The doctrine decimal arithmetick, simple interest, &c. as also of compound interest and annuities generally performed for any time of payment or rate of interest by help of a particular table of forbearance of 1l principal, with enlarged rules, formerly abridged for portability in a letter case / by John Collins ; and since his death, both made publick by J.D.
         Collins, John, 1625-1683.
      
       
         
           1685
        
      
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         ESTC R23930
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         ocm 07929253
         40487
         
           
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             The doctrine decimal arithmetick, simple interest, &c. as also of compound interest and annuities generally performed for any time of payment or rate of interest by help of a particular table of forbearance of 1l principal, with enlarged rules, formerly abridged for portability in a letter case / by John Collins ; and since his death, both made publick by J.D.
             Collins, John, 1625-1683.
          
           [5], 102, [1] p.
           
             Printed by R. Holt for Nath. Ponder,
             London :
             1685.
          
           
             Note in manuscript: p. [103]
             Reproduction of original in the Cambridge University Library.
          
        
      
    
     
       
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         eng
      
       
         
           Interest -- Great Britain.
           Decimal system.
        
      
    
     
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               The
               Doctrine
               of
               DECIMAL
               ARITHMETICK
               ,
               Simple
               Interest
               ,
               &c.
               AS
               ALSO
               Of
               Compound
               Interest
               AND
               ANNUITIES
               ;
               Generally
               performed
               for
               any
               time
               of
               Payment
               ,
               or
               Rate
               of
               Interest
               ,
               by
               help
               of
               a
               particular
               Table
               of
               Forbearance
               of
               1
               l.
               Principal
               ,
               with
               Inlarged
               Rules
               .
            
             
               Formerly
               abridged
               for
               portability
               in
               a
               Letter
               Case
               .
            
             
               By
               
                 John
                 Collins
              
               Accomptant
               ,
               Philomath
               .
               And
               since
               his
               Death
               both
               made
               Publick
               by
               
                 J.
                 D.
              
               
            
             
               LONDON
               ,
               Printed
               by
               
                 R.
                 Holt
              
               for
               
                 Nath.
                 Ponder
              
               at
               the
               Peacock
               in
               the
               Poultry
               ,
               near
               the
               Stocks-Market
               ,
               1685.
               
            
          
           
             
             
             
               THE
               EPISTLE
               TO
               THE
               READER
               .
            
             
               
                 Courteous
                 Reader
                 ,
              
            
             
               IT
               is
               the
               accustomed
               way
               to
               Dedicate
               Books
               to
               some
               Honourable
               Person
               ,
               that
               thereby
               the
               Book
               might
               have
               the
               greater
               Esteem
               .
               This
               Book
               needs
               no
               such
               Dedication
               ,
               for
               the
               Name
               of
               the
               Author
               (
               which
               will
               never
               dye
               ,
               Ingenious
               Mr.
               John
               
               ted
               at
               the
               end
               of
               the
               Book
               ,
               whereby
               the
               Reader
               may
               see
               it
               no
               ways
               derogates
               from
               the
               Old
               Copy
               ,
               and
               thereby
               may
               see
               how
               full
               and
               plain
               the
               New
               Rules
               are
               in
               comparison
               to
               the
               Old.
               
            
             
               This
               Book
               is
               a
               fit
               Companion
               for
               all
               Gentlemen
               ,
               Merchants
               ,
               Scriveners
               ,
               and
               other
               Trades-men
               ,
               that
               deal
               much
               in
               lending
               of
               Money
               upon
               Interest
               ,
               Mortgages
               ,
               buying
               of
               Estates
               either
               in
               Fee
               ,
               Copy
               ,
               or
               Lease
               ,
               holding
               Annuities
               ,
               Rent
               Charges
               ,
               Forbearance
               of
               Money
               ,
               Discompt
               ,
               or
               any
               other
               way
               concerning
               Interest
               ,
               &c.
               
            
             
               When
               any
               Person
               does
               perfectly
               understand
               the
               large
               Rules
               ,
               he
               may
               if
               he
               pleases
               lay
               by
               the
               Book
               ,
               and
               only
               use
               the
               Compendium
               with
               the
               
               Tables
               to
               be
               carried
               about
               in
               a
               Letter
               Case
               ;
               and
               I
               hope
               in
               perusing
               this
               small
               Treatise
               the
               Reader
               will
               find
               that
               which
               will
               give
               him
               Satisfaction
               ,
               both
               as
               to
               the
               Rules
               and
               Tables
               .
            
             
               
                 Yours
                 ,
                 
                   J.
                   D.
                
                 
              
            
          
        
         
           
             
             
             
               Decimal
               Arithmetick
               .
            
             
               A
               
                 Decimal
                 Fraction
              
               is
               such
               a
               one
               whose
               Denominator
               is
               understood
               ,
               and
               not
               expressed
               ;
               and
               is
               an
               Unit
               with
               as
               many
               Cyphers
               following
               it
               ,
               as
               there
               are
               Figures
               and
               Cyphers
               in
               the
               Numerator
               .
            
             
               Corollary
               ,
               Wherefore
               the
               annexing
               of
               Cyphers
               towards
               the
               right
               hand
               of
               a
               Decimal
               ,
               alters
               not
               its
               value
               .
               A
               
                 Decimal
                 Fraction
              
               of
               Coin
               may
               be
               easily
               valued
               without
               the
               help
               of
               Tables
               .
               For
               each
               Unit
               in
               the
               first
               place
               is
               in
               value
               2
               s.
               5
               in
               the
               second
               place
               1
               s.
               and
               the
               rest
               Farthings
               ;
               but
               if
               they
               exceed
               25
               /
               48
               there
               must
               be
               two
               farthings
               abated
               .
            
             
               
                 
                   Example
                   .
                
                 
                   
                     So
                  
                   
                     ,854
                  
                   
                     is
                     in
                     value
                  
                   
                     17
                     s.
                     1
                     d.
                     
                  
                
                 
                   
                     ,418
                  
                   
                     8.
                     4½
                  
                
              
            
             
             
               Addition
               and
               Substraction
               in
               Decimals
               is
               the
               same
               ,
               as
               in
               whole
               Numbers
               ,
               keeping
               the
               place
               of
               Units
               just
               under
               each
               other
               .
            
             
               Multiplication
               in
               Decimals
               is
               the
               same
               ,
               as
               in
               
                 Common
                 Arithmetick
              
               ,
               saving
               as
               many
               Decimal
               Parts
               as
               are
               in
               both
               Multipliers
               ,
               so
               many
               must
               be
               cut
               off
               from
               the
               Product
               ,
               which
               if
               it
               have
               not
               so
               many
               places
               ,
               the
               Defect
               is
               to
               be
               supplied
               with
               Cyphers
               towards
               the
               left
               hand
               .
            
             
               Division
               is
               the
               same
               as
               in
               whole
               Numbers
               ,
               without
               regard
               to
               Decimals
               till
               the
               Work
               is
               done
               ,
               and
               then
               use
               the
               Converse
               of
               the
               Rule
               for
               Multiplication
               
                 (
                 viz.
              
               )
               so
               many
               Decimals
               as
               are
               in
               the
               Dividend
               ,
               so
               many
               there
               must
               be
               in
               the
               Divisor
               and
               Quote
               ,
               and
               if
               there
               be
               not
               so
               many
               ,
               the
               Quotient
               must
               be
               supplied
               with
               Cyphers
               towards
               the
               left
               hand
               .
            
             
               
               
                 Simple
                 Interest
                 .
              
               
                 
                   PROP.
                   1.
                   
                
                 
                   TO
                   compute
                   the
                   Interest
                   for
                   a
                   day
                   ,
                   6
                   /
                   365
                   is
                   the
                   Interest
                   of
                   100
                   l.
                   for
                   a
                   Day
                   the
                   1
                   /
                   100
                   ,
                   whereof
                   is
                   the
                   Interest
                   of
                   1
                   l.
                   for
                   a
                   Day
                   
                     (
                     viz.
                  
                   )
                   6
                   /
                   36500
                   ;
                   Or
                   6
                   (
                   with
                   Cyphers
                   put
                   on
                   at
                   pleasure
                   )
                   divided
                   by
                   36500
                   is
                   ,
                   000164383
                   the
                   Interest
                   of
                   1
                   l.
                   for
                   a
                   Day
                   .
                
                 
                   Prop.
                   2.
                   
                   The
                   Decimals
                   of
                   Days
                   in
                   the
                   Table
                   at
                   the
                   end
                   will
                   serve
                   to
                   find
                   the
                   amount
                   of
                   1
                   l.
                   Simple
                   Interest
                   of
                   any
                   Rate
                   for
                   any
                   time
                   under
                   365
                   Days
                   or
                   a
                   Year
                   .
                
                 
                   If
                   you
                   take
                   the
                   Decimal
                   for
                   one
                   day
                   (
                   or
                   more
                   )
                   and
                   multiply
                   that
                   by
                   ,
                   06.
                   7.
                   8.
                   
                   
                     &c.
                     per
                     Cent.
                  
                   or
                   any
                   other
                   Rate
                   ,
                   the
                   Product
                   will
                   give
                   the
                   Interest
                   of
                   one
                   pound
                   for
                   a
                   Day
                   ,
                   or
                   more
                   
                   under
                   366
                   Days
                   at
                   Simple
                   Interest
                   .
                
                 
                   
                     Example
                     1.
                     
                  
                   
                     
                       
                         
                           The
                           Decimal
                           for
                           a
                           day
                           is
                        
                         
                           ,002739726
                        
                      
                       
                         
                            
                        
                         
                            
                        
                         
                           ,06
                        
                      
                       
                         
                           The
                           Interest
                           of
                           1
                           l.
                           for
                           a
                           day
                        
                         
                           ,00016438356
                        
                      
                    
                  
                
                 
                   
                     Example
                     2.
                     
                  
                   
                     
                       
                         
                           The
                           Decimal
                           of
                           121
                           days
                           is
                        
                         
                           ,331506849
                        
                      
                       
                         
                            
                        
                         
                           ,06
                        
                      
                       
                         
                           The
                           Interest
                           of
                           1
                           l.
                           for
                           121
                           days
                        
                         
                           ,01989041094
                        
                      
                       
                         
                           ,002739726
                        
                         
                           Decimal
                           for
                           a
                           day
                        
                      
                       
                         
                           ,07
                        
                         
                           
                             per
                             Cent.
                          
                           
                        
                      
                       
                         
                           ,00019178082
                        
                         
                           The
                           Interest
                           of
                           1
                           l.
                           for
                           a
                           day
                           at
                           7
                           
                             l.
                             per
                             Cent.
                          
                           
                        
                      
                    
                  
                   
                     And
                     so
                     of
                     any
                     other
                     rate
                     of
                     Interest
                     .
                  
                
              
               
                 
                 
                   Prop.
                   2.
                   
                   
                     Forbearance
                     of
                     Money
                     at
                     Simple
                     Interest
                     .
                  
                
                 
                   The
                   Interest
                   of
                   1
                   l.
                   for
                   any
                   Number
                   of
                   days
                   ,
                   at
                   what
                   rate
                   of
                   Interest
                   you
                   please
                   ,
                   be
                   first
                   found
                   by
                   the
                   first
                   Proposition
                   ,
                   that
                   Product
                   multiplied
                   by
                   the
                   Sum
                   propounded
                   ,
                   gives
                   the
                   Interest
                   thereof
                   for
                   the
                   time
                   required
                   .
                
                 
                   
                     Example
                     .
                  
                   
                     To
                     know
                     the
                     Amount
                     of
                     140
                     l.
                     for
                     121
                     days
                     ,
                     at
                     6
                     
                       l.
                       per
                       Cent.
                    
                     Simple
                     Interest
                     .
                  
                   
                     
                       
                         
                           The
                           Decimal
                           of
                           1
                           l.
                           for
                           121
                           days
                        
                         
                           1,019890410
                        
                      
                       
                         
                           Multiplied
                           by
                        
                         
                           140
                        
                      
                       
                         
                           Which
                           is
                           142
                           l.
                           15
                           s.
                           8
                           d.
                           
                        
                         
                           40795616400
                        
                      
                       
                         
                            
                        
                         
                           1,019890410
                        
                      
                       
                         
                            
                        
                         
                           142,784657400
                        
                      
                    
                  
                
              
               
                 
                 
                   Prop.
                   3.
                   
                   
                     Rebate
                     ,
                     or
                     the
                     Present
                     worth
                     of
                     Money
                     due
                     hereafter
                     .
                  
                
                 
                   Find
                   the
                   Interest
                   of
                   1
                   l.
                   for
                   the
                   time
                   given
                   ,
                   as
                   in
                   Prop.
                   1.
                   
                   And
                   thereto
                   add
                   an
                   Unit
                   by
                   it
                   .
                   Divide
                   any
                   other
                   Sum
                   propounded
                   ,
                   and
                   the
                   Quote
                   is
                   its
                   present
                   Worth.
                   
                
                 
                   
                     Example
                     .
                  
                   
                     If
                     142
                     l.
                     15
                     s.
                     8
                     d.
                     be
                     due
                     at
                     the
                     end
                     of
                     121
                     days
                     ,
                     what
                     is
                     it
                     worth
                     in
                     ready
                     Money
                     ?
                     
                  
                   
                   
                     Worth
                     in
                     ready
                     Money
                     140
                     l.
                     at
                     6
                     
                       l.
                       per
                       Cent.
                    
                     Simple
                     Interest
                     ,
                     and
                     may
                     be
                     done
                     for
                     any
                     other
                     rate
                     of
                     Interest
                     ,
                     working
                     by
                     the
                     first
                     Proportion
                     and
                     this
                     former
                     Rule
                     .
                  
                
              
               
                 
                   Prop.
                   4.
                   
                   
                     Equation
                     of
                     Payments
                  
                   .
                
                 
                   By
                   Prop.
                   3.
                   compute
                   all
                   the
                   Present
                   Worths
                   ,
                   and
                   then
                   by
                   Proportion
                   .
                   If
                   all
                   those
                   Present
                   Worths
                   amounted
                   to
                   the
                   Total
                   of
                   all
                   those
                   Payments
                   ,
                   what
                   did
                   one
                   pound
                   amount
                   to
                   in
                   the
                   said
                   time
                   ?
                   From
                   the
                   result
                   substract
                   an
                   Unit
                   ,
                   the
                   Remainder
                   is
                   the
                   Interest
                   of
                   1
                   l.
                   for
                   the
                   time
                   sought
                   ,
                   which
                   divide
                   by
                   the
                   Interest
                   of
                   1
                   l.
                   for
                   a
                   day
                   ,
                   the
                   Quote
                   is
                   the
                   Number
                   of
                   days
                   sought
                   .
                
                 
                   If
                   you
                   are
                   to
                   Aequate
                   an
                   Annuity
                   ,
                   at
                   Simple
                   Interest
                   .
                   I
                   presume
                   a
                   Compendium
                   may
                   be
                   found
                   in
                   Mengolus
                   his
                   Arithmetical
                   Quadratures
                   (
                   a
                   Book
                   I
                   never
                   saw
                   )
                   who
                   it
                   's
                   probable
                   by
                   a
                   Compendium
                   gets
                   the
                   fact
                   of
                   an
                   Arithmetical
                   
                   Progression
                   ,
                   and
                   adds
                   Fractions
                   that
                   have
                   a
                   constant
                   Numerator
                   ,
                   and
                   an
                   Arithmetical
                   Progression
                   for
                   their
                   Denominators
                   .
                
                 
                   So
                   much
                   for
                   Simple
                   Interest
                   ,
                   my
                   Design
                   being
                   more
                   for
                   the
                   Explanation
                   of
                   the
                   Tables
                   for
                   Compound
                   Interest
                   and
                   Annuities
                   .
                
              
            
             
               
                 Of
                 Compound
                 Interest
                 .
              
               
                 THe
                 Original
                 thereof
                 is
                 Derived
                 from
                 Simple
                 Interest
                 ,
                 for
                 if
                 it
                 be
                 Lawful
                 to
                 take
                 Interest
                 at
                 all
                 ,
                 then
                 it
                 is
                 as
                 Lawful
                 to
                 put
                 out
                 the
                 Interest-Money
                 to
                 Use
                 ,
                 as
                 the
                 Principal
                 .
              
               
                 For
                 ease
                 in
                 Calculating
                 Questions
                 that
                 concern
                 Compound
                 Interest
                 ,
                 Arithmeticians
                 do
                 usually
                 frame
                 Tables
                 in
                 store
                 ,
                 to
                 shew
                 what
                 1
                 l.
                 Principal
                 forborn
                 at
                 any
                 Rate
                 for
                 any
                 determinate
                 
                 time
                 shall
                 amount
                 unto
                 ;
                 the
                 Construction
                 whereof
                 is
                 by
                 the
                 Golden
                 Rule
                 ,
                 as
                 followeth
                 ;
              
               
                 As
                 100
                 l.
                 Principal
                 is
                 to
                 the
                 amount
                 thereof
                 at
                 the
                 years
                 end
                 ;
              
               
                 So
                 is
                 an
                 Unit.
                 To
                 its
                 amount
                 (
                 to
                 wit.
                 )
              
               
                 So
                 is
                 1.
                 1
                 ,
                 06.
                 
                 If
                 6
                 be
                 the
                 rate
                 of
                 Interest
                 ,
                 then
                 it
                 will
                 hold
                 again
                 for
                 the
                 next
                 year
                 .
              
               
                 As
                 1.
                 1
                 ,
                 06
                 ,
                 so
                 1
                 ,
                 06
                 ,
                 to
                 1
                 ,
                 1236
                 ,
                 the
                 principal
                 and
                 Interest
                 at
                 the
                 second
                 year
                 .
              
               
                 Now
                 because
                 an
                 Unit
                 is
                 in
                 the
                 first
                 place
                 ,
                 which
                 doth
                 not
                 divide
                 ,
                 it
                 followeth
                 ,
                 that
                 the
                 second
                 years
                 amount
                 Squares
                 the
                 Number
                 1
                 ,
                 06
                 ,
                 being
                 the
                 Quotient
                 of
                 1
                 ,
                 06
                 divided
                 by
                 100
                 ,
                 and
                 that
                 is
                 the
                 amount
                 of
                 1
                 l.
                 forborn
                 a
                 year
                 ,
                 the
                 Compound
                 Interest
                 the
                 third
                 year
                 Cubes
                 it
                 ,
                 &c.
                 
                 And
                 the
                 said
                 Number
                 1
                 ,
                 06
                 is
                 by
                 Arithmeticians
                 called
                 the
                 
                   Ratio
                   ,
                   Quote
                
                 or
                 Denominator
                 of
                 the
                 Ratio
                 propounded
                 ,
                 and
                 the
                 Logarythm
                 
                 thereof
                 multiplied
                 by
                 the
                 time
                 doth
                 raise
                 those
                 Powers
                 agreeable
                 to
                 the
                 nature
                 of
                 Logarythms
                 .
              
               
                 By
                 the
                 former
                 Proportion
                 was
                 the
                 following
                 Table
                 for
                 years
                 made
                 ,
                 or
                 for
                 Abridgment
                 by
                 Addition
                 ,
                 only
                 by
                 help
                 of
                 a
                 Table
                 of
                 1,06
                 multiplied
                 by
                 all
                 the
                 Digits
                 ;
                 And
                 this
                 raising
                 of
                 Powers
                 is
                 by
                 some
                 called
                 Involution
                 ,
                 and
                 as
                 for
                 that
                 of
                 Months
                 may
                 be
                 made
                 by
                 finding
                 mean
                 Proportionals
                 ,
                 and
                 those
                 of
                 days
                 by
                 help
                 of
                 the
                 Common
                 Logarythms
                 ,
                 or
                 without
                 ,
                 supplied
                 far
                 enough
                 downward
                 ,
                 by
                 help
                 of
                 mean
                 Proportionals
                 ,
                 and
                 a
                 Decimal
                 Table
                 for
                 time
                 ,
                 and
                 three
                 Months
                 here
                 is
                 understood
                 to
                 be
                 the
                 precise
                 ¼
                 of
                 a
                 whole
                 year
                 ,
                 and
                 so
                 of
                 the
                 rest
                 .
              
               
                 That
                 which
                 we
                 add
                 concerning
                 it
                 ,
                 is
                 ,
                 That
                 it self
                 is
                 in
                 effect
                 no
                 other
                 than
                 a
                 Table
                 of
                 Logarythms
                 ,
                 but
                 of
                 another
                 kind
                 than
                 those
                 in
                 Print
                 ,
                 yet
                 herein
                 agreeing
                 therewith
                 ,
                 that
                 in
                 both
                 the
                 
                 Logarythm
                 of
                 an
                 Unit
                 is
                 O
                 ,
                 and
                 therefore
                 this
                 Table
                 may
                 be
                 continued
                 for
                 any
                 large
                 time
                 by
                 one
                 or
                 some
                 few
                 Multiplications
                 ,
                 it
                 is
                 here
                 continued
                 to
                 each
                 year
                 for
                 50
                 years
                 ,
                 then
                 for
                 every
                 10
                 years
                 to
                 100
                 ,
                 whereby
                 you
                 may
                 perceive
                 that
                 an
                 Inheritance
                 ,
                 or
                 a
                 Sum
                 due
                 after
                 such
                 a
                 time
                 is
                 worth
                 little
                 more
                 than
                 a
                 three
                 hundred
                 and
                 fortieth
                 part
                 of
                 its
                 present
                 Worth.
                 
              
               
                 And
                 in
                 the
                 next
                 place
                 it
                 will
                 supply
                 the
                 Defect
                 of
                 all
                 other
                 Tables
                 (
                 especially
                 those
                 that
                 relate
                 to
                 the
                 said
                 rate
                 of
                 Interest
                 )
                 whether
                 of
                 Discount
                 of
                 Money
                 or
                 of
                 Forbearance
                 of
                 and
                 Discount
                 of
                 Annuities
                 ,
                 or
                 for
                 the
                 Purchase
                 thereof
                 .
              
               
                 In
                 the
                 Tables
                 following
                 the
                 number
                 of
                 years
                 are
                 the
                 Logarythms
                 or
                 Indexes
                 ,
                 and
                 the
                 Amounts
                 are
                 the
                 Numbers
                 to
                 which
                 the
                 Logary
                 thms
                 belong
                 ,
                 and
                 because
                 this
                 is
                 no
                 full
                 Table
                 of
                 Logarythms
                 to
                 ten
                 or
                 one
                 hundred
                 thousand
                 ,
                 we
                 therefore
                 use
                 Multiplication
                 
                 and
                 Division
                 to
                 supply
                 those
                 Defects
                 ,
                 wherefore
                 the
                 first
                 Prop.
                 is
                 ;
              
               
                 
                   Prop.
                   1.
                   
