making
           the
           
             Horizontal
             Dyal
          
           .
        
         
         
           Then
           draw
           close
           by
           the
           edge
           of
           your
           straight
           Ruler
           a
           Line
           parallel
           to
           the
           edge
           ,
           and
           at
           about
           1
           /
           20
           part
           of
           an
           Inch
           a
           second
           Line
           parallel
           to
           that
           ,
           and
           at
           about
           ⅛
           of
           an
           Inch
           a
           third
           Line
           parallel
           to
           both
           .
           Then
           place
           one
           Foot
           of
           your
           Compasses
           at
           the
           beginning
           of
           the
           first
           degree
           on
           the
           Quadrant
           descibed
           on
           the
           Board
           ,
           as
           at
           B
           ,
           and
           open
           the
           other
           Foot
           to
           the
           end
           of
           the
           first
           degree
           ,
           and
           transfer
           that
           distance
           upon
           your
           Rule
           ,
           from
           B
           to
           the
           first
           mark
           or
           devision
           ,
           between
           the
           two
           first
           drawn
           Lines
           .
           Then
           place
           one
           Foot
           of
           your
           Compasses
           again
           at
           the
           begining
           of
           the
           first
           degree
           on
           the
           Quadrant
           described
           on
           the
           Board
           ,
           as
           at
           B
           ,
           and
           open
           the
           other
           Foot
           to
           the
           end
           of
           the
           second
           Degree
           ,
           and
           transfer
           that
           distance
           upon
           your
           Rule
           from
           B
           to
           the
           second
           mark
           or
           devision
           between
           the
           two
           first
           drawn
           Lines
           ;
           And
           thus
           measure
           the
           distance
           of
           every
           Degree
           from
           the
           first
           Degree
           described
           on
           the
           Quadrant
           ,
           and
           transfer
           it
           to
           the
           Rule
           .
           But
           for
           distinction
           sake
           ,
           you
           may
           draw
           every
           tenth
           devision
           from
           the
           first
           Line
           parallel
           
           to
           the
           edge
           of
           the
           third
           Line
           ,
           and
           mark
           them
           in
           succession
           from
           the
           beginning
           with
           10
           ,
           20
           ,
           30
           ,
           to
           90
           :
           and
           the
           fifth
           Devisions
           you
           may
           draw
           half
           way
           between
           the
           second
           and
           the
           third
           parallel
           Lines
           ;
           the
           single
           Devisions
           only
           between
           the
           two
           first
           parallel
           Lines
           .
           So
           is
           your
           Line
           of
           Chords
           made
           .
        
      
       
         
           The
           Vse
           of
           the
           Line
           of
           Chords
           .
        
         
           AS
           its
           use
           is
           very
           easie
           ,
           so
           its
           convenience
           is
           very
           great
           ;
           for
           placing
           one
           Foot
           of
           your
           Compasses
           at
           the
           first
           Devision
           on
           the
           Scale
           ,
           and
           opening
           the
           other
           to
           the
           60
           th
           Degree
           ,
           you
           may
           with
           the
           points
           of
           your
           Compasses
           (
           so
           extended
           )
           describe
           a
           Circle
           ,
           and
           the
           several
           Devisions
           ,
           on
           the
           Scale
           shall
           be
           the
           Degrees
           of
           the
           four
           Quadrants
           of
           that
           Circle
           ,
           as
           you
           may
           try
           by
           working
           backwards
           ,
           to
           what
           you
           were
           just
           now
           taught
           in
           the
           Making
           the
           Scale
           :
           For
           as
           before
           you
           measured
           the
           distance
           of
           the
           Degrees
           of
           the
           Quadrant
           ,
           and
           transferr'd
           them
           to
           the
           Scale
           ,
           so
           now
           you
           only
           measure
           the
           D●visions
           on
           the
           Scale
           ,
           and
           transfer
           them
           to
           the
           Quadrant
           ,
           Semi-Circle
           ,
           or
           whole
           Circle
           described
           on
           your
           Paper
           .
           For
           Example
           :
        
         
           If
           you
           would
           measure
           30
           Degrees
           in
           your
           described
           Circle
           ,
           place
           one
           Foot
           of
           your
           Compasses
           at
           the
           begining
           of
           Devisions
           on
           the
           Scale
           ,
           as
           at
           A
           ,
           and
           extend
           the
           other
           Foot
           to
           the
           Divisions
           marked
           30
           ,
           and
           that
           distance
           transferred
           to
           the
           Circle
           ,
           shall
           be
           the
           distance
           of
           30
           degrees
           in
           that
           Circle
           .
           Do
           the
           like
           for
           any
           other
           number
           of
           Degrees
           .
        