                   
                     To
                     continue
                     the
                     said
                     Table
                  
                   .
                
                 
                   Multiply
                   the
                   Numbers
                   together
                   that
                   belong
                   to
                   any
                   Numbers
                   of
                   years
                   ,
                   that
                   added
                   together
                   make
                   the
                   years
                   of
                   Continuance
                   required
                   .
                
                 
                   
                     Example
                     .
                  
                   
                     Let
                     it
                     be
                     required
                     to
                     find
                     the
                     Amount
                     of
                     1
                     l.
                     for
                     50
                     years
                     .
                  
                   
                     
                       
                         
                           20
                           Years
                        
                         
                            
                        
                         
                           3,20713
                        
                      
                       
                         
                           30
                           Years
                        
                         
                            
                        
                         
                           5,74349
                        
                      
                       
                         
                           50
                           Years
                        
                         
                           
                             Product
                             is
                          
                        
                         
                           18,42015
                        
                      
                    
                  
                   
                     and
                     is
                     the
                     Number
                     sought
                     ,
                     omitting
                     the
                     five
                     superfluous
                     places
                     of
                     Decimals
                     .
                  
                
                 
                   
                   
                     Another
                     Example
                     .
                  
                   
                     It
                     is
                     required
                     to
                     find
                     the
                     Amount
                     of
                     1
                     l.
                     forborn
                     20
                     years
                     three
                     quarters
                     .
                  
                   
                     
                       
                         
                           20
                           
                             Years
                             is
                          
                        
                         
                           3,20713
                        
                      
                       
                         
                           9
                           Months
                        
                         
                           1,04467
                        
                      
                       
                         
                           
                             The
                             Product
                          
                        
                         
                           3,25180
                        
                      
                    
                  
                   
                     And
                     the
                     like
                     may
                     be
                     done
                     for
                     days
                     ,
                     and
                     the
                     Converse
                     when
                     an
                     Amount
                     is
                     given
                     ,
                     the
                     time
                     thereto
                     may
                     be
                     found
                     by
                     Division
                     ,
                     searching
                     in
                     the
                     Table
                     what
                     Number
                     amongst
                     the
                     Decimals
                     for
                     time
                     agrees
                     to
                     the
                     Divisors
                     and
                     last
                     Quote
                     .
                     See
                     Prop.
                     8.
                     the
                     First
                     Section
                     .
                  
                   
                     And
                     here
                     it
                     is
                     worth
                     noting
                     ,
                     That
                     many
                     Questions
                     may
                     be
                     put
                     concerning
                     Compound
                     Interest
                     ,
                     which
                     are
                     of
                     the
                     like
                     difficulty
                     ,
                     as
                     to
                     raise
                     the
                     printed
                     
                       Logarythmetical
                       Cannon
                    
                     .
                  
                
                 
                   
                   
                     For
                     Example
                     such
                     a
                     Question
                     may
                     be
                     put
                     ;
                  
                   
                     One
                     pound
                     was
                     put
                     out
                     at
                     Compound
                     Interest
                     ,
                     and
                     in
                     10
                     years
                     time
                     amounted
                     to
                     10
                     l.
                     in
                     what
                     space
                     of
                     time
                     did
                     it
                     amount
                     to
                     2
                     l.
                     the
                     answer
                     is
                     the
                     Logarythm
                     of
                     the
                     Number
                     two
                     (
                     to
                     wit
                     )
                     3,01023
                     years
                     which
                     was
                     not
                     raised
                     without
                     much
                     toyl
                     ,
                     and
                     the
                     rate
                     of
                     Interest
                     in
                     those
                     Logarythms
                     is
                     near
                     26
                     
                       l.
                       per
                       Cent.
                    
                     to
                     wit
                     25,89292
                     .
                  
                   
                     
                       The
                       Uses
                       of
                       the
                       said
                       Table
                       .
                    
                  
                
              
               
                 
                   Prop.
                   2.
                   
                   
                     A
                     Sum
                     forborn
                     for
                     any
                     time
                     ,
                     to
                     find
                     to
                     what
                     it
                     shall
                     amount
                     to
                     at
                  
                   6
                   l.
                   per
                   Cent.
                   
                     Compound
                     Interest
                  
                   .
                
                 
                   Find
                   in
                   the
                   Table
                   ,
                   or
                   Compute
                   by
                   1.
                   
                   Prop.
                   the
                   amount
                   of
                   1
                   l.
                   for
                   the
                   said
                   Time
                   ,
                   and
                   then
                   it
                   holds
                   .
                
                 
                 
                   As
                   1
                   l.
                   is
                   to
                   its
                   Amount
                   ;
                
                 
                   So
                   any
                   other
                   Sum
                   to
                   its
                   Amounts
                   :
                   Wherefore
                   the
                   Amount
                   of
                   1
                   l.
                   must
                   be
                   multiplyed
                   by
                   the
                   Sum
                   proposed
                   .
                
                 
                   
                     Example
                     .
                  
                   
                     What
                     shall
                     136
                     l.
                     15
                     s.
                     06
                     d.
                     amount
                     unto
                     being
                     forborn
                     20
                     years
                     at
                     6
                     
                       per
                       Centum
                    
                     ?
                  
                   
                     
                       
                         
                           The
                           Amount
                           of
                           1
                           l.
                           for
                        
                         
                           3,20713
                        
                      
                       
                         
                           20
                           years
                           is
                        
                      
                       
                         
                           Which
                           multiplied
                           by
                        
                         
                           136,775
                        
                      
                       
                         
                           The
                           Product
                           is
                        
                         
                           438,655
                        
                      
                    
                  
                   
                     Reduced
                     is
                     438
                     l.
                     13
                     s.
                     1
                     d.
                     4●
                  
                
              
               
                 
                   Prop.
                   3.
                   
                   
                     A
                     Sum
                     of
                     Money
                     due
                     hereafter
                     ,
                     to
                     find
                     what
                     it
                     is
                     worth
                     in
                     ready
                     Money
                     .
                  
                
                 
                   Find
                   in
                   the
                   Table
                   what
                   1
                   l.
                   forborn
                   ,
                   the
                   like
                   time
                   shall
                   amount
                   unto
                   at
                   Compound
                   Interest
                   ,
                   then
                   it
                   holds
                   .
                
                 
                 
                   As
                   the
                   said
                   Amount
                   is
                   to
                   an
                   Unit
                   ;
                
                 
                   So
                   is
                   any
                   Sum
                   propounded
                   ,
                   to
                   its
                   present
                   Worth.
                   
                
                 
                   Corollary
                   .
                   Therefore
                   if
                   an
                   Unit
                   be
                   the
                   Sum
                   whereof
                   you
                   would
                   find
                   the
                   present
                   Worth
                   ,
                   you
                   will
                   frame
                   the
                   Numbers
                   in
                   the
                   usual
                   Table
                   for
                   Discount
                   ,
                   and
                   for
                   all
                   other
                   Sums
                   :
                   Because
                   an
                   Unit
                   doth
                   not
                   Multiply
                   ,
                   it
                   will
                   follow
                   they
                   must
                   be
                   divided
                   by
                   the
                   Amount
                   of
                   1
                   l.
                   for
                   the
                   like
                   time
                   .
                
                 
                   Discount
                   ,
                   or
                   the
                   present
                   Worth
                   of
                   Money
                   due
                   hereafter
                   .
                
                 
                   
                     Example
                     first
                     ,
                     for
                     making
                     the
                     Table
                     of
                     Discount
                     .
                  
                   
                     An
                     Unit
                     divided
                     by
                     3,20713
                     ,
                     the
                     Quotient
                     is
                     311804
                     ,
                     the
                     present
                     Worth
                     of
                     1
                     l
                     due
                     20
                     years
                     hence
                     .
                  
                
                 
                   
                     Example
                     second
                     .
                  
                   
                     If
                     400
                     l.
                     be
                     due
                     20
                     years
                     hence
                     ,
                     
                     What
                     is
                     it
                     worth
                     in
                     ready
                     Money
                     ,
                     abating
                     Compound
                     Interest
                     at
                     6
                     
                       per
                       Centum
                       per
                       Annum
                    
                     ?
                  
                   
                     Divide
                     400
                     by
                     3,20713
                     ,
                     the
                     Amount
                     of
                     1
                     l.
                     forborn
                     20
                     years
                     at
                     Compound
                     Interest
                     ,
                     and
                     the
                     Quotient
                     is
                     124
                     l.
                     722
                     ,
                     or
                     124
                     l.
                     14
                     s.
                     5
                     d.
                     ¼
                     And
                     how
                     to
                     reduce
                     sundry
                     Payments
                     ,
                     to
                     an
                     Equation
                     of
                     time
                     at
                     Compound
                     Interest
                     .
                     See
                     
                       first
                       Example
                    
                     of
                     Prop.
                     8.
                     
                  
                
              
               
                 
                   Prop.
                   4.
                   
                   
                     Of
                     Forbearance
                     of
                     Annuities
                     .
                     To
                     find
                     the
                     Arrearages
                     of
                     an
                     Annuity
                     .
                  
                
                 
                   The
                   Difference
                   between
                   the
                   Forbearance
                   of
                   an
                   Annuity
                   ,
                   and
                   of
                   a
                   Principal
                   put
                   out
                   to
                   Interest
                   ,
                   is
                   this
                   ,
                   that
                   every
                   year
                   there
                   is
                   a
                   Principal
                   like
                   the
                   first
                   added
                   .
                
                 
                   The
                   Proportion
                   holds
                   .
                
                 
                   As
                   ,
                   06
                   the
                   Compound
                   Interest
                   of
                   1.
                   l.
                   for
                   a
                   year
                   ,
                   is
                   to
                   the
                   Amount
                   less
                   
                   by
                   an
                   Unit
                   of
                   one
                   of
                   one
                   pound
                   forborn
                   at
                   Compound
                   Interest
                   for
                   the
                   time
                   proposed
                   .
                
                 
                   So
                   is
                   any
                   Annuity
                   or
                   yearly
                   payment
                   of
                   Rent
                   forborn
                   the
                   like
                   time
                   ,
                   and
                   at
                   the
                   same
                   Rate
                   ,
                   to
                   the
                   Arrearages
                   thereof
                   due
                   .
                   And
                   when
                   the
                   Rent
                
                 
                   
                     
                       
                         is
                         payable
                      
                       
                         Half-yearly
                         ,
                      
                    
                     
                       
                         Quarterly
                         ,
                      
                    
                  
                
                 
                   the
                   first
                   term
                   in
                   the
                   proportion
                   must
                
                 
                   
                     
                       
                         be
                         the
                         Compound
                         Interest
                         of
                         1
                         l.
                         for
                         acordingly
                         ,
                         &c.
                         
                      
                       
                         Half
                         a
                         year
                         ,
                      
                    
                     
                       
                         Quarter
                         ,
                      
                    
                  
                
                 
                   
                     Example
                     .
                  
                   
                     Let
                     it
                     be
                     required
                     to
                     find
                     what
                     one
                     pound
                     a
                     year
                     Annuity
                     forborn
                     for
                     30
                     years
                     at
                     6
                     
                       per
                       Centum
                    
                     shall
                     amount
                     to
                     .
                  
                   
                     One
                     pound
                     forborn
                     at
                     Compound
                     Interest
                     so
                     long
                     amounts
                     to
                     5
                     ,
                     74349
                     which
                     lessened
                     by
                     an
                     Unit
                     is
                     4
                     ,
                     74349
                     which
                     divided
                     by
                     06
                     ,
                     the
                     Quotient
                     is
                     79
                     ,
                     0581
                     and
                     this
                     is
                     the
                     Number
                     
                     found
                     in
                     the
                     Vulgar
                     Tables
                     for
                     forbearance
                     of
                     Annuities
                     .
                  
                
                 
                   
                     Second
                     Example
                     .
                  
                   
                     Let
                     it
                     be
                     required
                     to
                     find
                     what
                     20
                     l.
                     Annuity
                     forborn
                     for
                     15
                     years
                     shall
                     amount
                     unto
                     at
                     6
                     
                       per
                       Centum
                    
                     .
                  
                   
                     1
                     l.
                     Principal
                     forborn
                     15
                     years
                     amounts
                     to
                     2
                     ,
                     39655
                     from
                     which
                     subtracting
                     an
                     Unite
                     it
                     holds
                     .
                  
                   
                     As
                     ,
                     06
                     to
                     1,39655
                     so
                     20
                     to
                     465
                     ,
                     516
                     ,
                     that
                     is
                     475
                     l.
                     10
                     s.
                     4
                     d.
                     
                  
                
                 
                   
                     Third
                     Example
                     .
                  
                   
                     A
                     Quarterly
                     Rent
                     of
                     25
                     l.
                     was
                     respited
                     20¾
                     years
                     ,
                     by
                     the
                     first
                     Proportion
                     the
                     amount
                     of
                     1
                     l.
                     so
                     long
                     forborn
                     was
                     3
                     ,
                     34978.
                     
                     And
                     the
                     Interest
                     of
                     one
                     pound
                     for
                     a
                     quarter
                     is
                     0
                     ,
                     14675
                     Wherefore
                     by
                     Proportion
                     ,
                     As
                     ,
                     014675
                     Is
                     to
                     2
                     ,
                     34978
                     :
                     So
                     is
                     25
                     to
                     4003
                     ,
                     032
                     that
                     is
                     4003
                     l.
                     00
                     s.
                     7¾
                     d.
                     
                  
                   
                   
                     
                       This
                       Useful
                       Proportion
                       I
                       thus
                       demonstrate
                       which
                       the
                       Reader
                       may
                       pass
                       by
                       .
                    
                  
                   
                     Imagine
                     the
                     Land
                     or
                     Stock
                     that
                     yields
                     an
                     Annuity
                     to
                     be
                     such
                     a
                     Principal
                     sent
                     out
                     for
                     the
                     whole
                     term
                     as
                     will
                     bring
                     in
                     so
                     much
                     yearly
                     Interest
                     as
                     the
                     Annuity
                     comes
                     to
                     ,
                     then
                     at
                     last
                     the
                     whole
                     at
                     Compound
                     Interest
                     is
                     to
                     be
                     repaid
                     ,
                     whereof
                     so
                     much
                     is
                     supposed
                     to
                     be
                     repaid
                     in
                     the
                     Value
                     of
                     the
                     Land
                     ,
                     as
                     its
                     first
                     Principal
                     came
                     to
                     ,
                     and
                     the
                     rest
                     in
                     Money
                     ;
                     wherefore
                     out
                     of
                     the
                     whole
                     Amount
                     of
                     that
                     Principal
                     and
                     its
                     Interest
                     ,
                     the
                     Principal
                     must
                     be
                     deducted
                     unless
                     to
                     shun
                     it
                     by
                     that
                     which
                     Geometers
                     call
                     conversion
                     .
                     See
                     Commentators
                     on
                     16
                     
                       Def.
                       Quinti
                       Euclidis
                    
                     &c.
                     we
                     say
                     ,
                  
                   
                     As
                     the
                     first
                     term
                     is
                     to
                     the
                     difference
                     of
                     the
                     first
                     and
                     second
                     ;
                  
                   
                     So
                     the
                     Third
                     Term
                     to
                     the
                     difference
                     
                     of
                     the
                     third
                     and
                     fourth
                     .
                  
                   
                     The
                     Plain
                     Proportion
                     grounded
                     upon
                     the
                     former
                     Considerations
                     runs
                     thus
                     ,
                  
                   
                     As
                     1
                     l.
                     Principal
                     .
                     Is
                     to
                     its
                     Amount
                     for
                     the
                     time
                     forborn
                     ;
                  
                   
                     So
                     the
                     Principal
                     that
                     shall
                     bring
                     in
                     any
                     Annuity
                     proposed
                     .
                     To
                     the
                     Sum
                     of
                     the
                     said
                     Principal
                     and
                     of
                     the
                     Arrearages
                     of
                     the
                     Annuity
                     .
                  
                   
                     Then
                     it
                     will
                     hold
                     by
                     conversion
                     of
                     Reason
                     .
                     As
                     1
                     l.
                     forborn
                     at
                     Compound
                     Interest
                     is
                     to
                     its
                     Amount
                     less
                     by
                     an
                     Unit
                     for
                     the
                     time
                     forborn
                     ;
                  
                   
                     So
                     is
                     the
                     Principal
                     of
                     an
                     Annuity
                     ,
                     forborn
                     the
                     like
                     time
                     ,
                  
                   
                     To
                     the
                     Arrearages
                     of
                     the
                     Annuity
                     .
                  
                   
                     And
                     instead
                     of
                     the
                     third
                     term
                     of
                     this
                     Proportion
                     ,
                     we
                     may
                     take
                     in
                     a
                     fraction
                     equivalent
                     thereto
                     ,
                     the
                     Numerator
                     whereof
                     is
                     the
                     Annuity
                     or
                     yearly
                     payment
                     of
                     Rent
                     ,
                     and
                     the
                     Denominator
                     the
                     Interest
                     of
                     1
                     l.
                     for
                     a
                     year
                     ;
                     for
                     to
                     find
                     the
                     Principal
                     of
                     an
                     Annuity
                     say
                     ,
                  
                   
                   
                     As
                     6
                     is
                     to
                     100.
                     
                     Or
                     rather
                     ,
                     06
                     :
                     1.
                     
                  
                   
                     So
                     is
                     the
                     Annuity
                     to
                     its
                     Principal
                     .
                  
                   
                     And
                     both
                     these
                     latter
                     Proportions
                     compounded
                     into
                     one
                     will
                     be
                     the
                     proportion
                     first
                     delivered
                     ,
                     the
                     Units
                     in
                     each
                     being
                     expunged
                     as
                     insignificant
                     either
                     in
                     Multiplication
                     or
                     Division
                     .
                  
                
              
               
                 
                   Prop.
                   5.
                   
                   
                     To
                     find
                     the
                     present
                     worth
                     of
                     an
                     Annuity
                     .
                  
                
                 
                   If
                   an
                   Annuity
                   be
                   forborn
                   till
                   the
                   last
                   payment
                   be
                   due
                   ,
                   then
                   for
                   as
                   much
                   as
                   the
                   Interest
                   of
                   each
                   particular
                   payment
                   is
                   by
                   the
                   former
                   or
                   4th
                   .
                   Proposition
                   computed
                   ,
                   if
                   by
                   the
                   3d.
                   Proportion
                   the
                   same
                   ,
                   together
                   with
                   the
                   rebate
                   of
                   each
                   payment
                   be
                   destroyed
                   (
                   to
                   wit
                   )
                   the
                   present
                   worth
                   of
                   the
                   whole
                   Arrearage
                   be
                   computed
                   it
                   shall
                   be
                   the
                   present
                   worth
                   of
                   the
                   Annuity
                   ,
                   the
                   Proportion
                   in
                   both
                   those
                   Propositions
                   being
                   after
                   the
                   manner
                   of
                   the
                   
                   4th
                   .
                   prop.
                   composed
                   into
                   one
                   it
                   will
                   hold
                   for
                   Annual
                   payments
                   at
                   6
                   
                     per
                     Centum
                  
                   .
                
                 
                   As
                   the
                   fact
                   of
                   (
                   ,06
                   )
                   the
                   Interest
                   of
                   1
                   l.
                   for
                   a
                   year
                   ,
                   and
                   of
                   the
                   Amount
                   of
                   one
                   pound
                   Compound
                   Interest
                   for
                   the
                   time
                   proposed
                   ,
                   is
                   to
                   the
                   said
                   Amount
                   less
                   an
                   Unit.
                   
                
                 
                   So
                   is
                   the
                   Annuity
                   or
                   yearly
                   Rent
                   to
                   the
                   present
                   worth
                   thereof
                   .
                
                 
                   
                     Example
                     .
                     First
                     for
                     making
                     the
                     Tables
                     .
                  
                   
                     To
                     find
                     the
                     present
                     worth
                     of
                     an
                     Annuity
                     of
                     1
                     
                       l.
                       per
                       Annum
                    
                     ,
                     to
                     continue
                     25
                     years
                     at
                     6
                     
                       per
                       Centum
                    
                     compound
                     Interest
                     .
                  
                   
                     The
                     Amount
                     of
                     1
                     l.
                     for
                     that
                     time
                     is
                     4,29187
                     which
                     Multiplyed
                     by
                     ,06
                     the
                     fact
                     is
                     ,257512
                     ,
                     whereby
                     dividing
                     3,29187
                     the
                     Quote
                     is
                     12
                     l.
                     ,78335
                     the
                     present
                     worth
                     sought
                     .
                  
                
                 
                   
                   
                     Example
                     .
                     Secondly
                     for
                     half-yearly
                     Payments
                     .
                  
                   
                     An
                     Annuity
                     of
                     40
                     l.
                     payable
                     ,
                     20
                     l.
                     each
                     half
                     year
                     is
                     to
                     befold
                     for
                     12
                     years
                     at
                     6
                     
                       per
                       Centum
                    
                     .
                  
                   
                     
                       
                         
                           The
                           Compound
                           Interst
                           of
                           1
                           l.
                           for
                           half
                           a
                           year
                           is
                           —
                        
                         
                           ,029564
                        
                      
                       
                         
                           The
                           amount
                           of
                           1
                           l.
                           forborn
                           12
                           years
                           —
                        
                         
                           2,012196
                        
                      
                    
                  
                   
                     Multiply
                     these
                     two
                     together
                     ,
                     and
                     that
                     added
                     together
                     makes
                     the
                     fact
                     of
                     both
                     ;
                  
                   
                     Which
                     is
                     —
                     ,058487
                     It
                     therefore
                     holds
                     ,
                  
                   
                     As
                     ,058487
                     is
                     to
                     ,1,012196
                     .
                  
                   
                     So
                     is
                     20
                     to
                     346
                     ,
                     166
                     that
                     is
                     346
                     l.
                     3
                     s.
                     4
                     d.
                     the
                     present
                     worth
                     thereof
                     .
                  
                   
                     
                       
                         
                           If
                           this
                           Annuity
                           were
                           paid
                           yearly
                           it
                           
                           must
                           be
                           of
                           less
                           Value
                           because
                           the
                           mony
                           is
                           longer
                           in
                           coming
                           in
                           ,
                           and
                           accordingly
                           the
                           worth
                           of
                           it
                        
                         
                           
                             l.
                             s.
                             d.
                          
                           
                        
                      
                       
                         
                           would
                           be
                           but
                           —
                        
                         
                           335
                           —
                           7
                           —
                           1
                        
                      
                       
                         
                           Admit
                           it
                           were
                           required
                           to
                           know
                           what
                           an
                           addition
                           of
                           8
                           years
                           more
                           is
                           worth
                           after
                           12
                           are
                           expired
                           .
                        
                         
                            
                        
                      
                       
                         
                           The
                           worth
                           of
                           the
                           said
                           Annuity
                           for
                           20
                           years
                           ,
                           is
                           —
                        
                         
                           458.
                           15.
                           11
                        
                      
                       
                         
                           The
                           difference
                           of
                           these
                           two
                           is
                           —
                           being
                           the
                           present
                           worth
                           of
                           the
                           8
                           years
                           sought
                           .
                        
                         
                           123.
                           8.
                           10
                        
                      
                    
                  
                
              
               
                 
                   Prop.
                   6.
                   
                   
                     To
                     find
                     what
                     Annuity
                     any
                     Sum
                     of
                     ready
                     Money
                     shall
                     purchase
                     .
                  
                
                 
                   This
                   is
                   but
                   the
                   Converse
                   of
                   the
                   former
                   Proposition
                   ,
                   and
                   it
                   holds
                   therefore
                   ;
                
                 
                 
                   As
                   the
                   Amount
                   of
                   1
                   l.
                   forborn
                   at
                   Compound
                   Interest
                   less
                   an
                   Unit
                   is
                   to
                   the
                   fact
                   of
                   ,
                   06
                   and
                   of
                   the
                   Amount
                   of
                   one
                   pound
                   so
                   forborn
                   ,
                
                 
                   So
                   is
                   any
                   Sum
                   of
                   ready
                   mony
                   to
                   the
                   Annuity
                   it
                   shall
                   purchase
                   .
                
                 
                   In
                   this
                   and
                   the
                   two
                   former
                   propositions
                   by
                   ,06
                   is
                   understood
                   the
                   Compound
                   Interest
                   of
                   1
                   l.
                   for
                   a
                   year
                   ,
                   and
                   when
                   the
                   payment
                   is
                   by
                   quarters
                   or
                   half
                   years
                   ,
                   instead
                   thereof
                   must
                   be
                   put
                   in
                   the
                   Interest
                   of
                   a
                   quarter
                   or
                   half
                   a
                   year
                   .
                   And
                   instead
                   of
                   the
                   Annuity
                   or
                   yearly
                   payment
                   ,
                   the
                   Quarterly
                   or
                   Half-yearly
                   payment
                   accordingly
                   .
                
                 
                   
                     Corollary
                     .
                  
                   
                     If
                     1
                     l.
                     be
                     the
                     sum
                     of
                     ready
                     mony
                     then
                     the
                     two
                     middle
                     Terms
                     of
                     the
                     proportion
                     are
                     the
                     fact
                     above
                     mentioned
                     ,
                     and
                     you
                     will
                     frame
                     the
                     other
                     Vulgar
                     Table
                     for
                     this
                     purpose
                     .
                  
                
                 
                   
                   
                     Example
                     the
                     first
                     .
                  
                   
                     To
                     find
                     what
                     Annuity
                     1
                     l.
                     shall
                     purchase
                     to
                     continue
                     30
                     years
                     ,
                     it
                     holds
                     ;
                  
                   
                     As
                     4,74349
                     to
                     ,06
                     .
                     So
                     5,74349
                     to
                     0,07264
                     .
                  
                
                 
                   
                     Example
                     Second
                     .
                  
                   
                     Let
                     it
                     be
                     required
                     to
                     find
                     what
                     rent
                     payable
                     yearly
                     8
                     l.
                     shall
                     purchase
                     at
                     6
                     
                       per
                       Centum
                    
                     to
                     continue
                     21
                     years
                     .
                  
                   
                     As
                     2,39956
                     the
                     Amount
                     less
                     an
                     Unit
                     of
                     1
                     l.
                     for
                     21
                     years
                     is
                     to
                     ,20397
                     the
                     fact
                     of
                     ,06
                     and
                     the
                     amount
                     ,
                  
                   
                     So
                     is
                     8
                     to
                     ,68
                     or
                     13
                     s.
                     7¼
                     d.
                     the
                     Annuity
                     sought
                     .
                  
                   
                     Memorandum
                     ,
                     That
                     by
                     the
                     Fact
                     is
                     meant
                     that
                     you
                     should
                     multiply
                     the
                     foregoing
                     Figures
                     by
                     ,06
                     .
                     Viz.
                     2,39956
                     by
                     ,06
                     ,
                  
                   
                     Which
                     makes
                     2,2039736
                     .
                  
                   
                   
                     Now
                     whereas
                     the
                     Lease
                     of
                     a
                     house
                     of
                     1
                     
                       l.
                       per
                       Annum
                    
                     to
                     continue
                     21
                     years
                     is
                     commonly
                     sold
                     for
                     8
                     l.
                     or
                     8
                     years
                     purchase
                     ,
                     and
                     your
                     mony
                     will
                     purchase
                     a
                     certainty
                     but
                     of
                     13
                     s.
                     7
                     d.
                     ●
                     
                       per
                       Annum
                    
                     ,
                     you
                     see
                     by
                     this
                     supposition
                     you
                     are
                     abated
                     6
                     s.
                     5
                     d.
                     3
                     /
                     ●nt
                     of
                     Taxes
                     Reparations
                     and
                     Casualties
                     ;
                     and
                     verygood
                     Reason
                     there
                     is
                     for
                     great
                     abatements
                     ,
                     for
                     a
                     Tenant
                     taking
                     a
                     Lease
                     on
                     a
                     Tunber
                     house
                     ,
                     if
                     it
                     be
                     burnt
                     down
                     by
                     a
                     Fire
                     beginning
                     at
                     his
                     Neighbours
                     as
                     leases
                     commonly
                     Run
                     ,
                     is
                     bound
                     to
                     build
                     it
                     up
                     again
                     and
                     hath
                     no
                     relief
                     either
                     in
                     Law
                     or
                     Equity
                     against
                     his
                     Landlord
                     ,
                     as
                     I
                     am
                     informed
                     by
                     able
                     Council
                     ,
                     only
                     he
                     hath
                     the
                     benefit
                     of
                     a
                     Benevolence
                     ,
                     his
                     Action
                     against
                     them
                     where
                     the
                     fire
                     began
                     (
                     who
                     perchance
                     are
                     ruined
                     .
                     )
                  
                   
                   
                     
                       
                         
                           s.
                           
                        
                         
                            
                        
                         
                           
                             s.
                             d.
                          
                           
                        
                      
                       
                         
                            
                        
                         
                           will
                           purchase
                           an
                        
                         
                           —
                           11
                           —
                           11
                        
                      
                       
                         
                           10
                        
                         
                           Annuity
                           to
                           continue
                           21
                           years
                           of
                        
                         
                           —
                           12
                           —
                           9
                        
                      
                       
                         
                           10
                        
                         
                            
                        
                         
                           —
                           14
                           —
                           5½
                        
                      
                       
                         
                            
                        
                         
                            
                        
                         
                           —
                           15
                        
                      
                       
                         
                            
                        
                         
                            
                        
                         
                           —
                           17
                        
                      
                       
                         
                            
                        
                         
                            
                        
                         
                           1
                           —
                           5
                           —
                           3½
                           —
                           1-00-0
                        
                      
                    
                  
                   
                     Hence
                     it
                     appears
                     that
                     the
                     Value
                     of
                     Leases
                     of
                     Houses
                     cannot
                     be
                     estimated
                     near
                     the
                     Truth
                     by
                     the
                     Common
                     Tables
                     for
                     Annuities
                     at
                     the
                     currant
                     rate
                     of
                     Interest
                     ,
                     and
                     that
                     if
                     any
                     one
                     would
                     use
                     them
                     to
                     this
                     purpose
                     it
                     were
                     much
                     nearer
                     the
                     truth
                     first
                     to
                     abridge
                     the
                     Rent
                     as
                     aforesaid
                     .
                  
                
              
               
                 
                   Prop.
                   7.
                   
                   
                     Any
                     number
                     of
                     years
                     in
                     a
                     Lease
                     or
                     Annuity
                     being
                     propounded
                     to
                     find
                     the
                     present
                     Worth
                     of
                     any
                     greater
                     or
                     lesser
                     Number
                     of
                     years
                     therein
                     .
                  
                
                 
                   This
                   is
                   one
                   of
                   the
                   most
                   usual
                   and
                   useful
                   Propositions
                   of
                   this
                   Nature
                   ,
                   and
                   
                   as
                   propounded
                   is
                   not
                   sufficiently
                   Limited
                   ,
                   and
                   the
                   Question
                   in
                   this
                   Cas●
                   will
                   be
                   ,
                   What
                   is
                   the
                   most
                   equitable
                   rate
                   of
                   Interest
                   whereby
                   to
                   resolve
                   the
                   Proposition
                   ;
                   to
                   find
                   out
                   which
                   it
                   is
                   either
                   necessary
                   to
                   assign
                   how
                   many
                   years
                   purchase
                   the
                   Fee
                   Simple
                   or
                   Inheritance
                   is
                   worth
                   ,
                   or
                   the
                   present
                   Worth
                   of
                   a
                   Lease
                   of
                   any
                   Number
                   of
                   years
                   therein
                   .
                
                 
                   1.
                   
                   If
                   the
                   Worth
                   of
                   the
                   Inheritance
                   be
                   assigned
                   ,
                   then
                   thereby
                   divide
                   100
                   the
                   Quote
                   shews
                   the
                   Annual
                   Interest
                   for
                   .
                
                 
                   
                     Example
                     :
                  
                   
                     Let
                     the
                     Fee
                     Simple
                     or
                     Copy-hold
                     Lands
                     be
                     worth
                     16
                     years
                     8
                     months
                     Purchase
                     ,
                     then
                     dividing
                     100
                     by
                     16⅔
                     the
                     Quotient
                     is
                     6
                     ,
                     whereof
                     6
                     pound
                     in
                     the
                     100
                     is
                     an
                     equitable
                     Rate
                     of
                     Interest
                     whereby
                     to
                     compute
                     the
                     present
                     worth
                     of
                     a
                     Lease
                     of
                     any
                     number
                     of
                     
                     years
                     therein
                     ,
                     and
                     so
                     
                       è
                       contra
                    
                     if
                     mony
                     were
                     at
                     8
                     
                       per
                       Centum
                    
                     ,
                     the
                     Laws
                     of
                     Arithmetick
                     allow
                     the
                     worth
                     of
                     the
                     Inheritance
                     of
                     the
                     best
                     Land
                     that
                     is
                     ,
                     to
                     be
                     but
                     12½
                     years
                     Purchase
                     ,
                     which
                     some
                     would
                     confirm
                     ,
                     from
                     this
                     reason
                     ,
                     because
                     otherwise
                     their
                     money
                     would
                     yield
                     a
                     better
                     income
                     at
                     Simple
                     or
                     Compound
                     Interest
                     ,
                     but
                     the
                     most
                     proper
                     Reason
                     is
                     derived
                     from
                     the
                     Nature
                     of
                     a
                     Geometrical
                     Progression
                     decreasing
                     
                       ad
                       Infinitum
                    
                     ;
                     for
                     instance
                     ,
                     admit
                     you
                     have
                     a
                     Tenant
                     in
                     the
                     Tenure
                     or
                     Possession
                     of
                     1
                     
                       l.
                       per
                       Annum
                    
                     ,
                     and
                     you
                     say
                     to
                     him
                     ,
                     pay
                     the
                     rent
                     now
                     that
                     will
                     be
                     due
                     at
                     the
                     end
                     of
                     
                       
                         
                           1
                        
                         
                           Years
                           ,
                           &c.
                           
                             ad
                             infinitum
                          
                           .
                        
                      
                       
                         
                           2
                        
                      
                       
                         
                           3
                        
                      
                       
                         
                           4
                        
                      
                    
                     and
                     you
                     will
                     rebate
                     him
                     after
                     the
                     rate
                     of
                     Compound
                     Interest
                     .
                     I
                     say
                     the
                     Total
                     of
                     all
                     those
                     Payments
                     shall
                     never
                     exceed
                     12
                     l.
                     10
                     s.
                     00
                     d.
                     
                  
                   
                   
                     
                       The
                       Proportion
                       for
                       casting
                       up
                       the
                       sum
                       of
                       a
                       sinite
                       Geometrical
                       Progression
                       runs
                       thus
                       ,
                    
                  
                   
                     As
                     the
                     difference
                     of
                     an
                     assumed
                     extreme
                     and
                     its
                     next
                     inward
                     mean
                     is
                     to
                     the
                     next
                     inward
                     mean
                     ;
                  
                   
                     So
                     is
                     the
                     difference
                     of
                     the
                     remote
                     extremes
                     to
                     the
                     sum
                     of
                     the
                     Progression
                     ,
                     except
                     the
                     assumed
                     extreme
                     .
                  
                   
                     The
                     reason
                     wherof
                     is
                     ,
                     That
                     if
                     a
                     rank
                     of
                     Numbers
                     be
                     in
                     Geometrical
                     Progression
                     their
                     sums
                     and
                     differences
                     are
                     likewise
                     in
                     the
                     same
                     Proportion
                     .
                     See
                     35
                     of
                     9
                     Book
                     of
                     Euclid
                     ,
                     or
                     Briggs
                     his
                     
                       Arithmetica
                       Logarithmica
                    
                     .
                  
                
                 
                   
                     Example
                     .
                  
                   
                     
                       
                         
                           6
                           ,
                        
                         
                           18
                           ,
                        
                         
                           54
                           ,
                        
                         
                           162
                           ,
                        
                         
                           486
                           ,
                        
                         
                            
                        
                      
                       
                         
                           3
                           ,
                        
                         
                           9
                           ,
                        
                         
                           27
                           ,
                        
                         
                           81
                           ,
                        
                         
                           243
                           ,
                        
                         
                           729
                        
                      
                    
                  
                   
                     
                       
                         
                           Wherefore
                           it
                           holds
                           by
                           Euclid
                           .
                        
                         
                           6
                        
                      
                       
                         
                           As
                           one
                           difference
                        
                      
                       
                         
                           Is
                           to
                           its
                           Consequent
                           —
                        
                         
                           9
                        
                      
                       
                       
                         
                           So
                           is
                           the
                           Sum
                           of
                           all
                           the
                           differences
                           (
                           which
                           is
                           here
                           the
                           difference
                           between
                           the
                           first
                           and
                           last
                           term
                           )
                           —
                        
                         
                           726
                        
                      
                    
                  
                   
                     To
                     the
                     Sum
                     of
                     all
                     the
                     Consequents
                     is
                     1089.
                     
                  
                   
                     Wherefore
                     the
                     sum
                     of
                     the
                     whole
                     progression
                     is
                     —
                     1092.
                     
                  
                   
                     And
                     supposing
                     this
                     Progression
                     to
                     decrease
                     infinitely
                     ,
                     then
                     will
                     the
                     first
                     term
                     be
                     o
                     ,
                     and
                     the
                     sum
                     of
                     all
                     the
                     Differences
                     729
                     ,
                     and
                     it
                     holds
                     .
                     As
                     
                  
                   
                     Wherefore
                     the
                     sum
                     of
                     this
                     infinite
                     Progression
                     is
                     1093½
                     ,
                     and
                     can
                     never
                     exceed
                     it
                     ,
                     and
                     the
                     said
                     progression
                     continued
                     but
                     in
                     part
                     towards
                     the
                     left
                     hand
                     ,
                     would
                     stand
                     thus
                     ,
                     &c.
                     
                     1
                     /
                     729
                     1
                     /
                     243
                     1
                     /
                     81
                     1
                     /
                     27
                     1
                     /
                     9
                     ⅓
                     I.
                     
                  
                   
                     2.
                     
                     But
                     admit
                     the
                     present
                     worth
                     of
                     a
                     Lease
                     for
                     a
                     certain
                     number
                     of
                     years
                     be
                     given
                     ,
                     some
                     third
                     term
                     must
                     be
                     further
                     
                     given
                     ,
                     let
                     that
                     be
                     the
                     yearly
                     rent
                     ,
                     and
                     then
                     you
                     cannot
                     assign
                     the
                     rate
                     ;
                     (
                     and
                     the
                     contrary
                     )
                     in
                     this
                     Case
                     to
                     find
                     the
                     rate
                     is
                     one
                     of
                     the
                     most
                     difficult
                     Questions
                     that
                     commonly
                     happens
                     about
                     Annuities
                     ,
                     because
                     the
                     Proposition
                     in
                     the
                     5
                     ,
                     6
                     ,
                     (
                     also
                     
                       4th
                       .
                    
                     )
                     Prop.
                     will
                     not
                     hold
                     conversly
                     ,
                     there
                     are
                     but
                     two
                     terms
                     in
                     the
                     Proposition
                     given
                     ,
                     which
                     contain
                     but
                     a
                     bare
                     
                       ratio
                       ,
                       &c.
                    
                     therefore
                     though
                     out
                     of
                     Tables
                     of
                     Forbearance
                     of
                     Money
                     at
                     compound
                     Interest
                     ,
                     you
                     can
                     make
                     those
                     for
                     Annuities
                     ,
                     yet
                     the
                     converse
                     will
                     not
                     hold
                     .
                  
                   
                     In
                     this
                     Case
                     you
                     must
                     either
                     by
                     help
                     of
                     the
                     5
                     Prop.
                     and
                     common
                     Logarithms
                     ,
                     or
                     of
                     Tables
                     of
                     the
                     present
                     worth
                     of
                     Annuities
                     ,
                     calculated
                     to
                     the
                     best
                     rate
                     that
                     shall
                     suit
                     the
                     Inheritance
                     ,
                     find
                     the
                     present
                     worth
                     of
                     the
                     Number
                     of
                     years
                     proposed
                     according
                     to
                     two
                     rates
                     assumed
                     as
                     near
                     the
                     truth
                     as
                     you
                     can
                     possible
                     ,
                     and
                     then
                     if
                     you
                     have
                     not
                     lighted
                     upon
                     the
                     given
                     
                     worth
                     of
                     the
                     years
                     assigned
                     ,
                     use
                     the
                     help
                     of
                     this
                     Approximation
                     .
                  
                   
                     As
                     the
                     difference
                     of
                     the
                     present
                     worths
                     found
                     ,
                     is
                     to
                     the
                     difference
                     of
                     the
                     assumed
                     rates
                     of
                     Interest
                     ;
                  
                   
                     So
                     the
                     difference
                     between
                     the
                     given
                     worth
                     and
                     the
                     truest
                     of
                     those
                     Tryal
                     worths
                     ;
                  
                   
                     To
                     the
                     difference
                     between
                     the
                     rate
                     of
                     Interest
                     of
                     the
                     tryal
                     worth
                     and
                     that
                     sought
                     .
                  
                   
                     And
                     when
                     the
                     rate
                     of
                     Interest
                     is
                     truly
                     found
                     ,
                     compute
                     accordingly
                     the
                     present
                     worth
                     of
                     the
                     years
                     sought
                     .
                  
                   
                     But
                     this
                     were
                     to
                     send
                     away
                     the
                     Reader
                     ,
                     as
                     if
                     we
                     could
                     in
                     this
                     Case
                     give
                     no
                     answer
                     to
                     the
                     question
                     ,
                     by
                     help
                     of
                     the
                     table
                     here
                     used
                     ;
                     whereto
                     I
                     answer
                     ,
                     That
                     if
                     the
                     worth
                     of
                     the
                     Inheritance
                     be
                     assigned
                     ,
                     repair
                     to
                     the
                     following
                     Proposition
                     .
                  
                   
                     But
                     if
                     not
                     ,
                     let
                     the
                     Casualty
                     as
                     in
                     the
                     6th
                     .
                     Proposition
                     be
                     reduced
                     to
                     a
                     certainty
                     ;
                     viz.
                     if
                     it
                     concern
                     the
                     Lease
                     of
                     a
                     house
                     which
                     is
                     a
                     Casualty
                     ,
                     abridge
                     
                     the
                     Annual
                     Rent
                     ,
                     and
                     then
                     you
                     may
                     by
                     the
                     
                       5th
                       .
                       Prop.
                    
                     cast
                     up
                     the
                     Value
                     of
                     any
                     Number
                     of
                     Years
                     therein
                     .
                  
                   
                     But
                     herein
                     I
                     would
                     not
                     be
                     misunderstood
                     ,
                     as
                     if
                     when
                     a
                     Lease
                     of
                     a
                     House
                     of
                     1
                     l.
                     yearly
                     for
                     21
                     Years
                     is
                     sold
                     for
                     8
                     l.
                     10
                     s.
                     the
                     which
                     will
                     purchase
                     an
                     Annuity
                     or
                     Certainty
                     of
                     14
                     s.
                     5
                     ½
                     
                       per
                       Annum
                    
                     ,
                     and
                     any
                     Number
                     of
                     years
                     in
                     this
                     Certainty
                     shall
                     be
                     equivolent
                     to
                     as
                     many
                     in
                     that
                     Casualty
                     ,
                     that
                     therefore
                     Tables
                     made
                     to
                     both
                     Rates
                     ,
                     and
                     a
                     Computation
                     to
                     both
                     the
                     Yearly
                     Rents
                     must
                     needs
                     agree
                     ,
                     because
                     all
                     Tables
                     of
                     Annuities
                     are
                     made
                     for
                     Certainties
                     not
                     Casualties
                     .
                  
                   
                     Or
                     lastly
                     ,
                     repair
                     to
                     the
                     first
                     and
                     last
                     Prop.
                     and
                     you
                     will
                     there
                     find
                     how
                     to
                     cast
                     up
                     the
                     Amount
                     of
                     1
                     l.
                     Principal
                     for
                     any
                     time
                     ,
                     and
                     at
                     any
                     Rate
                     ,
                     where
                     the
                     true
                     manner
                     of
                     such
                     Equations
                     is
                     shewed
                     .
                  
                   
                     In
                     this
                     second
                     Case
                     is
                     couched
                     two
                     usual
                     Questions
                     ,
                     most
                     commoly
                     propounded
                     
                     without
                     sufficient
                     Limits
                     :
                     As
                     ,
                  
                   
                     1.
                     