         
           You
           may
           draw
           your
           Dyal
           first
           on
           a
           large
           sheet
           of
           Paper
           ,
           if
           your
           Dyal
           Plane
           be
           so
           large
           ,
           if
           it
           be
           not
           so
           large
           ,
           draw
           it
           on
           a
           smaller
           piece
           of
           Paper
           ;
           Then
           rub
           the
           back-side
           of
           your
           Paper-Dyal
           with
           Smal-coal
           ,
           till
           it
           
           be
           well
           black't
           ;
           and
           laying
           your
           Paper
           Dyal
           on
           your
           Dyal
           Plane
           ,
           so
           that
           the
           East
           ,
           West
           ,
           North
           ,
           or
           South
           Lines
           of
           your
           Paper
           agree
           exactly
           with
           the
           East
           ,
           West
           ,
           North
           ,
           or
           South
           scituation
           of
           your
           Dyal
           Plane
           .
           Then
           with
           Wax
           or
           Pitch
           fasten
           the
           Corners
           of
           the
           Paper
           on
           the
           Plane
           ,
           and
           laying
           a
           straight
           Ruler
           on
           the
           Hour-Lines
           of
           your
           Dyal
           ,
           draw
           with
           the
           blunted
           point
           of
           a
           Needle
           by
           the
           side
           of
           the
           Ruler
           ,
           and
           the
           Smal-coal
           rub'd
           on
           the
           back-side
           the
           Paper
           will
           leave
           a
           mark
           of
           the
           Lines
           on
           the
           Plane
           .
        
         
           If
           you
           will
           have
           the
           Lines
           drawn
           Red
           ,
           you
           may
           rub
           the
           back-side
           of
           your
           Paper
           with
           Vermillion
           ;
           if
           Blew
           ,
           with
           Verditer
           ;
           if
           Yellow
           ,
           with
           Orpment
           ,
           &c.
           
           Then
           draw
           upon
           these
           marked
           Lines
           with
           Oyl
           Colours
           ,
           as
           you
           please
           .
        
         
      
       
         
         
           An
           Explanation
           of
           some
           Words
           of
           Art
           used
           in
           this
           BOOK
           .
        
         
           ANgle
           .
           The
           meeting
           or
           joyning
           of
           two
           Lines
           .
        
         
           Arch.
           A
           part
           of
           a
           Circle
           .
        
         
           Axis
           .
           The
           straight
           Line
           that
           runs
           through
           the
           Center
           of
           a
           Sphere
           ,
           and
           both
           ways
           through
           the
           Circumference
           :
           though
           in
           Dyalling
           it
           is
           all
           one
           with
           the
           Diameter
           of
           a
           Circle
           .
        
         
           Clinatory
           .
           See
           Fol.
           8
           ,
           9
           ,
           10.
           
        
         
           Chord
           .
           See
           Fol.
           44
           ,
           45
           ,
           46.
           
        
         
           Complement
           .
           The
           number
           that
           is
           wanting
           to
           make
           up
           another
           number
           90
           Degr.
           or
           180
           Degr.
           or
           360
           Degrees
           .
        
         
           Contingent
           .
           A
           Line
           crossing
           the
           Substile
           at
           right
           Angles
           .
        
         
           Degree
           .
           See
           Fol.
           12.
           
        
         
           Diameter
           .
           The
           longest
           straight
           Line
           that
           can
           be
           contained
           within
           a
           Circle
           ,
           viz.
           the
           Line
           that
           passes
           through
           the
           Center
           to
           the
           Circumference
           both
           ways
           .
        
         
           
             Dyal
             Plane
          
           .
           See
           Fol.
           7.
           
        
         
           Elevation
           of
           the
           Pole.
           So
           many
           degrees
           as
           the
           Pole
           is
           elevated
           above
           the
           Horizon
           .
        
         
           Equinoctial
           .
           The
           Equinoctial
           is
           a
           great
           Circle
           that
           runs
           evenly
           between
           the
           two
           Poles
           of
           the
           World.
           But
           when
           we
           name
           the
           Equinoctial
           in
           this
           Book
           ,
           we
           mean
           a
           small
           Circle
           which
           represents
           it
           ,
           and
           is
           the
           Circle
           or
           Arch
           of
           a
           Circle
           which
           is
           divided
           into
           equal
           parts
           to
           find
           thereby
           the
           unequal
           parts
           on
           the
           
             Line
             of
             Contingence
          
           .
           In
           the
           
             Horizontal
             Dyal
          
           it
           is
           that
           Arch
           of
           a
           Circle
           marked
           GCH
           .
        