                     When
                     a
                     Lease
                     is
                     sunk
                     by
                     a
                     Fine
                     to
                     a
                     certain
                     Yearly
                     Rent
                     ,
                     for
                     a
                     certain
                     term
                     of
                     time
                     ,
                     What
                     the
                     whole
                     Lease
                     is
                     worth
                     :
                     Or
                     ,
                  
                   
                     2.
                     
                     What
                     any
                     number
                     of
                     years
                     to
                     be
                     added
                     ,
                     after
                     the
                     term
                     in
                     Lease
                     is
                     expired
                     ,
                     is
                     worth
                     .
                  
                   
                     In
                     Order
                     to
                     the
                     Resolution
                     of
                     either
                     of
                     these
                     Questions
                     it
                     must
                     be
                     agreed
                     how
                     much
                     the
                     sunk
                     Rent
                     was
                     ,
                     or
                     at
                     least
                     as
                     much
                     given
                     as
                     before
                     was
                     required
                     ,
                     and
                     then
                     as
                     before
                     you
                     have
                     a
                     foundation
                     whereon
                     to
                     raise
                     a
                     Rate
                     of
                     Interest
                     ,
                     for
                     there
                     is
                     now
                     given
                     the
                     yearly
                     Rent
                     sunk
                     ,
                     its
                     present
                     worth
                     ,
                     and
                     the
                     time
                     ,
                     and
                     the
                     Rate
                     being
                     found
                     ,
                     you
                     may
                     then
                     ,
                     according
                     as
                     is
                     done
                     in
                     the
                     
                       5th
                       .
                       Prop.
                    
                     resolve
                     both
                     these
                     Questions
                     .
                  
                
              
               
                 
                 
                   Prop.
                   8.
                   
                   
                     A
                     Table
                     for
                     the
                     forbearance
                     of
                     Money
                     at
                     any
                     Rate
                     of
                     Interest
                     being
                     in
                     store
                     to
                     extend
                     it
                     to
                     serve
                     to
                     all
                     other
                     Rates
                     .
                  
                
                 
                   It
                   was
                   before
                   asserted
                   that
                   any
                   such
                   Table
                   was
                   a
                   Table
                   of
                   Logarithms
                   ,
                   and
                   if
                   filled
                   up
                   with
                   Proportionable
                   Numbers
                   (
                   by
                   1.
                   
                   Prop.
                   )
                   or
                   otherwise
                   suitable
                   to
                   such
                   time
                   or
                   Decimals
                   thereof
                   ,
                   as
                   may
                   come
                   in
                   use
                   ,
                   might
                   for
                   these
                   purposes
                   be
                   more
                   convenient
                   than
                   those
                   already
                   made
                   ,
                   because
                   it
                   would
                   admit
                   a
                   manifold
                   Proof
                   ,
                   as
                   also
                   because
                   the
                   differences
                   would
                   not
                   be
                   so
                   vast
                   near
                   the
                   beginning
                   ,
                   but
                   in
                   some
                   other
                   respects
                   inferiour
                   thereto
                   .
                   And
                   so
                   contrarily
                   ,
                   a
                   Number
                   being
                   assigned
                   to
                   find
                   the
                   Logarithm
                   thereto
                   made
                   ,
                   upon
                   any
                   kind
                   of
                   Rate
                   or
                   Supposition
                   ,
                   it
                   may
                   easily
                   be
                   done
                   out
                   of
                   the
                   Common
                   Logarithms
                   ,
                   for
                   the
                   differences
                   of
                   all
                   Logarithms
                   are
                   either
                   
                   equal
                   or
                   directly
                   Proportional
                   .
                
                 
                   
                     Example
                     first
                     .
                  
                   
                     As
                     74108
                     ,
                     Speidells
                     difference
                     of
                     the
                     Logarithm
                     of
                     13
                     and
                     14.
                     
                  
                   
                     Is
                     to
                     32184
                     
                       d.
                       Brigs
                    
                     his
                     difference
                     of
                     those
                     Logarithms
                     ;
                  
                   
                     So
                     is
                     16000
                     ,
                     Speidells
                     difference
                     of
                     the
                     Logarithms
                     of
                     62
                     and
                     63.
                     
                  
                   
                     To
                     69487
                     ,
                     the
                     difference
                     of
                     those
                     Logarithms
                     in
                     Mr.
                     Brigs
                     ,
                     or
                     the
                     Common
                     Tables
                     .
                  
                   
                     Moreover
                     
                       Van
                       Schooten
                    
                     in
                     his
                     Miscellanies
                     gives
                     you
                     an
                     Account
                     of
                     all
                     Numbers
                     under
                     1000
                     ,
                     that
                     are
                     prime
                     or
                     incomposite
                     ,
                     to
                     wit
                     ,
                     1226
                     in
                     Number
                     ,
                     viz.
                     the
                     which
                     no
                     other
                     Number
                     will
                     divide
                     ,
                     to
                     the
                     which
                     if
                     the
                     differences
                     be
                     first
                     found
                     by
                     Proportion
                     ,
                     which
                     in
                     this
                     Case
                     having
                     the
                     two
                     fixt
                     Terms
                     fixed
                     ,
                     may
                     be
                     converted
                     into
                     a
                     Multiplication
                     or
                     Division
                     ,
                     and
                     that
                     Multiplier
                     or
                     Divisor
                     being
                     Multiplied
                     
                     by
                     all
                     the
                     Digits
                     into
                     an
                     Addition
                     or
                     Substraction
                     ,
                     the
                     Logarithms
                     of
                     all
                     the
                     Composite
                     Numbers
                     will
                     easily
                     be
                     made
                     out
                     of
                     the
                     rest
                     ,
                     by
                     the
                     continual
                     Addition
                     of
                     the
                     Logarithm
                     of
                     2
                     ,
                     or
                     otherwise
                     .
                  
                   
                     In
                     the
                     Table
                     here
                     used
                     the
                     time
                     is
                     the
                     Logarithm
                     ,
                     and
                     the
                     Amount
                     the
                     Number
                     thereto
                     belonging
                     ,
                     and
                     a
                     Proportion
                     accordingly
                     may
                     be
                     applied
                     to
                     any
                     kind
                     of
                     Logarithms
                     ,
                     to
                     find
                     the
                     Excess
                     of
                     time
                     above
                     a
                     year
                     ,
                     in
                     which
                     a
                     100
                     l.
                     at
                     6
                     
                       per
                       Centum
                    
                     did
                     amount
                     to
                     108
                     l.
                     But
                     it
                     may
                     be
                     more
                     easily
                     thus
                     done
                     .
                  
                   
                     As
                     ,
                     02530586
                     ,
                     the
                     Logarithm
                     of
                     the
                     Amount
                     1
                     ,
                     06.
                     
                  
                   
                     Is
                     to
                     1
                     ,
                     viz.
                     One
                     year
                     the
                     time
                     that
                     1
                     l.
                     Principal
                     was
                     forborn
                     ;
                  
                   
                     So
                     is
                     ,
                     03342375
                     the
                     Logarithm
                     of
                     the
                     Amount
                     1
                     ,
                     08.
                     
                  
                   
                     To
                     1
                     ,
                     32079
                     ,
                     the
                     time
                     required
                     ,
                     and
                     that
                     is
                     1
                     Year
                     ,
                     3
                     Months
                     ,
                     and
                     about
                     26
                     Days
                     ,
                     and
                     thus
                     the
                     nearest
                     way
                     of
                     
                     resolving
                     such
                     a
                     Proposition
                     ,
                     having
                     the
                     Common
                     Logarithms
                     in
                     Store
                     ,
                     is
                     by
                     a
                     Division
                     of
                     the
                     Logarithms
                     :
                     But
                     supposing
                     no
                     such
                     Tables
                     ,
                     it
                     may
                     be
                     supplied
                     by
                     two
                     Divisions
                     by
                     help
                     of
                     this
                     Table
                     ,
                     which
                     I
                     shall
                     explain
                     in
                     two
                     Cases
                     .
                  
                   
                     Sect.
                     1.
                     
                     
                       The
                       Amount
                       of
                    
                     1
                     l.
                     
                       being
                       proposed
                       ,
                       to
                       find
                       what
                       time
                       it
                       must
                       be
                       forborn
                       ,
                       at
                    
                     6
                     per
                     Centum
                     
                       to
                       amount
                       unto
                       as
                       much
                    
                     .
                  
                   
                     Divide
                     the
                     given
                     Amount
                     by
                     some
                     Amount
                     in
                     the
                     Table
                     ,
                     next
                     lesser
                     ,
                     and
                     that
                     Quotient
                     ,
                     again
                     by
                     the
                     next
                     lesser
                     Amount
                     ,
                     reserving
                     the
                     Quotient
                     .
                  
                   
                     If
                     the
                     time
                     in
                     the
                     Tables
                     belonging
                     to
                     the
                     two
                     first
                     Divisors
                     ,
                     and
                     last
                     Quote
                     be
                     added
                     together
                     ,
                     it
                     is
                     the
                     time
                     sought
                     .
                  
                
                 
                   
                   
                     Example
                     .
                  
                   
                     1
                     l.
                     in
                     a
                     Year
                     at
                     8
                     
                       per
                       Centum
                    
                     did
                     amount
                     to
                     1
                     s.
                     ,
                     08
                     ,
                     in
                     what
                     time
                     at
                     6
                     
                       per
                       Centum
                    
                     ,
                     shall
                     it
                     amount
                     to
                     so
                     much
                     .
                  
                   
                     
                       
                         
                            
                        
                         
                            
                        
                         
                            
                        
                         
                            
                        
                         
                           In
                           Decimals
                        
                      
                       
                         
                            
                        
                         
                            
                        
                         
                            
                        
                         
                           Time
                        
                         
                            
                        
                      
                       
                         
                            
                        
                         
                           Dividend
                        
                         
                           108
                        
                         
                            
                        
                         
                            
                        
                      
                       
                         
                           1.
                           
                        
                         
                           Divisor
                           —
                        
                         
                           106
                           —
                        
                         
                           1
                           Year
                        
                         
                           1
                        
                      
                       
                         
                            
                        
                         
                           Quote
                           —
                        
                         
                           1,018867
                        
                         
                           Second
                           Dividend
                        
                         
                            
                        
                      
                       
                         
                           2.
                           
                        
                         
                           Divisor
                           —
                        
                         
                           1,014675
                        
                         
                           —
                           3
                           Months
                        
                         
                           ,25
                        
                      
                       
                         
                            
                        
                         
                            
                        
                         
                           1,0041
                        
                         
                           Quote
                           26
                           days
                           ferè
                        
                         
                           ,07079
                        
                      
                       
                         
                            
                        
                         
                            
                        
                         
                            
                        
                         
                            
                        
                         
                           1,32079
                        
                      
                    
                  
                   
                   
                     But
                     to
                     save
                     the
                     Reader
                     this
                     trouble
                     we
                     have
                     added
                     the
                     Equated
                     time
                     for
                     these
                     Rates
                     .
                  
                   
                     
                       
                         
                            
                        
                         
                           l.
                           
                        
                         
                           years
                        
                      
                       
                         
                           100
                           l.
                           shall
                        
                         
                           105
                        
                         
                           In
                        
                         
                           ,83732
                        
                      
                       
                         
                           at
                           6
                           per
                        
                         
                           106
                        
                         
                           1
                        
                      
                       
                         
                           Centum
                        
                         
                           107
                        
                         
                           1,16114
                        
                      
                       
                         
                           amount
                        
                         
                           108
                        
                         
                           1,32079
                        
                      
                       
                         
                           unto
                        
                         
                           109
                        
                         
                           1,47896
                        
                      
                    
                  
                   
                     And
                     by
                     the
                     second
                     Proposition
                     the
                     present
                     worth
                     of
                     sundry
                     payments
                     due
                     hereafter
                     being
                     computed
                     ,
                     after
                     the
                     manner
                     of
                     this
                     Example
                     ,
                     a
                     ●ue
                     time
                     may
                     be
                     found
                     when
                     the
                     total
                     of
                     all
                     those
                     Payments
                     may
                     equitably
                     be
                     paid
                     at
                     once
                     .
                  
                   
                   
                     Sect.
                     2.
                     
                     
                       The
                       Rate
                       of
                       Compound
                       Interest
                       ,
                       and
                       the
                       time
                       being
                       given
                       to
                       find
                       what
                    
                     1
                     l.
                     
                       Principal
                       did
                       amount
                       to
                       in
                       that
                       time
                       .
                    
                  
                   
                     Or
                     rather
                     let
                     it
                     be
                     thus
                     proposed
                     :
                  
                   
                     How
                     long
                     shall
                     one
                     pound
                     at
                     6
                     
                       per
                       Cent.
                    
                     be
                     forborn
                     to
                     amount
                     to
                     as
                     much
                     as
                     1
                     l.
                     forborn
                     any
                     space
                     of
                     time
                     at
                     any
                     other
                     Rate
                     of
                     Interest
                     doth
                     amount
                     unto
                     ,
                     and
                     what
                     is
                     the
                     said
                     Amount
                     ?
                  
                   
                     By
                     the
                     time
                     Proposed
                     multiply
                     the
                     Equated
                     time
                     ,
                     next
                     before
                     found
                     (
                     in
                     the
                     first
                     Case
                     )
                     that
                     agrees
                     to
                     the
                     Rate
                     proposed
                     ,
                     and
                     you
                     have
                     the
                     time
                     sought
                     ,
                     and
                     what
                     it
                     shall
                     amount
                     ,
                     is
                     found
                     by
                     the
                     first
                     Proposition
                     .
                  
                   
                     For
                     instance
                     ,
                     if
                     1
                     l.
                     be
                     forborn
                     18
                     years
                     at
                     8
                     
                       per
                       Centum
                    
                     ,
                     what
                     shall
                     it
                     amount
                     to
                     ?
                  
                
              
            
             
               
               
                 Or
                 〈…〉
              
               
                 How
                 long
                 shall
                 1
                 l.
                 at
                 6
                 
                   per
                   Centum
                
                 be
                 forborn
                 ,
                 to
                 amount
                 10
                 as
                 much
                 ,
                 as
                 if
                 the
                 said
                 1
                 l.
                 had
                 been
                 forborn
                 18
                 years
                 at
                 8
                 
                   per
                   Centum
                
                 ,
                 and
                 what
                 is
                 the
                 said
                 Amount
                 ?
              
               
                 By
                 the
                 former
                 Example
                 the
                 Equated
                 time
                 or
                 Logarithm
                 of
                 the
                 Ratio
                 found
                 ,
                 was
                 ,
              
               
                 
                   
                     
                        
                    
                     
                       years
                    
                  
                   
                     
                        
                    
                     
                       1,3207
                    
                  
                   
                     
                       This
                       Multiplied
                       by
                       18
                       ,
                       the
                       Product
                       is
                    
                     
                       23,7726
                    
                  
                
              
               
                 To
                 wit
                 the
                 time
                 of
                 forbearance
                 .
              
               
                 And
                 the
                 Product
                 of
                 the
                 Interest
                 Sums
                 belonging
                 to
                 the
                 true
                 time
                 is
                 3,99601
                 —
                 or
                 3
                 l.
                 19
                 s.
                 11
                 d.
                 the
                 Amount
                 of
                 1
                 l.
                 forborn
                 18
                 years
                 at
                 Compound
                 Interest
                 ,
                 and
                 the
                 Amount
                 of
                 1
                 l.
                 being
                 in
                 Store
                 ,
                 you
                 see
                 before
                 that
                 thereby
                 all
                 other
                 Questions
                 concerning
                 Annuities
                 are
                 Resolved
                 .
              
               
                 But
                 when
                 the
                 Law
                 settles
                 a
                 New
                 
                 Rate
                 of
                 Interest
                 ,
                 it
                 may
                 be
                 more
                 speedy
                 to
                 frame
                 a
                 Table
                 thereto
                 ,
                 or
                 use
                 such
                 as
                 the
                 Scale
                 of
                 Interest
                 ,
                 or
                 other
                 Authors
                 afford
                 .
                 Now
                 what
                 I
                 have
                 hitherto
                 wrote
                 was
                 chiefly
                 to
                 explain
                 the
                 Use
                 of
                 the
                 Table
                 ,
                 and
                 to
                 shew
                 ,
                 That
                 in
                 case
                 of
                 necessity
                 ,
                 with
                 a
                 little
                 more
                 pains
                 ,
                 it
                 takes
                 away
                 those
                 Multitudes
                 of
                 Tables
                 that
                 are
                 made
                 ,
                 as
                 well
                 for
                 quarterly
                 as
                 yearly
                 Payments
                 ,
                 at
                 several
                 Rates
                 for
                 Interest
                 and
                 Annuity
                 Questions
                 ,
                 and
                 by
                 reason
                 it
                 ,
                 with
                 its
                 Precepts
                 ,
                 is
                 contained
                 in
                 one
                 quarter
                 of
                 a
                 sheet
                 of
                 Paper
                 ,
                 which
                 I
                 made
                 my
                 constant
                 Companion
                 in
                 my
                 Letter
                 Case
                 ,
                 that
                 thou
                 mightest
                 reap
                 the
                 like
                 benefit
                 of
                 it
                 ,
                 it
                 is
                 also
                 Printed
                 apart
                 .
                 It
                 is
                 not
                 my
                 intent
                 to
                 inlarge
                 upon
                 a
                 Multitude
                 of
                 Particular
                 Questions
                 ,
                 which
                 would
                 all
                 be
                 reduced
                 unto
                 or
                 resolved
                 by
                 some
                 of
                 the
                 former
                 Propositions
                 .
                 That
                 I
                 leave
                 to
                 the
                 Practice
                 of
                 the
                 Studious
                 .
              
            
          
           
             
             
               ADVERTISEMENT
               .
            
             
               MErcennus
               in
               the
               Preface
               of
               his
               
                 Synopsis
                 Mathematica
              
               ,
               speaking
               of
               certain
               Supplements
               made
               to
               Geometry
               ,
               and
               amongst
               the
               rest
               of
               
               Torricello's
               Hyperbolical
               Solid
               of
               an
               infinite
               length
               ,
               found
               equal
               to
               a
               finite
               Cylinder
               ,
               saith
               ,
               That
               a
               certain
               Geometer
               found
               the
               like
               in
               a
               Space
               made
               by
               a
               curved
               Line
               drawn
               through
               the
               tops
               ,
               all
               right
               proportional
               Lines
               (
               supposed
               )
               and
               by
               a
               right
               Line
               ,
               on
               which
               the
               said
               Proportional
               Lines
               stand
               as
               Perpendiculars
               at
               a
               like
               parallel
               distance
               from
               each
               other
               ;
               if
               it
               may
               be
               said
               to
               be
               a
               Space
               which
               is
               not
               closed
               ,
               unless
               perchance
               at
               an
               infinite
               distance
               ,
               which
               Proportionals
               ,
               he
               saith
               ,
               
               would
               not
               long
               after
               be
               published
               :
               He
               wrote
               it
               in
               1644
               ,
               but
               as
               yet
               I
               cannot
               hear
               of
               any
               such
               Treatise
               .
            
             
               Now
               ,
               as
               I
               said
               before
               ,
               the
               time
               being
               the
               Logarithms
               ,
               and
               the
               Amounts
               the
               Proportional
               Numbers
               thereto
               belonging
               ,
               by
               the
               help
               of
               the
               Curved
               Line
               he
               mentions
               (
               which
               may
               also
               be
               described
               by
               mean
               or
               continual
               Proportionals
               in
               Lines
               without
               the
               help
               of
               Numbers
               )
               the
               Logarithmetical
               Lines
               of
               Numbers
               ,
               Sines
               ,
               Tangents
               ,
               Versed
               Sines
               ,
               on
               
               Gunter's
               Rule
               may
               be
               Graduated
               ,
               and
               the
               Meridian
               Line
               of
               
               Mercator's
               Projection
               ,
               or
               the
               true
               Sea
               Chart
               (
               being
               in
               the
               same
               Ratio
               with
               the
               Logarithmetical
               Tangents
               )
               supplied
               ,
               and
               whereas
               he
               mentions
               by
               one
               Curved
               Figure
               ,
               there
               will
               also
               arise
               another
               for
               the
               same
               purpose
               ,
               when
               the
               equal
               parts
               increasing
               in
               Arithmetical
               Progression
               ,
               are
               raised
               as
               Perpendiculars
               on
               their
               Proportional
               Numbers
               placed
               in
               a
               base
               Line
               ,
               and
               
               then
               the
               tops
               of
               those
               Perpendiculars
               joyned
               with
               a
               slexuous
               Curved
               Line
               passing
               through
               them
               ;
               but
               the
               Properties
               of
               these
               Figures
               as
               their
               Areas
               or
               Contents
               ,
               Centors
               of
               Gravity
               ,
               round
               Solids
               ,
               and
               their
               first
               and
               second
               Segments
               ,
               &c.
               are
               not
               as
               yet
               treated
               of
               by
               Geometers
               ,
               and
               perchance
               might
               be
               more
               worthy
               their
               Contemplation
               than
               divers
               other
               Speculations
               ,
               which
               seem
               to
               be
               of
               less
               Use
               ,
               to
               which
               (
               amongst
               many
               )
               might
               be
               added
               the
               Curves
               made
               by
               the
               Annuity
               Lines
               ,
               and
               the
               Curve
               in
               
               Mercator's
               Chart
               that
               represents
               a
               Semicircle
               of
               the
               great
               Arch
               ,
               with
               a
               method
               of
               discribing
               it
               by
               Points
               ,
               or
               Instrument
               (
               if
               possible
               )
               from
               its
               own
               Intrinsick
               Nature
               ,
               without
               the
               help
               of
               Calculations
               or
               other
               Projections
               ;
               also
               how
               to
               cut
               a
               Cylinder
               that
               the
               Surface
               thereof
               unrolled
               shall
               render
               the
               Curve
               proposed
               of
               the
               like
               Nature
               ,
               standing
               upon
               the
               Stage
               of
               Proposal
               ,
               
               have
               troubled
               all
               France
               and
               Galileus
               for
               35
               years
               together
               ,
               and
               since
               his
               death
               received
               their
               Resolution
               .
            
          
           
             
             
               
                 A
                 Table
                 of
                 Decimals
                 of
                 Days
                 ,
                 which
                 may
                 serve
                 for
                 any
                 Rate
                 of
                 Simple
                 Interest
                 ,
                 and
                 a
                 Table
                 of
                 Forbearance
                 ,
                 or
                 Amount
                 of
              
               1
               l.
               
                 Compound
                 Interest
                 at
              
               6
               l.
               per
               Cent.
               per
               Annum
               ,
               for
               365
               
                 Days
                 and
              
               11
               Months
               .
            
             
               
                 
                   
                     Days
                  
                   
                     
                       Decimals
                       of
                       days
                    
                  
                   
                     Amounts
                  
                
                 
                   
                     1
                  
                   
                     ,002739726
                  
                   
                     1,000159617
                  
                
                 
                   
                     2
                  
                   
                     ,005479452
                  
                   
                     1,000319336
                  
                
                 
                   
                     3
                  
                   
                     ,008219178
                  
                   
                     1,000479037
                  
                
                 
                   
                     4
                  
                   
                     ,010958904
                  
                   
                     1,000638768
                  
                
                 
                   
                     5
                  
                   
                     ,013698630
                  
                   
                     1,000798522
                  
                
                 
                   
                     6
                  
                   
                     ,016438356
                  
                   
                     1,000958305
                  
                
                 
                   
                     7
                  
                   
                     ,019178082
                  
                   
                     1,001118111
                  
                
                 
                   
                     8
                  
                   
                     ,021917808
                  
                   
                     1,001277942
                  
                
                 
                   
                     9
                  
                   
                     ,024657534
                  
                   
                     1,001437800
                  
                
                 
                   
                     10
                  
                   
                     ,027397260
                  
                   
                     1,001597683
                  
                
                 
                   
                     11
                  
                   
                     ,030136986
                  
                   
                     1,001757592
                  
                
                 
                   
                     12
                  
                   
                     ,032876712
                  
                   
                     1,001917526
                  
                
                 
                   
                     13
                  
                   
                     ,035616438
                  
                   
                     1,002077486
                  
                
                 
                   
                     14
                  
                   
                     ,038356164
                  
                   
                     1,002237471
                  
                
                 
                   
                     15
                  
                   
                     041095890
                  
                   
                     1,002397482
                  
                
                 
                 
                   
                     16
                  
                   
                     ,043835616
                  
                   
                     1,002557511
                  
                
                 
                   
                     17
                  
                   
                     ,046575342
                  
                   
                     1,002717580
                  
                
                 
                   
                     18
                  
                   
                     ,049315068
                  
                   
                     1,002877667
                  
                
                 
                   
                     19
                  
                   
                     ,052054794
                  
                   
                     1,003077802
                  
                
                 
                   
                     20
                  
                   
                     ,054794520
                  
                   
                     1,003197919
                  
                
                 
                   
                     21
                  
                   
                     ,057534246
                  
                   
                     1,003358083
                  
                
                 
                   
                     22
                  
                   
                     ,060273972
                  
                   
                     1,003518273
                  
                
                 
                   
                     23
                  
                   
                     ,063013699
                  
                   
                     1,003678488
                  
                
                 
                   
                     24
                  
                   
                     ,065753425
                  
                   
                     1,003938729
                  
                
                 
                   
                     25
                  
                   
                     ,068493151
                  
                   
                     1,003998995
                  
                
                 
                   
                     26
                  
                   
                     ,071232877
                  
                   
                     1,004159285
                  
                
                 
                   
                     27
                  
                   
                     ,073972602
                  
                   
                     1,004319605
                  
                
                 
                   
                     28
                  
                   
                     ,076712329
                  
                   
                     1,004479948
                  
                
                 
                   
                     29
                  
                   
                     ,079452055
                  
                   
                     1,004640310
                  
                
                 
                   
                     30
                  
                   
                     ,082191781
                  
                   
                     1,004800712
                  
                
                 
                   
                     31
                  
                   
                     ,084931507
                  
                   
                     1,004961132
                  
                
                 
                   
                     32
                  
                   
                     ,087671233
                  
                   
                     1,005121577
                  
                
                 
                   
                     33
                  
                   
                     ,090410959
                  
                   
                     1,005282467
                  
                
                 
                   
                     34
                  
                   
                     ,093150685
                  
                   
                     1,005442545
                  
                
                 
                   
                     35
                  
                   
                     ,095890411
                  
                   
                     1,005603068
                  
                
                 
                 
                   
                     36
                  
                   
                     ,098630137
                  
                   
                     1,005763616
                  
                
                 
                   
                     37
                  
                   
                     ,101369863
                  
                   
                     1,005924190
                  
                
                 
                   
                     38
                  
                   
                     ,104109589
                  
                   
                     1,006084789
                  
                
                 
                   
                     39
                  
                   
                     ,106849315
                  
                   
                     1,006245414
                  
                
                 
                   
                     40
                  
                   
                     ,109589041
                  
                   
                     1,006406528
                  
                
                 
                   
                     41
                  
                   
                     ,112328767
                  
                   
                     1,006566741
                  
                
                 
                   
                     42
                  
                   
                     ,115068493
                  
                   
                     1,006727443
                  
                
                 
                   
                     43
                  
                   
                     ,117808219
                  
                   
                     1,006888171
                  
                
                 
                   
                     44
                  
                   
                     ,120547945
                  
                   
                     1,007048924
                  
                
                 
                   
                     45
                  
                   
                     ,123287671
                  
                   
                     1,007209703
                  
                
                 
                   
                     46
                  
                   
                     ,126027397
                  
                   
                     1,007370508
                  
                
                 
                   
                     47
                  
                   
                     ,128767123
                  
                   
                     1,007531338
                  
                
                 
                   
                     48
                  
                   
                     ,131306849
                  
                   
                     1,007692194
                  
                
                 
                   
                     49
                  
                   
                     ,134246575
                  
                   
                     1,007853076
                  
                
                 
                   
                     50
                  
                   
                     ,136986301
                  
                   
                     1,008013983
                  
                
                 
                   
                     51
                  
                   
                     ,139726027
                  
                   
                     1,008174916
                  
                
                 
                   
                     52
                  
                   
                     ,142465753
                  
                   
                     1,008335850
                  
                
                 
                   
                     53
                  
                   
                     ,145205479
                  
                   
                     1,008496859
                  
                
                 
                   
                     54
                  
                   
                     ,147945205
                  
                   
                     1,008657870
                  
                
                 
                   
                     55
                  
                   
                     ,150684931
                  
                   
                     1,008817905
                  
                
                 
                 
                   
                     56
                  
                   
                     ,153424657
                  
                   
                     1,008979967
                  
                
                 
                   
                     57
                  
                   
                     ,156164383
                  
                   
                     1,009141054
                  
                
                 
                   
                     58
                  
                   
                     ,158904109
                  
                   
                     1,009302121
                  
                
                 
                   
                     59
                  
                   
                     ,161643835
                  
                   
                     1,009463306
                  
                
                 
                   
                     60
                  
                   
                     ,164383561
                  
                   
                     1,009624470
                  
                
                 
                   
                     61
                  
                   
                     ,167123287
                  
                   
                     1,009785661
                  
                
                 
                   
                     62
                  
                   
                     ,169863014
                  
                   
                     1,009946877
                  
                
                 
                   
                     63
                  
                   
                     ,172602739
                  
                   
                     1,010108118
                  
                
                 
                   
                     64
                  
                   
                     ,175342466
                  
                   
                     1,010269386
                  
                
                 
                   
                     65
                  
                   
                     ,178082192
                  
                   
                     1,010430680
                  
                
                 
                   
                     66
                  
                   
                     ,180821918
                  
                   
                     1,010591909
                  
                
                 
                   
                     67
                  
                   
                     ,183561644
                  
                   
                     1,010753343
                  
                
                 
                   
                     68
                  
                   
                     ,186301369
                  
                   
                     1,010914719
                  
                
                 
                   
                     69
                  
                   
                     ,189041096
                  
                   
                     1,011076110
                  
                
                 
                   
                     70
                  
                   
                     ,191780822
                  
                   
                     1,011237532
                  
                
                 
                   
                     71
                  
                   
                     ,194520548
                  
                   
                     1,011398513
                  
                
                 
                   
                     72
                  
                   
                     ,197260274
                  
                   
                     1,011560453
                  
                
                 
                   
                     73
                  
                   
                     ,200000000
                  
                   
                     1,011721952
                  
                
                 
                   
                     74
                  
                   
                     ,202739726
                  
                   
                     1,011883485
                  
                
                 
                   
                     75
                  
                   
                     ,205479452
                  
                   
                     1,012045028
                  
                
                 
                 
                   
                     76
                  
                   
                     ,208219178
                  
                   
                     1,012206604
                  
                
                 
                   
                     77
                  
                   
                     ,210958904
                  
                   
                     1,012368207
                  
                
                 
                   
                     78
                  
                   
                     ,213698630
                  
                   
                     1,012529835
                  
                
                 
                   
                     79
                  
                   
                     ,216438356
                  
                   
                     1,012691489
                  
                
                 
                   
                     80
                  
                   
                     ,219178082
                  
                   
                     1,012853169
                  
                
                 
                   
                     81
                  
                   
                     ,221917808
                  
                   
                     1,013014874
                  
                
                 
                   
                     82
                  
                   
                     ,224657534
                  
                   
                     1,013176606
                  
                
                 
                   
                     83
                  
                   
                     ,227397260
                  
                   
                     1,013338368
                  
                
                 
                   
                     84
                  
                   
                     ,230136986
                  
                   
                     1,013500145
                  
                
                 
                   
                     85
                  
                   
                     ,232876712
                  
                   
                     1,013661955
                  
                
                 
                   
                     86
                  
                   
                     ,235616418
                  
                   
                     1,013823790
                  
                
                 
                   
                     87
                  
                   
                     ,238356164
                  
                   
                     1,013985650
                  
                
                 
                   
                     88
                  
                   
                     ,241095891
                  
                   
                     1,014147538
                  
                
                 
                   
                     89
                  
                   
                     ,243835617
                  
                   
                     1,014309449
                  
                
                 
                   
                     90
                  
                   
                     ,246575342
                  
                   
                     1,014471385
                  
                
                 
                   
                     91
                  
                   
                     ,249315068
                  
                   
                     1,014633352
                  
                
                 
                   
                     92
                  
                   
                     ,252054794
                  
                   
                     1,014795341
                  
                
                 
                   
                     93
                  
                   
                     ,254794520
                  
                   
                     1,014957357
                  
                
                 
                   
                     94
                  
                   
                     ,257534246
                  
                   
                     1,015119399
                  
                
                 
                   
                     95
                  
                   
                     ,260273972
                  
                   
                     1,015281466
                  
                
                 
                 
                   
                     96
                  
                   
                     ,263013698
                  
                   
                     1,015443560
                  
                
                 
                   
                     97
                  
                   
                     ,265753424
                  
                   
                     1,015605678
                  
                
                 
                   
                     98
                  
                   
                     ,268493150
                  
                   
                     1,015767824
                  
                
                 
                   
                     99
                  
                   
                     ,271232876
                  
                   
                     1,015929992
                  
                
                 
                   
                     100
                  
                   
                     ,273972602
                  
                   
                     1,016092892
                  
                
                 
                   
                     101
                  
                   
                     ,276712320
                  
                   
                     1,016254415
                  
                
                 
                   
                     102
                  
                   
                     ,279452055
                  
                   
                     1,016416663
                  
                
                 
                   
                     103
                  
                   
                     ,282191781
                  
                   
                     1,016578938
                  
                
                 
                   
                     104
                  
                   
                     ,284931517
                  
                   
                     1,016741243
                  
                
                 
                   
                     105
                  
                   
                     ,287671243
                  
                   
                     1,016993540
                  
                
                 
                   
                     106
                  
                   
                     ,290410960
                  
                   
                     1,017065919
                  
                
                 
                   
                     107
                  
                   
                     ,293150695
                  
                   
                     1,017228295
                  
                
                 
                   
                     108
                  
                   
                     ,295890411
                  
                   
                     1,017396994
                  
                
                 
                   
                     109
                  
                   
                     ,298630137
                  
                   
                     1,017553130
                  
                
                 
                   
                     110
                  
                   
                     ,301369863
                  
                   
                     1,017715585
                  
                
                 
                   
                     111
                  
                   
                     ,304109589
                  
                   
                     1,017878065
                  
                
                 
                   
                     112
                  
                   
                     ,306849315
                  
                   
                     1,018045851
                  
                
                 
                   
                     113
                  
                   
                     ,309589041
                  
                   
                     1,018203108
                  
                
                 
                   
                     114
                  
                   
                     ,312328767
                  
                   
                     1,018365664
                  
                
                 
                   
                     115
                  
                   
                     ,315068493
                  
                   
                     1,018528254
                  
                
                 
                 
                   
                     116
                  
                   
                     ,317808219
                  
                   
                     1,018690866
                  
                
                 
                   
                     117
                  
                   
                     ,320547945
                  
                   
                     1,018853504
                  
                
                 
                   
                     118
                  
                   
                     ,323287671
                  
                   
                     1,019016177
                  
                
                 
                   
                     119
                  
                   
                     ,326027397
                  
                   
                     1,019178857
                  
                
                 
                   
                     120
                  
                   
                     ,328767123
                  
                   
                     1,019345733
                  
                
                 
                   
                     121
                  
                   
                     ,331506849
                  
                   
                     1,019504313
                  
                
                 
                   
                     122
                  
                   
                     ,334246575
                  
                   
                     1,019667083
                  
                
                 
                   
                     123
                  
                   
                     ,336986301
                  
                   
                     1,019829875
                  
                
                 
                   
                     124
                  
                   
                     ,339726027
                  
                   
                     1,019991694
                  
                
                 
                   
                     125
                  
                   
                     ,342465753
                  
                   
                     1,020155541
                  
                
                 
                   
                     126
                  
                   
                     ,345205479
                  
                   
                     1,020318411
                  
                
                 
                   
                     127
                  
                   
                     ,347945206
                  
                   
                     1,020481309
                  
                
                 
                   
                     128
                  
                   
                     ,350684942
                  
                   
                     1,020644233
                  
                
                 
                   
                     129
                  
                   
                     ,353424667
                  
                   
                     1,020807182
                  
                
                 
                   
                     130
                  
                   
                     ,356164393
                  
                   
                     1,020970158
                  
                
                 
                   
                     131
                  
                   
                     ,358904119
                  
                   
                     1,021133159
                  
                
                 
                   
                     132
                  
                   
                     ,361643845
                  
                   
                     1,021296189
                  
                
                 
                   
                     133
                  
                   
                     ,364383572
                  
                   
                     1,021461593
                  
                
                 
                   
                     134
                  
                   
                     ,367123298
                  
                   
                     1,021622323
                  
                
                 
                   
                     135
                  
                   
                     ,369863024
                  
                   
                     1,021785425
                  
                
                 
                 
                   
                     136
                  
                   
                     ,372602749
                  
                   
                     1,021948558
                  
                
                 
                   
                     137
                  
                   
                     ,375342476
                  
                   
                     1,022111715
                  
                
                 
                   
                     138
                  
                   
                     ,378082202
                  
                   
                     1,022274899
                  
                
                 
                   
                     139
                  
                   
                     ,380821928
                  
                   
                     1,022438109
                  
                
                 
                   
                     140
                  
                   
                     ,383561654
                  
                   
                     1,022601344
                  
                
                 
                   
                     141
                  
                   
                     ,386301379
                  
                   
                     1,022764607
                  
                
                 
                   
                     142
                  
                   
                     ,389041106
                  
                   
                     1,022927895
                  
                
                 
                   
                     143
                  
                   
                     ,391780832
                  
                   
                     1,023091208
                  
                
                 
                   
                     144
                  
                   
                     ,394520558
                  
                   
                     1,023254549
                  
                
                 
                   
                     145
                  
                   
                     ,397260284
                  
                   
                     1,023417914
                  
                
                 
                   
                     146
                  
                   
                     ,400000000
                  
                   
                     1,023581308
                  
                
                 
                   
                     147
                  
                   
                     ,402739736
                  
                   
                     1,023744727
                  
                
                 
                   
                     148
                  
                   
                     ,405479462
                  
                   
                     1,023908170
                  
                
                 
                   
                     149
                  
                   
                     ,408219188
                  
                   
                     1,024071642
                  
                
                 
                   
                     150
                  
                   
                     ,410958914
                  
                   
                     1,024235137
                  
                
                 
                   
                     151
                  
                   
                     ,413698640
                  
                   
                     1,024398660
                  
                
                 
                   
                     152
                  
                   
                     ,416438366
                  
                   
                     1,024562213
                  
                
                 
                   
                     153
                  
                   
                     ,419178092
                  
                   
                     1,024725785
                  
                
                 
                   
                     154
                  
                   
                     ,421917818
                  
                   
                     1,024989386
                  
                
                 
                   
                     155
                  
                   
                     ,425657544
                  
                   
                     1,025053613
                  
                
                 
                 
                   
                     156
                  
                   
                     ,427397270
                  
                   
                     1,025216666
                  
                
                 
                   
                     157
                  
                   
                     ,430136997
                  
                   
                     1,025380346
                  
                
                 
                   
                     158
                  
                   
                     ,432876722
                  
                   
                     1,025544052
                  
                
                 
                   
                     159
                  
                   
                     ,435616448
                  
                   
                     1,025707783
                  
                
                 
                   
                     160
                  
                   
                     ,438356174
                  
                   
                     1,025871541
                  
                
                 
                   
                     161
                  
                   
                     ,441095900
                  
                   
                     1,026035316
                  
                
                 
                   
                     162
                  
                   
                     ,443835626
                  
                   
                     1,026199125
                  
                
                 
                   
                     163
                  
                   
                     ,446575352
                  
                   
                     1,026362972
                  
                
                 
                   
                     164
                  
                   
                     ,449315078
                  
                   
                     1,026526834
                  
                
                 
                   
                     165
                  
                   
                     ,452054804
                  
                   
                     1,026690723
                  
                
                 
                   
                     166
                  
                   
                     ,454794531
                  
                   
                     1,026854641
                  
                
                 
                   
                     167
                  
                   
                     ,457534256
                  
                   
                     1,027018579
                  
                
                 
                   
                     168
                  
                   
                     ,460273982
                  
                   
                     1,027182546
                  
                
                 
                   
                     169
                  
                   
                     ,463013708
                  
                   
                     1,027346543
                  
                
                 
                   
                     170
                  
                   
                     ,465753434
                  
                   
                     1,027510559
                  
                
                 
                   
                     171
                  
                   
                     ,468493161
                  
                   
                     1,027674605
                  
                
                 
                   
                     172
                  
                   
                     ,471232887
                  
                   
                     1,027838677
                  
                
                 
                   
                     173
                  
                   
                     ,473972613
                  
                   
                     1,028002774
                  
                
                 
                   
                     174
                  
                   
                     ,476712339
                  
                   
                     1,028166899
                  
                
                 
                   
                     175
                  
                   
                     ,479452065
                  
                   
                     1,028331053
                  
                
                 
                 
                   
                     176
                  
                   
                     ,482191791
                  
                   
                     1,028495226
                  
                
                 
                   
                     177
                  
                   
                     ,484931517
                  
                   
                     1,028659434
                  
                
                 
                   
                     178
                  
                   
                     ,487671243
                  
                   
                     1,028823659
                  
                
                 
                   
                     179
                  
                   
                     ,490410969
                  
                   
                     1,028987914
                  
                
                 
                   
                     180
                  
                   
                     ,493150695
                  
                   
                     1,029152196
                  
                
                 
                   
                     181
                  
                   
                     ,495890421
                  
                   
                     1,029316503
                  
                
                 
                   
                     182
                  
                   
                     ,498630147
                  
                   
                     1,029480838
                  
                
                 
                   
                     183
                  
                   
                     ,501369873
                  
                   
                     1,029645199
                  
                
                 
                   
                     184
                  
                   
                     ,504109599
                  
                   
                     1,029809584
                  
                
                 
                   
                     185
                  
                   
                     ,506849325
                  
                   
                     1,029973997
                  
                
                 
                   
                     186
                  
                   
                     ,509589051
                  
                   
                     1,030138442
                  
                
                 
                   
                     187
                  
                   
                     ,512328777
                  
                   
                     1,030302901
                  
                
                 
                   
                     188
                  
                   
                     ,515068503
                  
                   
                     1,030467393
                  
                
                 
                   
                     189
                  
                   
                     ,517808229
                  
                   
                     1,030631911
                  
                
                 
                   
                     190
                  
                   
                     ,520547955
                  
                   
                     1,030796454
                  
                
                 
                   
                     191
                  
                   
                     ,523287681
                  
                   
                     1,030961026
                  
                
                 
                   
                     192
                  
                   
                     ,526027407
                  
                   
                     1,031125622
                  
                
                 
                   
                     193
                  
                   
                     ,528767133
                  
                   
                     1,031290244
                  
                
                 
                   
                     194
                  
                   
                     ,531506859
                  
                   
                     1,031454895
                  
                
                 
                   
                     195
                  
                   
                     ,534246585
                  
                   
                     1,031619570
                  
                
                 
                 
                   
                     196
                  
                   
                     ,536986311
                  
                   
                     1,0317●4●●●
                  
                
                 
                   
                     197
                  
                   
                     ,539726057
                  
                   
                     1,031949●●●
                  
                
                 
                   
                     198
                  
                   
                     ,542465763
                  
                   
                     1,032137521
                  
                
                 
                   
                     199
                  
                   
                     ,545205489
                  
                   
                     1,032278534
                  
                
                 
                   
                     200
                  
                   
                     ,547945215
                  
                   
                     1,032443342
                  
                
                 
                   
                     201
                  
                   
                     ,550684941
                  
                   
                     1,0326●8174
                  
                
                 
                   
                     202
                  
                   
                     ,553424667
                  
                   
                     1,032773034
                  
                
                 
                   
                     203
                  
                   
                     ,556164393
                  
                   
                     1,032937920
                  
                
                 
                   
                     204
                  
                   
                     ,558904119
                  
                   
                     1,033102832
                  
                
                 
                   
                     205
                  
                   
                     ,561643845
                  
                   
                     1,033267771
                  
                
                 
                   
                     206
                  
                   
                     ,564383571
                  
                   
                     1,033432736
                  
                
                 
                   
                     207
                  
                   
                     ,567123298
                  
                   
                     1,033597703
                  
                
                 
                   
                     208
                  
                   
                     ,569863024
                  
                   
                     1,033757985
                  
                
                 
                   
                     209
                  
                   
                     ,572602756
                  
                   
                     1,033927789
                  
                
                 