         
           Horizon
           .
           Is
           a
           great
           Circle
           encompassing
           the
           place
           we
           stand
           upon
           ;
           but
           in
           Dyalling
           it
           is
           represented
           by
           a
           straight
           Line
           ,
           as
           in
           Operat
           .
           III.
           In
           the
           
             South
             Dyal
          
           the
           Line
           VI
           A
           VI
           is
           the
           
             Horizontal
             Line
          
           .
        
         
         
           Latitude
           .
           The
           Latitude
           of
           a
           Place
           is
           the
           number
           of
           Degrees
           contained
           between
           the
           Equinoctial
           and
           the
           place
           inquired
           after
           .
        
         
           Line
           of
           Contingence
           .
           See
           Contingent
           .
        
         
           
             Magnetick
             Needle
          
           .
           The
           Needle
           touch'd
           with
           the
           Loadstone
           ,
           to
           make
           it
           point
           to
           the
           North.
           
        
         
           Meridian
           ,
           is
           a
           great
           Circle
           of
           Heaven
           passing
           through
           the
           North
           and
           South
           points
           of
           the
           Horizon
           ;
           but
           in
           Dyalling
           it
           is
           represented
           by
           a
           straight
           Line
           ,
           as
           in
           Operat
           .
           II.
           in
           the
           
             Horizontal
             Dyal
          
           the
           Line
           XII
           A
           is
           a
           
             Meridian
             Line
          
           .
        
         
           Nadir
           .
           The
           point
           directly
           under
           our
           Feet
           .
        
         
           
             Nautial
             Compass
          
           ,
           Is
           the
           Compass
           used
           by
           Navigators
           ,
           whereon
           is
           marked
           out
           all
           the
           32
           Winds
           or
           Points
           of
           the
           Compass
           .
        
         
           
             Oblique
             Plane
          
           .
           See
           Fol.
           7.
           
        
         
           Parallel
           .
           See
           Fol.
           6
        
         
           Perpendicular
           .
           See
           Fol.
           5.
           
        
         
           Pole.
           The
           North
           or
           South
           Points
           on
           the
           Globe
           of
           the
           Earth
           ,
           are
           called
           North
           or
           
             South
             Pole.
          
           
        
         
           Quadrant
           .
           The
           fourth
           part
           of
           a
           Circle
           .
        
         
           Radius
           .
           Half
           the
           Diameter
           of
           a
           Circle
           .
        
         
           
             Right
             Angle
          
           .
           A
           straight
           Line
           that
           falls
           perpendicularly
           upon
           another
           straight
           Line
           ,
           makes
           at
           the
           meeting
           of
           those
           two
           Lines
           a
           Right
           Angle
           .
        
         
           Semi-Circle
           .
           Half
           a
           Circle
           .
        
         
           Semi-Diameter
           ,
           The
           same
           Radius
           is
           .
        
         
           Sphere
           .
           The
           highest
           Heaven
           with
           all
           its
           imagined
           Circles
           is
           called
           the
           Sphere
           .
        
         
           Stile
           .
           The
           Gnomon
           or
           Cock
           of
           a
           Dyal
           .
        
         
           Substile
           .
           The
           Line
           the
           Stile
           stands
           on
           upon
           a
           Dyal
           Plane
           .
        
         
           Triangle
           .
           A
           figure
           consisting
           of
           3
           Sides
           and
           3
           Angles
           .
        
         
           Zenith
           .
           The
           Point
           directly
           over
           our
           Head.
           
        
         
           FINIS
           .
        
      
    
     
       
         
         
           A
           Catalogue
           of
           GLOBES
           Coelestial
           and
           Terrestrial
           ,
           
             Spheres
             ,
             Mapps
             ,
             Sea-Platts
          
           ,
           Mathematical
           Instruments
           ,
           and
           Books
           ,
           made
           and
           sold
           by
           
             Joseph
             Moxon
          
           ,
           on
           Ludgate-Hill
           ,
           at
           the
           Sign
           of
           Atlas
           .
        
         
           
             GLOBES
             26
             Inches
             Diameter
             .
             The
             price
             20
             l.
             the
             pair
             .
          
           
             GLOBES
             ,
             near
             15
             Inches
             Diameter
             .
             The
             price
             4
             l.
             
          
           
             GLOBES
             ,
             8
             Inches
             Diameter
             .
             The
             price
             2
             l.
             
          
           
             GLOBES
             ,
             6
             Inches
             Diameter
             .
             The
             price
             1
             l.
             10
             s.
             
          
           
             
               CONCAVE
               HEMISPHERES
            
             of
             the
             
               Starry
               Orb
            
             ;
             which
             serves
             for
             a
             Case
             to
             a
             
               Terrestrial
               Globe
            
             of
             3
             Inches
             Diameter
             ,
             made
             portable
             for
             the
             Pocket
             .
             Price
             15
             s.
             
          
           
             SPHERES
             ,
             according
             to
             the
             
               Copernican
               Hypothesis
            
             ,
             both
             General
             and
             Particular
             ,
             20
             Inches
             Diameter
             .
             Price
             of
             the
             General
             5
             l.
             Of
             the
             Particular
             6
             l.
             Of
             both
             together
             10.
             
          
           
             SPHERES
             ,
             according
             to
             the
             Ptolomaick
             Systeme
             ,
             14
             Inches
             Diameter
             .
             Price
             3
             l.
             
          
           
             SPHERES
             ,
             according
             to
             the
             Ptolomaick
             Systeme
             ,
             8
             Inches
             Diameter
             .
             Price
             1
             l.
             10
             s.
             
          
           
             
             Gunter's
             Quadrant
             ,
             13
             Inches
             Radius
             ,
             printed
             on
             Paper
             ,
             and
             pasted
             on
             a
             Board
             ,
             with
             a
             Nocturnal
             on
             the
             backside
             .
             Price
             5
             s.
             
          
           
             
             Gunter's
             Quadrant
             ,
             4
             Inches
             Radius
             ,
             printed
             on
             Paper
             ,
             and
             pasted
             on
             Brass
             ,
             with
             a
             Nocturnal
             on
             the
             backside
             ,
             and
             a
             Wooden
             Case
             covered
             with
             Leather
             fit
             for
             it
             :
             A
             new
             invention
             contrived
             for
             the
             Pocket
             .
             Price
             6
             s.
             
          
           
             A
             large
             
               Mapp
               of
               the
               World
            
             ,
             10
             Foot
             long
             ,
             and
             7
             Foot
             deep
             ,
             pasted
             on
             Cloath
             and
             coloured
             .
             Price
             2
             l.
             
          
           
             A
             
               Mapp
               of
               all
               the
               World
            
             ,
             4
             Foot
             long
             ,
             and
             3
             Foot
             deep
             ,
             pasted
             on
             Cloath
             and
             coloured
             .
             Price
             10
             s.
             In
             sheets
             2
             s.
             6
             d.
             
          
           
             A
             Mapp
             of
             the
             
               English
               Empire
            
             in
             America
             ,
             describing
             all
             places
             inhabited
             there
             by
             the
             English
             Nation
             ,
             as
             well
             on
             the
             Islands
             as
             on
             the
             Continent
             .
             Price
             15
             s.
             
          
           
             Six
             
               Scriptural
               Mapps
            
             ,
             1.
             
             Of
             all
             the
             Earth
             :
             And
             how
             after
             the
             Flood
             it
             was
             divided
             among
             the
             Sons
             of
             Noah
             .
             2.
             
             Of
             Paradise
             ,
             or
             the
             
               Garden
               of
               Eden
            
             ;
             with
             the
             Countries
             circumjacent
             inhabited
             by
             the
             Patriarchs
             .
             3.
             
             The
             40
             years
             travel
             of
             the
             Children
             of
             Israel
             through
             the
             Wilderness
             .
             4.
             
             Of
             Canaan
             ,
             or
             the
             
               Holy
               Land
            
             :
             and
             how
             it
             was
             divided
             among
             the
             twelve
             Tribes
             of
             Israel
             ,
             and
             
             travelled
             through
             by
             our
             Saviour
             and
             his
             Apostles
             .
             5.
             
             The
             Travels
             of
             St.
             Paul
             ,
             and
             others
             of
             the
             Apostles
             ,
             in
             their
             propagating
             the
             Gospel
             .
             6.
             
             Jerusalem
             ,
             as
             it
             stood
             in
             our
             Saviour's
             time
             ;
             with
             a
             Book
             of
             Explanations
             to
             these
             Mapps
             ▪
             entituled
             
               Sacred
               Geography
            
             Price
             6
             s.
             Useful
             to
             be
             bound
             up
             with
             Bibles
             .
          
           
             A
             Sea-Platt
             ,
             or
             Mapp
             of
             all
             the
             World
             ,
             according
             to
             Mercator
             ,
             in
             two
             large
             Royal
             Sheets
             of
             Paper
             ;
             set
             forth
             by
             Mr.
             
               Edward
               Wright
            
             ,
             and
             newly
             corrected
             by
             
               Joseph
               Moxon
            
             Hydrogr
             .
             &c.
             Price
             2
             s.
             