                   
                     210
                  
                   
                     ,575342478
                  
                   
                     1,034092859
                  
                
                 
                   
                     211
                  
                   
                     ,578082204
                  
                   
                     1,034257956
                  
                
                 
                   
                     212
                  
                   
                     ,580821929
                  
                   
                     1,034423079
                  
                
                 
                   
                     213
                  
                   
                     ,583561656
                  
                   
                     1,034588204
                  
                
                 
                   
                     214
                  
                   
                     ,586301382
                  
                   
                     1,034753404
                  
                
                 
                   
                     215
                  
                   
                     ,589041108
                  
                   
                     1,034918606
                  
                
                 
                 
                   
                     216
                  
                   
                     ,591780834
                  
                   
                     1,035083763
                  
                
                 
                   
                     217
                  
                   
                     ,594520559
                  
                   
                     1,035249089
                  
                
                 
                   
                     218
                  
                   
                     ,597260286
                  
                   
                     1,035414370
                  
                
                 
                   
                     219
                  
                   
                     ,600000000
                  
                   
                     1,035579678
                  
                
                 
                   
                     220
                  
                   
                     ,602739727
                  
                   
                     1,035745010
                  
                
                 
                   
                     221
                  
                   
                     ,605479453
                  
                   
                     1,035910371
                  
                
                 
                   
                     222
                  
                   
                     ,608219179
                  
                   
                     1,036075759
                  
                
                 
                   
                     223
                  
                   
                     ,610958905
                  
                   
                     1,036241173
                  
                
                 
                   
                     224
                  
                   
                     ,613698631
                  
                   
                     1,036406611
                  
                
                 
                   
                     225
                  
                   
                     ,616438357
                  
                   
                     1,036572078
                  
                
                 
                   
                     226
                  
                   
                     ,619178083
                  
                   
                     1,036737573
                  
                
                 
                   
                     227
                  
                   
                     ,621917809
                  
                   
                     1,036903089
                  
                
                 
                   
                     228
                  
                   
                     ,624657535
                  
                   
                     1,037068659
                  
                
                 
                   
                     229
                  
                   
                     ,627397261
                  
                   
                     1,037234207
                  
                
                 
                   
                     230
                  
                   
                     ,630136987
                  
                   
                     1,037399804
                  
                
                 
                   
                     231
                  
                   
                     ,632876713
                  
                   
                     1,037565430
                  
                
                 
                   
                     232
                  
                   
                     ,635616439
                  
                   
                     1,037731080
                  
                
                 
                   
                     233
                  
                   
                     ,638356165
                  
                   
                     1,037896757
                  
                
                 
                   
                     234
                  
                   
                     ,641095891
                  
                   
                     1,038062462
                  
                
                 
                   
                     235
                  
                   
                     ,643835617
                  
                   
                     1,038228192
                  
                
                 
                 
                   
                     236
                  
                   
                     ,646575343
                  
                   
                     1,038093948
                  
                
                 
                   
                     237
                  
                   
                     ,649315069
                  
                   
                     1,038559733
                  
                
                 
                   
                     238
                  
                   
                     ,652054795
                  
                   
                     1,038725542
                  
                
                 
                   
                     239
                  
                   
                     ,654794521
                  
                   
                     1,038891378
                  
                
                 
                   
                     240
                  
                   
                     ,657534247
                  
                   
                     1,039057241
                  
                
                 
                   
                     241
                  
                   
                     ,660273973
                  
                   
                     1,039223106
                  
                
                 
                   
                     242
                  
                   
                     ,663013699
                  
                   
                     1,039389046
                  
                
                 
                   
                     243
                  
                   
                     ,665753425
                  
                   
                     1,039554988
                  
                
                 
                   
                     244
                  
                   
                     ,668293152
                  
                   
                     1,039720972
                  
                
                 
                   
                     245
                  
                   
                     ,671232878
                  
                   
                     1,039886952
                  
                
                 
                   
                     246
                  
                   
                     ,673972604
                  
                   
                     1,040052974
                  
                
                 
                   
                     247
                  
                   
                     ,676712329
                  
                   
                     1,040219022
                  
                
                 
                   
                     248
                  
                   
                     ,679452056
                  
                   
                     1,040385096
                  
                
                 
                   
                     249
                  
                   
                     ,682191782
                  
                   
                     1,040551198
                  
                
                 
                   
                     250
                  
                   
                     ,684931508
                  
                   
                     1,040717326
                  
                
                 
                   
                     251
                  
                   
                     ,687671234
                  
                   
                     1,040888480
                  
                
                 
                   
                     252
                  
                   
                     ,690410959
                  
                   
                     1,041049661
                  
                
                 
                   
                     253
                  
                   
                     ,693150686
                  
                   
                     1,041215868
                  
                
                 
                   
                     254
                  
                   
                     ,695890412
                  
                   
                     1,041382102
                  
                
                 
                   
                     255
                  
                   
                     ,698630138
                  
                   
                     1,041548363
                  
                
                 
                 
                   
                     256
                  
                   
                     ,701369864
                  
                   
                     1,041714649
                  
                
                 
                   
                     257
                  
                   
                     ,704109589
                  
                   
                     1,041880960
                  
                
                 
                   
                     258
                  
                   
                     ,706849316
                  
                   
                     1,042047303
                  
                
                 
                   
                     259
                  
                   
                     ,709589042
                  
                   
                     1,042213669
                  
                
                 
                   
                     260
                  
                   
                     ,712328768
                  
                   
                     1,042380062
                  
                
                 
                   
                     261
                  
                   
                     ,715068494
                  
                   
                     1,042546482
                  
                
                 
                   
                     262
                  
                   
                     ,717808219
                  
                   
                     1,042712928
                  
                
                 
                   
                     263
                  
                   
                     ,720547946
                  
                   
                     1,042879401
                  
                
                 
                   
                     264
                  
                   
                     ,723287672
                  
                   
                     1,043045901
                  
                
                 
                   
                     265
                  
                   
                     ,726027398
                  
                   
                     1,043212426
                  
                
                 
                   
                     266
                  
                   
                     ,728767124
                  
                   
                     1,043378979
                  
                
                 
                   
                     267
                  
                   
                     ,731506850
                  
                   
                     1,043545559
                  
                
                 
                   
                     268
                  
                   
                     ,734246576
                  
                   
                     1,043712164
                  
                
                 
                   
                     269
                  
                   
                     ,736986302
                  
                   
                     1,043878797
                  
                
                 
                   
                     270
                  
                   
                     ,739726028
                  
                   
                     1,044045456
                  
                
                 
                   
                     271
                  
                   
                     ,742465754
                  
                   
                     1,044212141
                  
                
                 
                   
                     272
                  
                   
                     ,745205480
                  
                   
                     1,044378853
                  
                
                 
                   
                     273
                  
                   
                     ,747945206
                  
                   
                     1,044545592
                  
                
                 
                   
                     274
                  
                   
                     ,750684932
                  
                   
                     1,044712357
                  
                
                 
                   
                     275
                  
                   
                     ,753424658
                  
                   
                     1,044879150
                  
                
                 
                 
                   
                     276
                  
                   
                     ,756164384
                  
                   
                     1,045045969
                  
                
                 
                   
                     277
                  
                   
                     ,758904110
                  
                   
                     1,045212813
                  
                
                 
                   
                     278
                  
                   
                     ,761643836
                  
                   
                     1,045379786
                  
                
                 
                   
                     279
                  
                   
                     ,764383562
                  
                   
                     1,045548585
                  
                
                 
                   
                     280
                  
                   
                     ,767123288
                  
                   
                     1,045713509
                  
                
                 
                   
                     281
                  
                   
                     ,769863014
                  
                   
                     1,045884074
                  
                
                 
                   
                     282
                  
                   
                     ,772602740
                  
                   
                     1,046057440
                  
                
                 
                   
                     283
                  
                   
                     ,775342466
                  
                   
                     1,046214445
                  
                
                 
                   
                     284
                  
                   
                     ,778082192
                  
                   
                     1,046381477
                  
                
                 
                   
                     285
                  
                   
                     ,780821918
                  
                   
                     1,046548530
                  
                
                 
                   
                     286
                  
                   
                     ,783561644
                  
                   
                     1,046710807
                  
                
                 
                   
                     287
                  
                   
                     ,786301371
                  
                   
                     1,046882733
                  
                
                 
                   
                     288
                  
                   
                     ,789041097
                  
                   
                     1,047049872
                  
                
                 
                   
                     289
                  
                   
                     ,791780823
                  
                   
                     1,047217036
                  
                
                 
                   
                     290
                  
                   
                     ,794520548
                  
                   
                     1,047384229
                  
                
                 
                   
                     291
                  
                   
                     ,797260275
                  
                   
                     1,047551448
                  
                
                 
                   
                     292
                  
                   
                     ,800000000
                  
                   
                     1,047718696
                  
                
                 
                   
                     293
                  
                   
                     ,802739727
                  
                   
                     1,047885989
                  
                
                 
                   
                     294
                  
                   
                     ,805479453
                  
                   
                     1,048053264
                  
                
                 
                   
                     295
                  
                   
                     ,808219179
                  
                   
                     1,048220589
                  
                
                 
                 
                   
                     296
                  
                   
                     ,810958905
                  
                   
                     1,048387941
                  
                
                 
                   
                     297
                  
                   
                     ,813698631
                  
                   
                     1,048555320
                  
                
                 
                   
                     298
                  
                   
                     ,816438357
                  
                   
                     1,048722726
                  
                
                 
                   
                     299
                  
                   
                     ,819178083
                  
                   
                     1,048890158
                  
                
                 
                   
                     300
                  
                   
                     ,821917809
                  
                   
                     1,049057400
                  
                
                 
                   
                     301
                  
                   
                     ,824657535
                  
                   
                     1,049225103
                  
                
                 
                   
                     302
                  
                   
                     ,827397261
                  
                   
                     1,049392616
                  
                
                 
                   
                     303
                  
                   
                     ,830136987
                  
                   
                     1,049560107
                  
                
                 
                   
                     304
                  
                   
                     ,832876713
                  
                   
                     1,049727721
                  
                
                 
                   
                     305
                  
                   
                     ,835616439
                  
                   
                     1,049895336
                  
                
                 
                   
                     306
                  
                   
                     ,838356165
                  
                   
                     1,050062933
                  
                
                 
                   
                     307
                  
                   
                     ,841095891
                  
                   
                     1,050230335
                  
                
                 
                   
                     308
                  
                   
                     ,843835617
                  
                   
                     1,050398261
                  
                
                 
                   
                     309
                  
                   
                     ,846575343
                  
                   
                     1,050565953
                  
                
                 
                   
                     310
                  
                   
                     ,849315069
                  
                   
                     1,050733679
                  
                
                 
                   
                     311
                  
                   
                     ,852054795
                  
                   
                     1,050901432
                  
                
                 
                   
                     312
                  
                   
                     ,854794521
                  
                   
                     1,051020810
                  
                
                 
                   
                     313
                  
                   
                     ,857534247
                  
                   
                     1,051237020
                  
                
                 
                   
                     314
                  
                   
                     ,860273973
                  
                   
                     1,051404858
                  
                
                 
                   
                     315
                  
                   
                     ,863013699
                  
                   
                     1,051572714
                  
                
                 
                 
                   
                     316
                  
                   
                     ,865753425
                  
                   
                     1,051738180
                  
                
                 
                   
                     317
                  
                   
                     ,868493152
                  
                   
                     1,051908515
                  
                
                 
                   
                     318
                  
                   
                     ,871232877
                  
                   
                     1,052076452
                  
                
                 
                   
                     319
                  
                   
                     ,873972603
                  
                   
                     1,052244425
                  
                
                 
                   
                     320
                  
                   
                     ,876712329
                  
                   
                     1,052412418
                  
                
                 
                   
                     321
                  
                   
                     ,879452055
                  
                   
                     1,052580440
                  
                
                 
                   
                     322
                  
                   
                     ,882191782
                  
                   
                     1,052748489
                  
                
                 
                   
                     323
                  
                   
                     ,884931508
                  
                   
                     1,052916563
                  
                
                 
                   
                     324
                  
                   
                     ,887671234
                  
                   
                     1,053084180
                  
                
                 
                   
                     325
                  
                   
                     ,890410954
                  
                   
                     1,053252794
                  
                
                 
                   
                     326
                  
                   
                     ,893150686
                  
                   
                     1,053420949
                  
                
                 
                   
                     327
                  
                   
                     ,895890412
                  
                   
                     1,053589108
                  
                
                 
                   
                     328
                  
                   
                     ,898630138
                  
                   
                     1,053757318
                  
                
                 
                   
                     329
                  
                   
                     ,901369864
                  
                   
                     1,053925553
                  
                
                 
                   
                     330
                  
                   
                     ,904109589
                  
                   
                     1,054093831
                  
                
                 
                   
                     331
                  
                   
                     ,906849316
                  
                   
                     1,054262131
                  
                
                 
                   
                     332
                  
                   
                     ,909589042
                  
                   
                     1,054430478
                  
                
                 
                   
                     333
                  
                   
                     ,912328768
                  
                   
                     1,054598766
                  
                
                 
                   
                     334
                  
                   
                     ,915068494
                  
                   
                     1,054767113
                  
                
                 
                   
                     335
                  
                   
                     ,917808219
                  
                   
                     1,054935559
                  
                
                 
                 
                   
                     336
                  
                   
                     ,920547946
                  
                   
                     1,055103982
                  
                
                 
                   
                     337
                  
                   
                     ,923287672
                  
                   
                     1,055272407
                  
                
                 
                   
                     338
                  
                   
                     ,926027398
                  
                   
                     1,055440912
                  
                
                 
                   
                     339
                  
                   
                     ,928767124
                  
                   
                     1,055609416
                  
                
                 
                   
                     340
                  
                   
                     ,931506850
                  
                   
                     1,055778678
                  
                
                 
                   
                     341
                  
                   
                     ,934246576
                  
                   
                     1,055946508
                  
                
                 
                   
                     342
                  
                   
                     ,936986302
                  
                   
                     1,056115093
                  
                
                 
                   
                     343
                  
                   
                     ,939726028
                  
                   
                     1,056283706
                  
                
                 
                   
                     344
                  
                   
                     ,942465754
                  
                   
                     1,056452343
                  
                
                 
                   
                     345
                  
                   
                     ,945205480
                  
                   
                     1,056621012
                  
                
                 
                   
                     346
                  
                   
                     ,947945206
                  
                   
                     1,056789705
                  
                
                 
                   
                     347
                  
                   
                     ,950684932
                  
                   
                     1,056958443
                  
                
                 
                   
                     348
                  
                   
                     ,953424658
                  
                   
                     1,057127172
                  
                
                 
                   
                     349
                  
                   
                     ,956164384
                  
                   
                     1,057295946
                  
                
                 
                   
                     350
                  
                   
                     ,958904110
                  
                   
                     1,057464748
                  
                
                 
                   
                     351
                  
                   
                     ,961643836
                  
                   
                     1,057633576
                  
                
                 
                   
                     352
                  
                   
                     ,964383562
                  
                   
                     1,057802434
                  
                
                 
                   
                     353
                  
                   
                     ,967123288
                  
                   
                     1,057971313
                  
                
                 
                   
                     354
                  
                   
                     ,969863014
                  
                   
                     1,058140222
                  
                
                 
                   
                     355
                  
                   
                     ,972602741
                  
                   
                     1,058309157
                  
                
                 
                 
                   
                     356
                  
                   
                     ,975342467
                  
                   
                     1,058478129
                  
                
                 
                   
                     357
                  
                   
                     ,978082193
                  
                   
                     1,058647110
                  
                
                 
                   
                     358
                  
                   
                     ,980821919
                  
                   
                     1,058816127
                  
                
                 
                   
                     359
                  
                   
                     ,983561645
                  
                   
                     1,058985178
                  
                
                 
                   
                     360
                  
                   
                     ,986301371
                  
                   
                     1,059154242
                  
                
                 
                   
                     361
                  
                   
                     ,989041097
                  
                   
                     1,059323339
                  
                
                 
                   
                     362
                  
                   
                     ,991780823
                  
                   
                     1,059492461
                  
                
                 
                   
                     363
                  
                   
                     ,994520549
                  
                   
                     1,059661616
                  
                
                 
                   
                     364
                  
                   
                     ,997260275
                  
                   
                     1,059837952
                  
                
                 
                   
                     365
                  
                   
                     ,100000000
                  
                   
                     1,060000000
                  
                
                 
                 
                   
                     Months
                  
                   
                     Decimals
                  
                   
                     Amounts
                  
                
                 
                   
                     1
                  
                   
                     ,083333
                  
                   
                     1,004867
                  
                
                 
                   
                     2
                  
                   
                     ,166667
                  
                   
                     1,009659
                  
                
                 
                   
                     3
                  
                   
                     ,250000
                  
                   
                     1,014675
                  
                
                 
                   
                     4
                  
                   
                     ,333334
                  
                   
                     1,019613
                  
                
                 
                   
                     5
                  
                   
                     ,416667
                  
                   
                     1,024576
                  
                
                 
                   
                     6
                  
                   
                     ,500000
                  
                   
                     1,029564
                  
                
                 
                   
                     7
                  
                   
                     ,583334
                  
                   
                     1,034574
                  
                
                 
                   
                     8
                  
                   
                     ,666667
                  
                   
                     1,039610
                  
                
                 
                   
                     9
                  
                   
                     ,750000
                  
                   
                     1,044671
                  
                
                 
                   
                     10
                  
                   
                     ,833334
                  
                   
                     1,049756
                  
                
                 
                   
                     11
                  
                   
                     ,916667
                  
                   
                     1,054865
                  
                
              
            
          
           
             
             
               
                 A
                 Table
                 of
                 Forbearance
                 ,
                 or
                 Amount
                 of
              
               1
               l.
               
                 at
                 Compound
                 Interest
                 ,
                 at
              
               6
               l.
               per
               Cent.
               per
               Annum
               for
               50
               
                 years
                 ,
                 and
                 from
                 thence
                 continued
                 to
              
               100.
               
            
             
               
                 
                   
                     Years
                  
                   
                      
                  
                
                 
                   
                     1
                  
                   
                     1,06
                  
                
                 
                   
                     2
                  
                   
                     1,236
                  
                
                 
                   
                     3
                  
                   
                     1,191016
                  
                
                 
                   
                     4
                  
                   
                     1,262477
                  
                
                 
                   
                     5
                  
                   
                     1,338225
                  
                
                 
                   
                     6
                  
                   
                     1,418519
                  
                
                 
                   
                     7
                  
                   
                     1,503630
                  
                
                 
                   
                     8
                  
                   
                     1,593848
                  
                
                 
                   
                     9
                  
                   
                     1,689479
                  
                
                 
                   
                     10
                  
                   
                     1,790848
                  
                
                 
                   
                     11
                  
                   
                     1,898298
                  
                
                 
                   
                     12
                  
                   
                     2,012196
                  
                
                 
                   
                     13
                  
                   
                     2,132928
                  
                
                 
                   
                     14
                  
                   
                     2,260904
                  
                
                 
                   
                     15
                  
                   
                     2,396358
                  
                
                 
                   
                     Years
                  
                   
                      
                  
                
                 
                   
                     16
                  
                   
                     2,540352
                  
                
                 
                   
                     17
                  
                   
                     2,692773
                  
                
                 
                   
                     18
                  
                   
                     2,854339
                  
                
                 
                   
                     19
                  
                   
                     3,025599
                  
                
                 
                   
                     20
                  
                   
                     3,207135
                  
                
                 
                   
                     21
                  
                   
                     3,399564
                  
                
                 
                   
                     22
                  
                   
                     3,603537
                  
                
                 
                   
                     23
                  
                   
                     3,819750
                  
                
                 
                   
                     24
                  
                   
                     4,048935
                  
                
                 
                   
                     25
                  
                   
                     4,291871
                  
                
                 
                   
                     26
                  
                   
                     4,549383
                  
                
                 
                   
                     27
                  
                   
                     4,821346
                  
                
                 
                   
                     28
                  
                   
                     5,111687
                  
                
                 
                   
                     29
                  
                   
                     5,418388
                  
                
                 
                   
                     30
                  
                   
                     5,743491
                  
                
                 
                 
                   
                     31
                  
                   
                     6,088101
                  
                
                 
                   
                     32
                  
                   
                     6,453386
                  
                
                 
                   
                     33
                  
                   
                     6,840589
                  
                
                 
                   
                     34
                  
                   
                     7,250025
                  
                
                 
                   
                     35
                  
                   
                     7,686087
                  
                
                 
                   
                     36
                  
                   
                     8,147252
                  
                
                 
                   
                     37
                  
                   
                     8,636087
                  
                
                 
                   
                     38
                  
                   
                     9,154252
                  
                
                 
                   
                     39
                  
                   
                     9,703507
                  
                
                 
                   
                     46
                  
                   
                     10,285715
                  
                
                 
                   
                     41
                  
                   
                     10,902857
                  
                
                 
                   
                     42
                  
                   
                     11,557032
                  
                
                 
                   
                     43
                  
                   
                     12,250453
                  
                
                 
                   
                     44
                  
                   
                     12,985481
                  
                
                 
                   
                     45
                  
                   
                     13,764609
                  
                
                 
                   
                     46
                  
                   
                     14,590486
                  
                
                 
                   
                     47
                  
                   
                     15,465915
                  
                
                 
                   
                     48
                  
                   
                     16,393869
                  
                
                 
                   
                     49
                  
                   
                     17,377502
                  
                
                 
                   
                     50
                  
                   
                     18,420152
                  
                
                 
                   
                     60
                  
                   
                     32,987488
                  
                
                 
                   
                     70
                  
                   
                     59,075911
                  
                
                 
                   
                     80
                  
                   
                     105,795933
                  
                
                 
                   
                     90
                  
                   
                     189,464433
                  
                
                 
                   
                     100
                  
                   
                     339,398871
                  
                
              
            
          
        
         
      
       
         
           
             
             
               The
               Doctrine
               of
               DECIMAL
               ARITHMETICK
               ,
               Simple
               Interest
               ,
               &c.
               
            
             
               AS
               ALSO
               
                 Of
                 Compound
                 Interest
                 and
                 Annuities
              
               :
            
             
               Generally
               performed
               for
               any
               time
               of
               Payment
               ,
               or
               Rate
               of
               Interest
               ,
               by
               help
               of
               any
               particular
               Table
               of
               Forbearance
               of
               1
               l.
               Principal
               .
            
             
               
                 Abridged
                 for
                 Portability
                 in
                 a
                 Letter
                 Case
                 .
              
            
             
               By
               
                 John
                 Collins
              
               Accomptant
               ,
               Philomath
               .
            
          
        
         
           
             
               A
               
                 Decimal
                 Fraction
              
               is
               such
               a
               one
               whose
               Denominator
               is
               understood
               and
               not
               expressed
               ;
               and
               is
               an
               Unit
               with
               as
               many
               Cyphers
               following
               
               it
               ,
               as
               there
               are
               Figures
               and
               Cyphers
               in
               the
               Numerator
               .
            
             
               Corollary
               .
               Wherefore
               the
               annexing
               of
               Cyphers
               towards
               the
               right
               hand
               of
               a
               Decimal
               alters
               not
               its
               value
               .
               A
               Decimal
               Fraction
               of
               Coin
               may
               be
               easily
               valued
               without
               the
               help
               of
               Tables
               .
               For
               each
               Unit
               in
               the
               first
               place
               is
               in
               value
               2
               s.
               5
               d.
               in
               the
               second
               place
               1
               s.
               and
               the
               rest
               Farthings
               ;
               but
               if
               any
               exceed
               15
               /
               48
               there
               must
               be
               ½
               Farthings
               abated
               :
            
             
               
                 
                   
                     So
                  
                   
                     ,854
                  
                   
                     is
                     in
                     value
                  
                   
                     17
                     s.
                     1
                     d.
                     
                  
                
                 
                   
                     ,418
                  
                   
                     8
                     4
                     ½
                     .
                  
                
              
            
             
               Addition
               and
               Substraction
               in
               Decimals
               is
               the
               same
               as
               in
               whole
               Numbers
               ,
               keeping
               the
               place
               of
               Units
               under
               each
               other
               .
            
             
               Multiplication
               in
               Decimals
               ;
               as
               many
               Decimal
               parts
               as
               are
               in
               both
               Multipliers
               ,
               so
               many
               must
               be
               cut
               off
               from
               
               the
               Product
               ;
               which
               if
               it
               have
               not
               so
               many
               places
               the
               Defect
               is
               to
               be
               supplied
               with
               Cyphers
               towards
               the
               left
               hand
               .
            
             
               Division
               in
               Decimals
               is
               the
               Converse
               annex
               Cyphers
               sufficient
               (
               if
               need
               be
               )
               to
               the
               Dividend
               towards
               the
               right
               hand
               ,
               that
               it
               may
               have
               more
               Decimal
               Parts
               than
               the
               Divisor
               ,
               then
               as
               many
               Decimal
               Parts
               as
               are
               in
               the
               Dividend
               ,
               so
               many
               must
               be
               in
               the
               Divisor
               ,
               and
               Quote
               ,
               when
               the
               Division
               is
               finished
               ;
               and
               in
               case
               of
               defect
               ,
               the
               Quote
               is
               to
               be
               supplied
               with
               Cyphers
               towards
               the
               left
               hand
               .
            
             
               
                 Simple
                 Interest
                 .
              
               
                 
                   Prop.
                   1.
                   
                   
                     To
                     compute
                     the
                     Interest
                     of
                  
                   1
                   l.
                   
                     for
                     a
                     Day
                  
                   .
                
                 
                   6
                   /
                   105
                   is
                   the
                   Interest
                   of
                   100
                   l.
                   for
                   a
                   day
                   ,
                   the
                   1
                   /
                   100
                   whereof
                   is
                   the
                   Interest
                   of
                   1
                   l.
                   for
                   a
                   day
                   ,
                   viz.
                   6
                   /
                   16500
                   ,
                   Or
                   6
                   divided
                   by
                   36500
                   ,
                   namely
                   ,
                
                 
                 
                   
                     
                       
                         Days
                      
                       
                         
                           Interest
                           of
                        
                         1
                         l.
                         
                      
                    
                     
                       
                         1
                      
                       
                         ,000164384
                      
                    
                     
                       
                         2
                      
                       
                         ,000328768
                      
                    
                     
                       
                         3
                      
                       
                         ,000493152
                      
                    
                     
                       
                         4
                      
                       
                         ,000657536
                      
                    
                     
                       
                         5
                      
                       
                         ,000821920
                      
                    
                     
                       
                         6
                      
                       
                         ,000986304
                      
                    
                     
                       
                         7
                      
                       
                         ,001150688
                      
                    
                     
                       
                         8
                      
                       
                         ,001315072
                      
                    
                     
                       
                         9
                      
                       
                         ,001479456
                      
                    
                  
                
              
               
                 
                   Prop.
                   2.
                   
                   
                     Forbearance
                     of
                     Money
                     at
                     Simple
                     Interest
                     .
                  
                
                 
                   The
                   Interest
                   of
                   one
                   pound
                   for
                   any
                   number
                   of
                   Days
                   may
                   be
                   taken
                   from
                   this
                   Table
                   by
                   Addition
                   ,
                   (
                   instead
                   of
                   a
                   Multiplication
                   ,
                   by
                   the
                   number
                   of
                   days
                   ,
                   the
                   trouble
                   whereof
                   is
                   by
                   the
                   help
                   of
                   this
                   Table
                   spared
                   )
                   and
                   that
                   
                   Product
                   multiplied
                   by
                   any
                   other
                   given
                   Sum
                   ,
                   makes
                   the
                   Interest
                   thereof
                   for
                   the
                   time
                   given
                   .
                
              
               
                 
                   Prop.
                   3.
                   
                   
                     Rebate
                     ,
                     or
                     the
                     present
                     worth
                     of
                     Money
                     due
                     hereafter
                     .
                  
                
                 
                   Find
                   the
                   Interest
                   of
                   one
                   pound
                   ,
                   for
                   the
                   time
                   given
                   ,
                   and
                   thereto
                   adding
                   an
                   Unit.
                   By
                   it
                   divide
                   any
                   other
                   Sum
                   given
                   ,
                   and
                   the
                   Quote
                   is
                   its
                   present
                   worth
                   .
                
              
               
                 
                   Prop.
                   4.
                   
                   
                     Equation
                     of
                     Payments
                  
                   .
                
                 
                   By
                   Prop.
                   3.
                   
                   Compute
                   all
                   the
                   present
                   worths
                   ,
                   and
                   then
                   by
                   Proportion
                   .
                   If
                   all
                   those
                   present
                   worths
                   amounted
                   to
                   the
                   Total
                   of
                   all
                   those
                   Payments
                   ,
                   What
                   did
                   1
                   l.
                   amount
                   to
                   in
                   the
                   said
                   time
                   ?
                   From
                   the
                   Result
                   substract
                   an
                   Unit
                   ,
                   the
                   Remainder
                   is
                   the
                   Interest
                   of
                   1
                   l.
                   for
                   th●
                   time
                   sought
                   ,
                   which
                   divide
                   by
                   the
                   Interest
                   of
                   1
                   l.
                   for
                   a
                   day
                   ,
                   
                   the
                   Quote
                   is
                   the
                   number
                   of
                   days
                   sought
                   .
                   If
                   you
                   are
                   to
                   Equate
                   an
                   Annuity
                   at
                   Simple
                   Interest
                   ,
                   I
                   presume
                   a
                   Compendium
                   may
                   be
                   found
                   in
                   Mengolus
                   his
                   Arithmetical
                   Quadratures
                   ,
                   (
                   a
                   Book
                   I
                   never
                   saw
                   )
                   who
                   its
                   probable
                   by
                   a
                   Compendium
                   gets
                   the
                   Fact
                   of
                   an
                   Arithmetical
                   Progression
                   ,
                   and
                   adds
                   Fractions
                   that
                   have
                   a
                   constant
                   Numerator
                   ,
                   and
                   an
                   Arithmetical
                   Progression
                   for
                   their
                   Denominators
                   .
                
                 
                   
                     
                       
                         Days
                      
                       
                         Decimals
                      
                       
                         Amount
                      
                       
                         5
                         Years
                      
                       
                         Amounts
                      
                    
                     
                       
                         1
                      
                       
                         ,002739
                      
                       
                         1,000160
                      
                       
                         1
                      
                       
                         1,06
                      
                    
                     
                       
                         2
                      
                       
                         ,005479
                      
                       
                         1,000319
                      
                       
                         2
                      
                       
                         1,1236
                      
                    
                     
                       
                         3
                      
                       
                         ,008219
                      
                       
                         1,000479
                      
                       
                         3
                      
                       
                         1,191016
                      
                    
                     
                       
                         4
                      
                       
                         ,010959
                      
                       
                         1,000639
                      
                       
                         4
                      
                       
                         1,262477
                      
                    
                     
                       
                         5
                      
                       
                         ,013698
                      
                       
                         1,000798
                      
                       
                         5
                      
                       
                         1,338225
                      
                    
                     
                       
                         6
                      
                       
                         ,016438
                      
                       
                         1,000958
                      
                       
                         6
                      
                       
                         1,418519
                      
                    
                     
                       
                         7
                      
                       
                         ,019178
                      
                       
                         1,001118
                      
                       
                         7
                      
                       
                         1,503630
                      
                    
                     
                       
                         8
                      
                       
                         ,021918
                      
                       
                         1,001278
                      
                       
                         8
                      
                       
                         1,593848
                      
                    
                     
                       
                         9
                      
                       
                         ,024657
                      
                       
                         1,001438
                      
                       
                         9
                      
                       
                         1,689479
                      
                    
                     
                       
                         10
                      
                       
                         ,027397
                      
                       
                         1,001598
                      
                       
                         10
                      
                       
                         1,790848
                      
                    
                     
                       
                         11
                      
                       
                         ,030137
                      
                       
                         1,001757
                      
                       
                         11
                      
                       
                         1,898298
                      
                    
                     
                       
                         12
                      
                       
                         ,032877
                      
                       
                         1,001917
                      
                       
                         12
                      
                       
                         2,012196
                      
                    
                     
                       
                         13
                      
                       
                         ,035617
                      
                       
                         1,002077
                      
                       
                         13
                      
                       
                         2,132928
                      
                    
                     
                       
                         14
                      
                       
                         ,038357
                      
                       
                         1,002237
                      
                       
                         14
                      
                       
                         2,260904
                      
                    
                     
                       
                         15
                      
                       
                         ,041097
                      
                       
                         1,002397
                      
                       
                         15
                      
                       
                         2,3●6●58
                      
                    
                     
                     
                       
                         16
                      
                       
                         ,043837
                      
                       
                         1,002557
                      
                       
                         16
                      
                       
                         2,540352
                      
                    
                     
                       
                         17
                      
                       
                         ,046577
                      
                       
                         1,002717
                      
                       
                         17
                      
                       
                         2,692773
                      
                    
                     
                       
                         18
                      
                       
                         ,049316
                      
                       
                         1,002878
                      
                       
                         18
                      
                       
                         2,854339
                      
                    
                     
                       
                         19
                      
                       
                         ,05●055
                      
                       
                         1,003038
                      
                       
                         19
                      
                       
                         3,025599
                      
                    
                     
                       
                         20
                      
                       
                         ,054795
                      
                       
                         1,003198
                      
                       
                         20
                      
                       
                         3,207135
                      
                    
                     
                       
                         21
                      
                       
                         ,057536
                      
                       
                         1,003358
                      
                       
                         21
                      
                       
                         3,399564
                      
                    
                     
                       
                         22
                      
                       
                         ,060274
                      
                       
                         1,003518
                      
                       
                         22
                      
                       
                         3,603537
                      
                    
                     
                       
                         23
                      
                       
                         ,063016
                      
                       
                         1,003678
                      
                       
                         23
                      
                       
                         3,819750
                      
                    
                     
                       
                         24
                      
                       
                         ,065755
                      
                       
                         1,003839
                      
                       
                         24
                      
                       
                         4,048935
                      
                    
                     
                       
                         25
                      
                       
                         ,068495
                      
                       
                         1,003999
                      
                       
                         25
                      
                       
                         4,291871
                      
                    
                     
                       
                         26
                      
                       
                         ,071233
                      
                       
                         1,004159
                      
                       
                         26
                      
                       
                         4,549383
                      
                    
                     
                       
                         27
                      
                       
                         ,073973
                      
                       
                         1,004319
                      
                       
                         27
                      
                       
                         4,822346
                      
                    
                     
                       
                         28
                      
                       
                         ,076714
                      
                       
                         1,004480
                      
                       
                         28
                      
                       
                         5,111687
                      
                    
                     
                       
                         29
                      
                       
                         ,079454
                      
                       
                         1,004640
                      
                       
                         29
                      
                       
                         5,418388
                      
                    
                     
                       
                         30
                      
                       
                         ,082193
                      
                       
                         1,004801
                      
                       
                         30
                      
                       
                         5,743491
                      
                    
                     
                       
                         60
                      
                       
                         ,164386
                      
                       
                         1,009625
                      
                       
                         31
                      
                       
                         6,088101
                      
                    
                     
                       
                         90
                      
                       
                         ,246579
                      
                       
                         1,014472
                      
                       
                         32
                      
                       
                         6,453386
                      
                    
                     
                       
                         120
                      
                       
                         ,328772
                      
                       
                         1,019342
                      
                       
                         33
                      
                       
                         6,840589
                      
                    
                     
                       
                         150
                      
                       
                         ,410965
                      
                       
                         1,024335
                      
                       
                         34
                      
                       
                         7,250025
                      
                    
                     
                       
                         180
                      
                       
                         ,493158
                      
                       
                         1,029153
                      
                       
                         35
                      
                       
                         7,686087
                      
                    
                     
                       
                         210
                      
                       
                         ,575351
                      
                       
                         1,034093
                      
                       
                         36
                      
                       
                         8,147252
                      
                    
                     
                       
                         240
                      
                       
                         ,657544
                      
                       
                         1,039057
                      
                       
                         37
                      
                       
                         8,636087
                      
                    
                     
                       
                         270
                      
                       
                         ,7●9737
                      
                       
                         1,044●45
                      
                       
                         38
                      
                       
                         9,154252
                      
                    
                     
                       
                         300
                      
                       
                         ,821930
                      
                       
                         1,049●●7
                      
                       
                         39
                      
                       
                         9,7●35●7
                      
                    
                     
                       
                         330
                      
                       
                         ,904193
                      
                       
                         1,054093
                      
                       
                         40
                      
                       
                         10,285715
                      
                    
                     
                       
                         360
                      
                       
                         ,986316
                      
                       
                         1
                         ,
                         ●59154
                      
                       
                         50
                      
                       
                         18,420152
                      
                    
                     
                       
                         Mo.
                         1
                      
                       
                         ,083334
                      
                       
                         1,004867
                      
                       
                         60
                      
                       
                         32,927388
                      
                    
                     
                       
                         2
                      
                       
                         ,166667
                      
                       
                         1,0●9759
                      
                       
                         70
                      
                       
                         50,075911
                      
                    
                     
                       
                         3
                      
                       
                         ,250●●●
                      
                       
                         1,014●74
                      
                       
                         80
                      
                       
                         1●5,795933
                      
                    
                     
                       
                         6
                      
                       
                         ,500000
                      
                       
                         1
                         ,
                         ●29563
                      
                       
                         90
                      
                       
                         189,464433
                      
                    
                     
                       
                         9
                      
                       
                         ,750000
                      
                       
                         1,014●71
                      
                       
                         100
                      
                       
                         339,398471
                      
                    
                  
                
                 
                 
                   The
                   annexed
                   Table
                   is
                   a
                   Table
                   of
                   the
                   Forbearance
                   or
                   Amount
                   of
                   1
                   l.
                   at
                   Compound
                   Interest
                   at
                   6
                   
                     per
                     Cent.
                     per
                     An.
                  
                   This
                   Table
                   as
                   to
                   the
                   Years
                   ,
                   is
                   composed
                   by
                   the
                   continual
                   Multiplication
                   of
                   1,06
                   (
                   or
                   by
                   Addition
                   tabulating
                   the
                   same
                   )
                   and
                   as
                   to
                   the
                   Days
                   may
                   be
                   supplied
                   either
                   by
                   continual
                   Proportionals
                   ,
                   or
                   the
                   common
                   Logarithms
                   ,
                   which
                   also
                   are
                   no
                   other
                   than
                   Answers
                   to
                   Interest
                   Questions
                   ,
                   at
                   the
                   rate
                   of
                   near
                   26
                   
                     per
                     Cent.
                  
                   (
                   or
                   the
                   Amount
                   is
                   as
                   1
                   ,
                   to
                   1,2589292
                   )
                   supposing
                   1
                   l.
                   in
                   10
                   Years
                   to
                   amount
                   to
                   10
                   l.
                   the
                   Logarithms
                   (
                   distinguishing
                   the
                   first
                   Figure
                   with
                   a
                   Conmma
                   )
                   shew
                   the
                   Years
                   and
                   Decimals
                   when
                   it
                   amounted
                   to
                   2
                   l.
                   3
                   
                     l.
                     &c.
                  
                   
                   And
                   those
                   Logarithms
                   may
                   be
                   raised
                   from
                   the
                   former
                   .
                   For
                   the
                   differences
                   of
                   all
                   sorts
                   of
                   Logarithms
                   of
                   any
                   four
                   Numbers
                   ,
                   are
                   directly
                   Proportional
                   ,
                   and
                   may
                   be
                   raised
                   from
                   any
                   Table
                   of
                   Forbearance
                   of
                   Money
                   at
                   Compound
                   Interest
                   .
                
              
               
                 
                 
                   Prop.
                   1.
                   
                   
                     To
                     continue
                     the
                     said
                     Table
                     ,
                     or
                     to
                     find
                     the
                     Amount
                     of
                  
                   1
                   l.
                   
                     forborn
                     for
                     any
                     time
                     proposed
                  
                   .
                
                 
                   Multiply
                   those
                   Amounts
                   together
                   that
                   belong
                   to
                   such
                   time
                   ,
                   as
                   added
                   together
                   makes
                   the
                   time
                   given
                   .
                
              
               
                 
                   Prop.
                   2.
                   
                   
                     The
                     Amount
                     of
                  
                   1
                   l.
                   
                     being
                     given
                     ,
                     To
                     find
                     the
                     time
                     of
                     Forbearance
                     .
                  
                
                 
                   Search
                   the
                   Amount
                   in
                   the
                   Tables
                   ,
                   and
                   divide
                   by
                   the
                   next
                   lesser
                   amount
                   ,
                   and
                   that
                   Quote
                   again
                   by
                   the
                   next
                   lesser
                   Amount
                   ,
                   &c.
                   reserving
                   the
                   Quotes
                   ,
                   the
                   time
                   belonging
                   to
                   the
                   Divisors
                   ,
                   and
                   the
                   last
                   Quote
                   is
                   the
                   time
                   sought
                   .
                   Example
                   ,
                   1
                   l.
                   did
                   amount
                   to
                   1,08
                   in
                   1,32079
                   years
                   .
                
              
               
                 
                 
                   Prop.
                   3.
                   
                   
                     To
                     compute
                     the
                     Amount
                     of
                  
                   1
                   l.
                   
                     for
                     any
                     time
                     at
                     any
                     Rate
                     of
                     Interest
                     .
                  
                
                 
                   By
                   Prop.
                   2.
                   compute
                   in
                   what
                   time
                   at
                   6
                   
                     per
                     Cent.
                  
                   1
                   l.
                   shall
                   amount
                   to
                   as
                   much
                   as
                   in
                   one
                   Year
                   at
                   the
                   Rate
                   proposed
                   ,
                   that
                   keep
                   in
                   store
                   ,
                   and
                   multiply
                   by
                   the
                   time
                   proposed
                   ,
                   the
                   Fact
                   is
                   the
                   time
                   in
                   which
                   at
                   6
                   
                     per
                     Cent.
                  
                   1
                   l.
                   shall
                   amount
                   to
                   as
                   much
                   as
                   it
                   should
                   do
                   at
                   the
                   other
                   Rate
                   given
                   ;
                   to
                   know
                   which
                   ,
                   use
                   Prop.
                   1.
                   
                
                 
                   
                     Example
                     ,
                     100
                     l.
                     
                       did
                       amount
                       to
                    
                     105
                     l.
                     in
                     ,
                     83732
                     Years
                     .
                  
                   
                     
                       
                         
                            
                        
                         
                           l.
                           
                        
                         
                            
                        
                         
                            
                        
                      
                       
                         
                           Or
                           ,
                           1
                           l.
                           did
                           amount
                           to
                        
                         
                           1,05
                        
                         
                           In
                           Years
                        
                         
                           ,83732
                        
                      
                       
                         
                           1,06
                        
                         
                           1
                           ,
                        
                      
                       
                         
                           1,07
                        
                         
                           1,16114
                        
                      
                       
                         
                           1,08
                        
                         
                           1,32079
                        
                      
                       
                         
                           1,09
                        
                         
                           1,47896
                        
                      
                       
                         
                           1,10
                        
                         
                           1,63569
                        
                      
                    
                  
                   
                   
                     Admit
                     it
                     were
                     required
                     to
                     find
                     what
                     1
                     l.
                     amounted
                     to
                     in
                     20
                     Years
                     at
                     8
                     
                       per
                       cent
                    
                     .
                     multiply
                     1,32079
                     by
                     20
                     ,
                     the
                     Fact
                     or
                     Product
                     is
                     26,14158
                     ,
                     and
                     by
                     Prop.
                     1.
                     1
                     l.
                     at
                     6
                     
                       per
                       cent
                    
                     .
                     in
                     that
                     time
                     did
                     amount
                     to
                     4
                     6609.
                     
                  
                   
                     Now
                     if
                     the
                     Amount
                     of
                     1
                     l.
                     be
                     given
                     ,
                     Annuity
                     Problems
                     are
                     salved
                     thereby
                     .
                     And
                     for
                     the
                     advantage
                     of
                     this
                     Proposition
                     the
                     Decimals
                     of
                     time
                     were
                     added
                     .
                  
                
              
               
                 
                   Prop.
                   4.
                   
                   
                     Forbearance
                     of
                     Monies
                     at
                     Compound
                     Interest
                     .
                  
                
                 
                   As
                   an
                   Unit
                   is
                   to
                   its
                   Amount
                   in
                   the
                   Tables
                   suitable
                   to
                   the
                   time
                   given
                   :
                
                 
                   So
                   is
                   any
                   other
                   Sum
                   to
                   its
                   Amount
                   .
                
              
               
                 
                   Prop.
                   5.
                   