          
           
             
               Sea
               Platts
            
             for
             sailing
             to
             all
             parts
             of
             the
             World.
             Price
             6
             d.
             the
             sheet
             .
          
           
             The
             famous
             City
             of
             Batavia
             in
             the
             East-Indies
             ,
             built
             and
             inhabited
             by
             the
             Duth
             ;
             curiously
             engraved
             ,
             and
             printed
             on
             four
             large
             Sheets
             of
             Royal
             Paper
             .
             Price
             2
             s.
             6
             d.
             
          
           
             A
             small
             Mapp
             of
             all
             the
             World
             ,
             with
             Descriptions
             ,
             on
             one
             Sheet
             .
             Price
             6
             d.
             
          
        
         
           
             BOOKS
             .
          
           
             A
             Tutor
             to
             Astronomy
             and
             Geography
             ,
             or
             the
             Use
             of
             both
             the
             
               GLOBES
               Coelestial
            
             and
             Terrestrial
             ;
             by
             
               Joseph
               Moxon
            
             Hydrographer
             to
             the
             Kings
             most
             Excellent
             Majesty
             .
             Price
             5
             s.
             
          
           
             The
             Vse
             of
             the
             
               Copernican
               Spheres
            
             ,
             teaching
             to
             salve
             the
             Phaenomena
             by
             them
             ,
             as
             easily
             as
             by
             the
             
               Ptolomaick
               Spheres
            
             ;
             by
             
               Joseph
               Moxon
            
             Hydrographer
             &c.
             Price
             4
             s.
             
          
           
             
             Wright's
             Correction
             of
             Errors
             in
             the
             Art
             of
             Navigation
             .
             Price
             8
             s.
             
          
           
             New
             and
             rare
             Inventions
             of
             Water-works
             .
             Teaching
             how
             to
             raise
             Water
             higher
             than
             the
             Spring
             .
             By
             which
             Invention
             the
             perpetual
             Motion
             is
             proposed
             ,
             many
             hard
             labours
             performed
             ,
             and
             varieties
             of
             Motion
             and
             Sounds
             produced
             .
             By
             
               Isaac
               de
               Caus
            
             ,
             Engineer
             to
             King
             Charles
             the
             First
             .
             Price
             8
             s.
             
          
           
             
               Practical
               Perspective
            
             ,
             or
             
               Perspective
               made
               easie
            
             .
             Teaching
             by
             the
             Opticks
             how
             to
             delineate
             all
             Bodies
             ,
             Buildings
             and
             Landskips
             ,
             &c.
             
             By
             the
             Catropticks
             ,
             how
             to
             delineate
             confused
             Appearances
             ▪
             so
             ,
             as
             when
             seen
             in
             a
             Mirrour
             or
             Polisht
             Body
             of
             any
             intended
             shape
             ,
             the
             Reflection
             shall
             shew
             a
             design
             .
             By
             the
             Dioptricks
             ,
             how
             to
             draw
             part
             of
             many
             Figures
             into
             one
             ,
             when
             seen
             through
             a
             Glass
             or
             Christal
             
             cut
             into
             many
             Faces
             .
             By
             
               Joseph
               Moxon
            
             Hydrographer
             ,
             &c.
             Price
             7
             s.
             
          
           
             An
             exact
             Survey
             of
             the
             Microcosine
             .
             Being
             an
             Antaomy
             of
             the
             Bodies
             of
             Man
             and
             Woman
             ;
             wherein
             the
             Skin
             ,
             Veins
             ,
             Nerves
             ,
             Muscles
             ,
             Bones
             ,
             Sinews
             and
             Ligaments
             are
             accurately
             delineated
             .
             Engraven
             on
             large
             Copper
             Plates
             ,
             Printed
             and
             curiously
             pasted
             together
             ,
             so
             as
             at
             first
             sight
             you
             may
             behold
             all
             the
             parts
             of
             Man
             and
             Woman
             ;
             and
             by
             turning
             up
             the
             several
             Dissections
             of
             the
             Papers
             ,
             take
             a
             view
             of
             all
             their
             Inwards
             :
             with
             Alphabetical
             referrences
             to
             the
             Names
             of
             every
             Member
             and
             part
             of
             the
             Body
             .
             Set
             forth
             in
             Latine
             by
             Remelinus
             ,
             and
             
               Michael
               Spaher
            
             of
             Tyrol
             :
             and
             Englished
             by
             
               John
               Ireton
            
             Chyrurgeon
             :
             and
             lastly
             ,
             perused
             and
             corrected
             by
             several
             rare
             Anatomists
             .
             Price
             14
             s.
             
          
           
             Vignola
             ,
             or
             the
             
               Compleat
               Architect
            
             .
             Shewing
             in
             a
             plain
             and
             easie
             way
             ,
             the
             Rules
             of
             the
             five
             Orders
             in
             Architecture
             ,
             viz.
             
               Tuscan
               ,
               Dorick
               ,
               Ionick
               ,
               Corinthian
            
             and
             Composite
             :
             whereby
             any
             that
             can
             but
             read
             and
             understand
             English
             ,
             may
             readily
             learn
             the
             proportions
             that
             all
             Members
             in
             Building
             have
             to
             one
             another
             :
             set
             forth
             by
             Mr.
             
               James
               Barrozzio
            
             of
             Vignola
             ,
             and
             translated
             into
             English
             by
             
               Joseph
               Moxon
            
             Hydrographer
             ,
             &c.
             Price
             3
             s.
             6
             d.
             
          
           
             Christiologia
             ,
             or
             a
             brief
             ,
             but
             true
             Account
             of
             the
             certain
             year
             ,
             Month
             ,
             Day
             and
             Minute
             of
             the
             Birth
             of
             
               Jesus
               Christ.
            
             By
             
               John
               Butler
            
             B.
             D.
             and
             Chaplain
             to
             his
             Grace
             James
             Duke
             of
             Ormond
             ,
             &c.
             and
             Rector
             of
             Lichborough
             ,
             in
             the
             Diocess
             of
             Peterburgh
             .
             Price
             3
             s.
             6
             d.
             
          
           
             A
             Tutor
             to
             Astrology
             ,
             or
             
               Astrology
               made
               easie
            
             ;
             being
             a
             plain
             Introduction
             to
             the
             whole
             Art
             of
             Astrology
             .
             Whereby
             the
             meanest
             Apprehension
             may
             learn
             to
             erect
             a
             Figure
             ,
             and
             by
             the
             same
             give
             a
             determinate
             Judgment
             upon
             any
             Question
             of
             Nativity
             whatsoever
             .
             Also
             new
             Tables
             of
             Houses
             ,
             calculated
             for
             the
             Latitude
             of
             51
             deg
             .
             32
             min.
             Also
             Tables
             of
             Right
             and
             Oblique
             Ascensions
             to
             6
             deg
             .
             of
             Latitude
             .
             Whereunto
             is
             added
             an
             Ephemeris
             for
             three
             years
             ;
             with
             all
             other
             necessary
             Tables
             that
             belong
             to
             the
             Art
             of
             Astrology
             .
             Also
             how
             to
             erect
             a
             Figure
             the
             Rational
             way
             by
             the
             Tables
             of
             Triangles
             ,
             more
             methodically
             than
             hath
             yet
             been
             published
             ;
             digested
             into
             a
             small
             Pocket
             Volume
             ,
             for
             the
             conveniency
             of
             those
             that
             erect
             Figures
             abroad
             .
             By
             
               W.
               Eland
            
             .
             Price
             2
             s.
             
          
           
             The
             Use
             of
             a
             Mathematical
             Instrument
             called
             a
             Quadrant
             ,
             shewing
             very
             plainly
             and
             easily
             to
             know
             the
             exact
             height
             and
             distance
             
             of
             any
             Steeple
             ,
             Tree
             ,
             or
             House
             ,
             &c.
             
             Also
             to
             know
             the
             Hour
             of
             the
             Day
             by
             it
             ;
             the
             heighth
             of
             the
             Sun
             ,
             Moon
             or
             Stars
             ;
             and
             to
             know
             the
             time
             of
             the
             Sun-rising
             and
             setting
             ,
             and
             the
             length
             of
             every
             day
             in
             the
             year
             ,
             the
             place
             of
             the
             Sun
             in
             the
             Ecliptick
             ,
             the
             Azimuth
             ,
             right
             Ascension
             ,
             and
             Declination
             of
             the
             Sun
             :
             with
             many
             other
             necessary
             and
             delightful
             Conclusions
             ,
             performed
             very
             readily
             .
             Also
             the
             use
             of
             a
             Nocturnal
             ,
             whereby
             you
             may
             learn
             to
             know
             the
             Stars
             in
             Heaven
             ,
             and
             the
             hour
             of
             the
             Night
             by
             them
             .
             With
             many
             other
             delightful
             Operations
             .
             Price
             6
             d.
             
          
           
             A
             brief
             Discourse
             of
             a
             passage
             by
             the
             North-pole
             to
             
               Japan
               ,
               China
            
             ,
             &c.
             
             Pleaded
             by
             three
             Experiments
             ,
             and
             Answers
             to
             all
             objections
             that
             can
             be
             urged
             against
             a
             passage
             that
             way
             .
             As
             1.
             
             By
             a
             Navigation
             into
             the
             North-pole
             ,
             and
             two
             degrees
             beyond
             it
             .
             2.
             
             By
             a
             Navigation
             from
             Japan
             towards
             the
             North-pole
             .
             3.
             
             By
             an
             Experiment
             made
             by
             the
             Czar
             of
             Muscovy
             :
             whereby
             it
             appears
             that
             to
             the
             Northward
             of
             
               Nova
               Zembla
            
             is
             a
             free
             and
             open
             Sea
             as
             far
             as
             
               Japan
               ,
               China
            
             ,
             &c.
             
             With
             a
             Mapp
             of
             all
             the
             discovered
             Land
             nearest
             to
             the
             Pole.
             By
             
               Joseph
               Moxon
            
             Hydrographer
             &c.
             Price
             6
             d.
             
          
           
             
               Regulae
               Trium
               Ordinum
               Literarum
               Typographicarum
            
             :
             Or
             the
             Rules
             of
             the
             three
             Orders
             of
             Print-Letters
             ,
             viz.
             The
             Roman
             ,
             Italick
             ,
             English
             ,
             Capaitals
             and
             Small
             .
             Shewing
             how
             they
             are
             compounded
             of
             
               Geometrick
               Figures
            
             ,
             and
             mostly
             made
             by
             Rule
             and
             Compass
             .
             Useful
             for
             Writing-Masters
             ,
             Painters
             ,
             Carvers
             ,
             Masons
             ,
             and
             others
             that
             are
             lovers
             of
             Curiosity
             .
             By
             
               Joseph
               Moxon
            
             Hydrographer
             &c.
             Price
             5
             s.
             
          
           
             The
             Use
             of
             the
             
               Astronomical
               Playing
               Cards
            
             .
             Teaching
             an
             ordinary
             Capacity
             by
             them
             to
             be
             acquainted
             with
             all
             the
             Stars
             in
             Heaven
             :
             to
             know
             their
             Places
             ,
             Colours
             ,
             Natures
             and
             Bignesses
             .
             Also
             the
             Poetical
             Reasons
             for
             every
             Constellation
             ;
             very
             useful
             ,
             pleasant
             and
             delightful
             for
             all
             lovers
             of
             Ingeniety
             .
             By
             
               Joseph
               Moxon
            
             Hydrogr
             .
             &c.
             Price
             6
             d.
             
          
           
             The
             
               Astronomical
               Cards
            
             .
             By
             
               Joseph
               Moxon
            
             Hydrographer
             ,
             &c.
             Price
             plain
             1
             s.
             Coloured
             1
             s.
             6
             d.
             Best
             coloured
             and
             the
             Stars
             gilt
             5
             s.
             
          
           
             The
             
               Genteel
               House-keepers
               Pastime
            
             :
             Or
             ,
             the
             Mode
             of
             Carving
             at
             the
             Table
             represented
             in
             a
             Pack
             of
             
               Playing
               Cards
            
             .
             By
             w●ich
             ,
             together
             with
             the
             Instructions
             in
             this
             Book
             ,
             any
             ordinary
             Capacity
             may
             easily
             learn
             how
             to
             Cut
             up
             ,
             or
             Carve
             in
             M●de
             all
             the
             most
             usual
             Dishes
             of
             
               Flesh
               ,
               Fish
               ,
               Fowl
            
             ,
             and
             
               Baked
               M●●●●
            
             ;
             and
             how
             to
             make
             the
             several
             Services
             of
             the
             same
             at
             the
             Table
             ;
             with
             the
             several
             Sawces
             and
             Garnishes
             proper
             to
             each
             Dish
             of
             
             Meat
             .
             Set
             forth
             by
             several
             of
             the
             best
             Masters
             in
             the
             Faculty
             of
             Carving
             ,
             and
             published
             for
             publick
             Use.
             Price
             6
             d.
             
          
           
             
               Carving
               Cards
            
             .
             By
             the
             best
             Carvers
             at
             the
             Lord
             Mayors
             Table
             .
             Price
             1
             s.
             
          
           
             
               Compendium
               Euclidis
               Curiosi
            
             :
             Or
             Geometrical
             Operations
             .
             Shewing
             how
             with
             one
             single
             opening
             of
             the
             Compasses
             ,
             and
             a
             straight
             Ruler
             all
             the
             Propositions
             of
             Euclids
             first
             Five
             Books
             are
             performed
             .
             Translated
             out
             of
             Dutch
             into
             English.
             By
             
               Joseph
               Moxon
            
             .
             Hydrogr
             .
             &c.
             Price
             1
             s.
             
          
           
             An
             Introduction
             to
             the
             Art
             of
             Species
             .
             By
             Sir
             
               Jonas
               Moore
            
             .
             Price
             6
             d.
             
          
           
             Two
             Tables
             of
             Ranges
             ,
             according
             to
             degrees
             of
             Mounture
             .
             By
             
               Henry
               Bond
               ,
               Senior
            
             .
             Price
             6.
             d.
             
          
           
             
               Mechanick
               Exercises
            
             :
             Or
             the
             Doctrine
             of
             Handy-Works
             ,
             in
             six
             Monethly
             Exercises
             ;
             began
             January
             1.
             1677.
             and
             monethly
             continued
             till
             June
             1678.
             
             The
             first
             three
             ,
             viz.
             the
             Numb
             .
             I.
             Numb
             .
             II.
             Numb
             .
             III.
             teaching
             the
             
               Art
               of
               Smithing
            
             .
             The
             other
             three
             ,
             viz.
             Numb
             .
             IIII.
             Numb
             .
             V.
             Numb
             .
             VI.
             teaching
             the
             
               Art
               of
               faynery
            
             .
             Accommodated
             with
             suitable
             engraved
             Figures
             .
             By
             
               Joseph
               Moxon
            
             Hydrographer
             ,
             &c.
             price
             6
             d.
             each
             Exercise
             .
          
        
         
           At
           the
           place
           abovesaid
           ,
           you
           may
           also
           have
           all
           manner
           of
           
             Mapps
             ,
             Sea-Platts
             Drafts
             ,
             Mathematical
             Books
             ,
             Instruments
             ,
          
           &c.
           
           At
           the
           lowest
           prizes
           .
        
      
       
         
           ADVERTISEMENT
           .
        
         
           THere
           is
           invented
           by
           the
           Right
           Honourable
           the
           Farl
           of
           Castlemain
           ,
           a
           new
           kind
           of
           Globe
           ,
           call'd
           (
           for
           distinction
           sake
           )
           the
           
             English
             Globe
          
           ;
           being
           a
           fix'd
           and
           immovable
           one
           ,
           performing
           what
           the
           Ordinary
           ones
           do
           ,
           and
           much
           more
           ,
           even
           without
           their
           usual
           Appendancies
           ;
           as
           
             Wooden
             Horizons
             ,
             Brazen
             Meridians
             ,
             Vertical
             Circles
             ,
             Horary
             Circles
             ,
          
           &c.
           
           For
           it
           Composes
           it self
           to
           the
           site
           
           and
           Position
           of
           the
           World
           without
           the
           Marriners
           Compass
           ,
           or
           the
           like
           forreign
           Help
           ;
           and
           besides
           other
           useful
           and
           surprising
           Operations
           (
           relating
           both
           to
           the
           Sun
           and
           Moon
           ,
           and
           performed
           by
           the
           Shade
           alone
           )
           we
           have
           by
           it
           not
           only
           the
           constant
           proportion
           of
           Perpendiculars
           to
           their
           Shades
           ,
           with
           several
           Corollaries
           thence
           arising
           ,
           but
           also
           an
           easie
           ,
           new
           ,
           and
           most
           compendious
           way
           of
           describing
           Dyals
           on
           all
           Planes
           ,
           as
           well
           Geometrically
           ,
           as
           Mechanically
           :
           most
           of
           which
           may
           be
           taught
           any
           one
           in
           few
           Hours
           ,
           though
           never
           so
           unacquainted
           with
           Mathematicks
           .
        
         
           To
           this
           is
           added
           on
           the
           Pedestal
           a
           Projection
           of
           all
           the
           appearing
           Constellations
           in
           this
           Horizon
           ,
           with
           their
           Figures
           and
           Shapes
           .
           And
           besides
           ,
           several
           new
           things
           in
           it
           differing
           from
           the
           common
           Astrolabe
           ,
           (
           tending
           to
           a
           clearer
           and
           quicker
           way
           of
           Operating
           )
           the
           very
           Principles
           of
           all
           Steriographical
           Projections
           are
           laid
           down
           ,
           and
           Mathematically
           demonstrated
           ;
           as
           is
           every
           thing
           else
           of
           Moment
           throughout
           the
           whole
           Treatise
           .
        
         
           These
           Globes
           will
           be
           made
           and
           exposed
           to
           Sale
           about
           August
           next
           ,
           (
           God
           willing
           :
           )
           against
           which
           time
           the
           Book
           for
           its
           use
           will
           also
           be
           Printed
           ,
           and
           sold
           by
           
             Joseph
             Moxon
          
           ,
           on
           Ludgate-Hill
           ,
           at
           the
           Sign
           of
           Atlas
           .