                   
                     Discount
                     of
                     Money
                     at
                     Compound
                     Interest
                     ,
                     the
                     Converse
                     of
                     the
                     former
                     .
                  
                
                 
                   As
                   the
                   Tabular
                   Number
                   ,
                
                 
                 
                   Is
                   to
                   an
                   Unit
                   ,
                   its
                   present
                   Worth
                   :
                
                 
                   
                     So
                     is
                     any
                     other
                     Sum
                     ,
                  
                   
                     To
                     its
                     present
                     Worth.
                     
                  
                
                 
                   In
                   Annuity
                   Questions
                   the
                   Proportions
                   are
                   suited
                   for
                   yearly
                   Payments
                   ;
                   if
                   the
                   Payment
                   be
                   half-yearly
                   ,
                   then
                   instead
                   of
                   ,06
                   (
                   or
                   1,06
                   )
                   and
                   the
                   Annuity
                   in
                   any
                   term
                   ,
                   take
                   half
                   a
                   years
                   Interest
                   ,029565
                   ,
                   and
                   the
                   half
                   yearly
                   Payment
                   ;
                   and
                   for
                   quarterly
                   Payments
                   the
                   Quarters
                   Interest
                   ,014674
                   ,
                   and
                   the
                   quarterly
                   Payment
                   ,
                   &c.
                   
                
              
               
                 
                   Prop.
                   6.
                   
                   
                     Forbearance
                     of
                     Annuities
                  
                   .
                
                 
                   As
                   ,06
                   the
                   Annual
                   Interest
                   of
                   1
                   l.
                   
                
                 
                   Is
                   to
                   the
                   Amount
                   less
                   an
                   Unit
                   of
                   1
                   l.
                   forborn
                   any
                   term
                   :
                
                 
                   So
                   is
                   the
                   Annuity
                   or
                   yearly
                   Pension
                   ,
                
                 
                   To
                   the
                   Sum
                   for
                   the
                   whole
                   Arrearages
                   thereof
                   .
                
              
               
                 
                 
                   Prop.
                   7.
                   
                   
                     Discount
                     of
                     Annuities
                     ,
                     or
                     their
                     present
                     Worth.
                     
                  
                
                 
                   As
                   the
                   Fact
                   of
                   ,06
                   and
                   of
                   the
                   Amount
                   of
                   1
                   l
                   at
                   Compound
                   Interest
                   for
                   the
                   time
                   proposed
                   ,
                
                 
                   Is
                   to
                   the
                   said
                   Amount
                   less
                   an
                   Unit
                   :
                
                 
                   
                     So
                     is
                     any
                     Annuity
                     ,
                  
                   
                     To
                     its
                     present
                     Worth
                     ,
                  
                
                 
                 
                   
                     
                       To
                       this
                       Proposition
                       belongs
                       the
                       Purchace
                       of
                       the
                       Fee-simple
                       .
                    
                     
                       
                         For
                      
                       
                         yearly
                      
                       
                         Payments
                         divide
                         the
                         Rent
                      
                       
                         1
                         l.
                         
                      
                       
                         by
                         the
                         Interest
                      
                       
                         ,06
                      
                       
                         the
                         Quotes
                         are
                      
                       
                         16
                         ,
                         ⅔
                      
                    
                     
                       
                         half-yearly
                      
                       
                          
                      
                       
                         ,5
                      
                       
                          
                      
                       
                         ,0295613
                      
                       
                          
                      
                       
                         16,91303
                      
                    
                     
                       
                         quarterly
                      
                       
                          
                      
                       
                         ,25
                      
                       
                          
                      
                       
                         ,01674
                      
                       
                          
                      
                       
                         17,07843
                      
                    
                  
                
                 
                 
                   And
                   so
                   many
                   pounds
                   (
                   or
                   years
                   purchace
                   )
                   is
                   the
                   Inheritance
                   worth
                   (
                   as
                   may
                   be
                   proved
                   from
                   
                   Tacquet's
                   Arithmetick
                   )
                   which
                   Sums
                   are
                   no
                   other
                   than
                   the
                   Totals
                   of
                   the
                   present
                   Worths
                   of
                   the
                   infinite
                   Payments
                   to
                   be
                   made
                   .
                   Hereto
                   also
                   belong
                   Equation
                   of
                   Payments
                   at
                   Compound
                   Interest
                   :
                   for
                   having
                   computed
                   the
                   present
                   Worths
                   ,
                   by
                   proportion
                   ,
                   you
                   may
                   find
                   what
                   1
                   l.
                   amounted
                   to
                   in
                   the
                   time
                   sought
                   ,
                   and
                   by
                   the
                   second
                   Proposition
                   the
                   time
                   it self
                   .
                
              
               
                 
                   Prop.
                   8.
                   
                   
                     To
                     find
                     what
                     Annuity
                     any
                     Sum
                     of
                     ready
                     Money
                     shall
                     purchase
                     for
                     any
                     time
                     proposed
                     .
                  
                
                 
                   As
                   the
                   Amount
                   less
                   an
                   Unit
                   of
                   1
                   l.
                   forborn
                   at
                   Compound
                   Interest
                   ,
                   the
                   time
                   proposed
                   ,
                
                 
                   Is
                   to
                   the
                   Fact
                   of
                   ,
                   06
                   ,
                   and
                   of
                   the
                   Amount
                   of
                   1
                   l.
                   so
                   forborn
                   :
                
                 
                   So
                   is
                   any
                   Sum
                   of
                   ready
                   Money
                   ,
                
                 
                 
                   To
                   the
                   Annuity
                   it
                   shall
                   purchase
                   .
                
                 
                   From
                   these
                   three
                   Propositions
                   the
                   Tables
                   in
                   common
                   use
                   may
                   be
                   raised
                   ,
                   if
                   you
                   put
                   an
                   Unit
                   in
                   the
                   third
                   place
                   .
                
              
               
                 
                   Prop.
                   9.
                   
                   
                     The
                     Worth
                     of
                     an
                     Annuity
                     being
                     proposed
                     ,
                     To
                     find
                     the
                     time
                     of
                     its
                     Continuance
                     .
                  
                
                 
                   Get
                   the
                   difference
                   of
                   the
                   Facts
                   of
                   1,06
                   into
                   the
                   Annuity
                   ,
                
                 
                   And
                   of
                   ,06
                   into
                   the
                   Sum
                   of
                   the
                   present
                   Worth
                   and
                   Annuity
                   ,
                
                 
                   Then
                   ,
                   as
                   the
                   said
                   difference
                   ,
                   is
                   to
                   an
                   Unit
                   :
                
                 
                   So
                   is
                   the
                   Annuity
                   ,
                   To
                   the
                   Amount
                   of
                   1
                   l.
                   for
                   the
                   time
                   sought
                   (
                   to
                   be
                   found
                   by
                   the
                   second
                   Proposition
                   .
                   )
                
              
               
                 
                   Prop.
                   10.
                   
                   
                     An
                     Annuity
                     ,
                     its
                     present
                     Worth
                     ,
                     and
                     time
                     of
                     Continuance
                     proposed
                     ,
                     To
                     find
                     the
                     Rate
                     of
                     Interest
                     .
                  
                
                 
                   This
                   is
                   the
                   hardest
                   of
                   Annuity
                   Problems
                   ,
                   
                   and
                   not
                   to
                   be
                   resolved
                   with
                   Logarithms
                   without
                   Position
                   or
                   Trials
                   ;
                   the
                   use
                   is
                   to
                   find
                   the
                   value
                   of
                   any
                   other
                   Number
                   of
                   Years
                   therein
                   :
                   To
                   facilitate
                   which
                   ,
                   observe
                   ,
                   That
                   by
                   Prop.
                   8.
                   for
                   21
                   years
                   at
                   6
                   
                     per
                     Cent.
                  
                   you
                   may
                   purchase
                   Annuity
                   of
                
                 
                   
                     
                       
                         s.
                         
                      
                       
                         d.
                         
                      
                       
                         For
                      
                       
                         l.
                         
                      
                       
                         s.
                         
                      
                    
                     
                       
                         11
                      
                       
                         11
                      
                       
                         7
                      
                       
                         00
                      
                    
                     
                       
                         12
                      
                       
                         9
                      
                       
                         7
                      
                       
                         10
                      
                    
                     
                       
                         13
                      
                       
                         7
                      
                       
                         8
                      
                       
                         00
                      
                    
                     
                       
                         14
                      
                       
                         5
                      
                       
                         8
                      
                       
                         10
                      
                    
                     
                       
                         15
                      
                       
                         3
                      
                       
                         9
                      
                       
                         00
                      
                    
                     
                       
                         17
                      
                       
                          
                      
                       
                         10
                      
                       
                         00
                      
                    
                  
                
                 
                   And
                   these
                   are
                   the
                   Rates
                   for
                   Leases
                   of
                   Houses
                   of
                   such
                   a
                   time
                   ,
                   to
                   wit
                   ,
                   1
                   l.
                   a
                   year
                   for
                   21
                   years
                   ,
                   is
                   worth
                   about
                   7
                   l.
                   10
                   s.
                   or
                   8
                   l.
                   as
                   men
                   agree
                   ,
                   which
                   is
                   a
                   certainty
                   of
                   12
                   s.
                   9
                   d.
                   or
                   13
                   s.
                   7
                   
                     d.
                     per
                     Annum
                  
                   ,
                   whereby
                   you
                   have
                   a
                   direction
                   to
                   accord
                   an
                   abate
                   for
                   Casualty
                   ,
                   and
                   then
                   use
                   the
                   6
                   Proposition
                   .
                   
                   Most
                   of
                   the
                   many
                   Propositions
                   in
                   the
                   Learned
                   Doctor
                   Wallis
                   his
                   Arithmetick
                   concerning
                   Geometrical
                   Progression
                   ;
                   as
                   also
                   in
                   Mr.
                   
                   Dary's
                   sheet
                   of
                   Algebra
                   ,
                   may
                   be
                   easily
                   resolved
                   by
                   help
                   of
                   the
                   former
                   Table
                   :
                   But
                   this
                   I
                   have
                   handled
                   in
                   my
                   Supplements
                   to
                   Accomptantship
                   ,
                   where
                   also
                   somewhat
                   of
                   Logarithm
                   Curves
                   ,
                   derived
                   from
                   Mean
                   or
                   Continual
                   Proportionals
                   ,
                   or
                   Tables
                   of
                   Interest
                   ,
                   and
                   serve
                   for
                   making
                   the
                   Logarithm
                   Scales
                   of
                   Numbers
                   ,
                   Sines
                   ,
                   Tangents
                   ,
                   (
                   or
                   
                   Mercator's
                   Meridian
                   Line
                   )
                   Geometrically
                   .
                
              
               
                 
                   Prop.
                   9.
                   
                   
                     More
                     easily
                  
                   .
                
                 
                   As
                   on
                   Annuity
                   ,
                   less
                   the
                   Fact
                   of
                   ,06
                   into
                   its
                   present
                   Worth
                   ,
                
                 
                   
                     Is
                     to
                     the
                     Annuity
                     :
                  
                   
                     So
                     is
                     an
                     Unit
                     ,
                  
                   
                     To
                     the
                     Amount
                     of
                     1
                     l.
                     for
                     the
                     time
                     sought
                     .
                  
                
                 
                   If
                   the
                   Payments
                   be
                   half
                   yearly
                   ,
                   for
                   the
                   Annuity
                   in
                   the
                   first
                   and
                   third
                   
                   Terms
                   ,
                   take
                   half
                   the
                   Annuity
                   ,
                   and
                   for
                   ,06
                   in
                   the
                   first
                   Term
                   as
                   a
                   Multiplier
                   ,
                   take
                   ,02956
                   the
                   half
                   Years
                   Interest
                   .
                
                 
                   For
                   another
                   Rate
                   of
                   Interest
                   as
                   8
                   
                     per
                     Cent.
                  
                   take
                   in
                   ,08
                   as
                   a
                   Multiplier
                   ,
                   and
                   find
                   the
                   time
                   in
                   Years
                   and
                   Decimals
                   by
                   2.
                   
                   Prop.
                   as
                   at
                   6
                   
                     per
                     Cent.
                  
                   which
                   divide
                   by
                   the
                   fitted
                   Number
                   of
                   the
                   Rate
                   in
                   Prop.
                   3.
                   to
                   wit
                   1,32079
                   ,
                   the
                   Quote
                   is
                   the
                   true
                   time
                   sought
                   in
                   Years
                   and
                   Decimals
                   ,
                   which
                   is
                   easily
                   reduced
                   into
                   Days
                   by
                   the
                   Decimal
                   Table
                   of
                   Days
                   .
                
                 
                   
                     Example
                     .
                  
                   
                     50
                     l.
                     a
                     Year
                     at
                     8
                     
                       per
                       Cent.
                    
                     is
                     worth
                     490
                     l.
                     18
                     s.
                     2½
                     ,
                     or
                     490,91
                     ,
                     the
                     time
                     of
                     continuance
                     is
                     20
                     years
                     .
                     
                  
                   
                   
                     
                       An
                       Amount
                       is
                       proposed
                       for
                    
                     20
                     
                       years
                       to
                       be
                    
                     4,6609
                     ,
                     
                       what
                       is
                       the
                       Rate
                       of
                       Interest
                       ?
                    
                  
                   
                     1.
                     
                     The
                     time
                     in
                     which
                     1
                     l.
                     came
                     to
                     so
                     much
                     at
                     6
                     
                       per
                       Cent.
                    
                     is
                     26,4158
                     ,
                     found
                     by
                     the
                     second
                     Proposition
                     .
                  
                   
                     2.
                     
                     Divide
                     26,4158
                     by
                     20
                     ,
                     the
                     time
                     proposed
                     ,
                     the
                     Quote
                     is
                     132079
                     years
                     .
                  
                   
                     3.
                     1
                     l.
                     at
                     6
                     
                       per
                       Cent.
                    
                     in
                     that
                     time
                     amounted
                     to
                     1,08
                     ,
                     the
                     Ratio
                     sought
                     .
                  
                
              
            
          
           
             
             
               A
               PERPETUAL
               ALMANACK
               ,
            
             
               
                 
                   To
                   find
                   what
                   day
                   of
                   the
                   Week
                   the
                   first
                   of
                
                 March
                 
                   shall
                   happen
                   upon
                
                 .
              
               
                 ADD
                 to
                 the
                 Number
                 2
                 the
                 Year
                 of
                 our
                 Lord
                 ,
                 and
                 the
                 fourth
                 part
                 of
                 that
                 ,
                 neglecting
                 the
                 odd
                 ,
                 and
                 divide
                 by
                 7
                 ,
                 the
                 Remainder
                 is
                 the
                 day
                 of
                 the
                 Week
                 ;
                 but
                 if
                 none
                 remains
                 it
                 is
                 Saturday
                 ,
                 for
                 you
                 must
                 account
                 from
                 Sunday
                 ,
                 Monday
                 ,
                 
                   &
                   c..
                
                 
              
               
                 
                 
                   Example
                   .
                
                 
                   So
                   that
                   the
                   First
                   of
                   March
                   is
                   the
                   First
                   Day
                   ,
                   that
                   is
                   ,
                   Sunday
                   .
                
                 
                   
                     
                       
                         The
                         Number
                         —
                      
                       
                         2
                      
                    
                     
                       
                         The
                         Year
                         of
                         our
                         Lord
                         ,
                         1685.
                         
                      
                       
                         1685
                      
                    
                     
                       
                         The
                         fourth
                         Part
                         —
                      
                       
                         421
                      
                    
                     
                       
                         Divisor
                         —
                      
                       
                         
                      
                    
                  
                
              
            
             
               
               
                 To
                 find
                 on
                 what
                 day
                 of
                 the
                 Week
                 any
                 Day
                 of
                 any
                 Month
                 in
                 the
                 said
                 Year
                 hapneth
                 .
              
               
                 To
                 perform
                 this
                 Proposition
                 ,
                 the
                 following
                 Verse
                 being
                 in
                 Effect
                 a
                 Perpetual
                 Almanack
                 ,
                 is
                 to
                 be
                 kept
                 in
                 Memory
                 .
              
               
               
                 In
                 this
                 Verse
                 are
                 twelve
                 Words
                 relating
                 to
                 the
                 Number
                 of
                 the
                 twelve
                 Months
                 of
                 the
                 Year
                 ,
                 accounting
                 March
                 the
                 First
                 ;
                 wherefore
                 the
                 word
                 proper
                 to
                 that
                 Month
                 ,
                 is
                 An
                 ,
                 and
                 so
                 in
                 order
                 of
                 the
                 Alphabet
                 ,
                 which
                 will
                 never
                 exceed
                 Seven
                 ;
                 and
                 the
                 Number
                 of
                 the
                 said
                 Letter
                 shews
                 what
                 day
                 of
                 the
                 Month
                 proper
                 to
                 the
                 said
                 word
                 shall
                 be
                 the
                 same
                 day
                 of
                 the
                 Week
                 the
                 First
                 of
                 March
                 happ'ned
                 upon
                 ,
                 as
                 the
                 Example
                 above
                 .
              
            
             
               
                 To
                 find
                 the
                 Prime
                 or
                 Golden
                 Number
                 and
                 Epact
                 .
              
               
                 Add
                 to
                 the
                 Number
                 1
                 the
                 Year
                 of
                 our
                 Lord
                 ,
                 and
                 divide
                 by
                 19
                 ,
                 the
                 remainder
                 gives
                 the
                 Prime
                 .
                 Multiply
                 the
                 Prime
                 by
                 11
                 ,
                 and
                 divide
                 by
                 30
                 ,
                 gives
                 the
                 Epact
                 .
              
               
               
                 
                   A
                   Table
                   of
                   Primes
                   or
                   Golden
                   Numbers
                   and
                   Epacts
                   for
                   ever
                   .
                
                 
              
            
             
               
                 To
                 find
                 Easter
                 for
                 ever
                 .
              
               
                 Substract
                 the
                 Epact
                 (
                 if
                 less
                 than
                 28
                 or
                 29
                 )
                 from
                 47
                 ,
                 if
                 the
                 Epact
                 be
                 28
                 or
                 29
                 from
                 77
                 ,
                 the
                 remainder
                 is
                 Easter
                 limits
                 ;
                 so
                 the
                 first
                 Sunday
                 after
                 the
                 remainder
                 ,
                 beginning
                 from
                 March
                 ,
                 is
                 Easter
                 Sunday
                 .
              
            
             
               
                 To
                 find
                 the
                 Age
                 of
                 the
                 Moon
                 .
              
               
                 Add
                 to
                 the
                 Epact
                 the
                 Day
                 of
                 the
                 Month
                 ,
                 and
                 so
                 many
                 more
                 as
                 there
                 
                 are
                 Months
                 from
                 March
                 (
                 accounting
                 March
                 one
                 )
                 the
                 Sum
                 if
                 less
                 than
                 30
                 is
                 the
                 Moon
                 's
                 Age
                 (
                 if
                 more
                 )
                 Substract
                 30
                 ,
                 (
                 when
                 31
                 Days
                 in
                 the
                 Month
                 )
                 but
                 if
                 30
                 Days
                 or
                 less
                 ,
                 Substract
                 29
                 ,
                 the
                 Remainder
                 is
                 the
                 Moon
                 's
                 Age.
                 
              
            
             
               
                 
                   To
                   find
                   the
                   Southing
                   of
                   the
                   Moon
                   ,
                   and
                   High
                   Water
                   at
                
                 London-Bridge
                 .
              
               
                 Multiply
                 the
                 Moon
                 's
                 Age
                 by
                 8
                 /
                 10
                 shews
                 the
                 Southing
                 ,
                 to
                 which
                 add
                 3
                 hours
                 ,
                 shews
                 High-water
                 at
                 London-Bridge
                 .
              
            
             
               
                 To
                 find
                 it
                 another
                 way
                 .
              
               
                 Multiply
                 the
                 Moon
                 's
                 Age
                 by
                 4
                 ,
                 and
                 divide
                 by
                 5
                 ,
                 the
                 Quotient
                 shews
                 it
                 ,
                 every
                 Unit
                 that
                 remains
                 is
                 in
                 value
                 12
                 Minutes
                 ,
                 at
                 full
                 Moon
                 reject
                 15
                 from
                 it
                 .
                 Add
                 to
                 this
                 3
                 hours
                 ,
                 shews
                 High-water
                 at
                 London-Bridge
                 .
              
            
             
               
               
                 To
                 find
                 what
                 Day
                 of
                 the
                 Month
                 the
                 Sun
                 enters
                 into
                 any
                 Sign
                 of
                 the
                 Zodiack
                 ,
                 by
                 the
                 following
                 Verse
                 .
              
               
                 Aries
                 Taurus
                 Gemini
                 Cancer
                 Leo
                 Virgo
              
               
                 ♈
                 ♉
                 ♊
                 ♋
                 ♌
                 ♍
              
               
                 
                   Evil
                   attends
                   its
                   Object
                   ,
                   unva●●'d
                   Vice
                   ,
                
              
               
                 Libra
                 Scorpio
                 Sagittar
                 .
                 Capricorn
                 Aquar
                 .
                 Pisces
              
               
                 ♎
                 ♏
                 ♐
                 ♑
                 ♒
                 ♓
              
               
                 
                   Vain
                   Villains
                   ,
                   jest
                   into
                   a
                   Paradise
                   .
                
              
               
                 In
                 which
                 are
                 twelve
                 Words
                 to
                 represent
                 the
                 twelve
                 Months
                 of
                 the
                 Year
                 ,
                 the
                 first
                 March
                 ,
                 the
                 second
                 
                   April
                   ,
                   &c.
                
                 and
                 over
                 the
                 respective
                 Words
                 are
                 the
                 Characters
                 of
                 the
                 twelve
                 Signs
                 of
                 the
                 Zodiack
                 ,
                 thereby
                 denoting
                 ,
                 that
                 in
                 the
                 Month
                 to
                 which
                 the
                 Word
                 belongs
                 ,
                 the
                 Sun
                 is
                 in
                 that
                 Sign
                 over
                 head
                 :
                 And
                 if
                 it
                 be
                 required
                 to
                 know
                 the
                 day
                 of
                 the
                 Month
                 in
                 which
                 the
                 Sun
                 enters
                 into
                 any
                 of
                 those
                 Signs
                 ;
                 if
                 the
                 first
                 Letter
                 of
                 the
                 Word
                 ,
                 proper
                 
                 to
                 the
                 Month
                 ,
                 be
                 a
                 Consonant
                 ,
                 the
                 Sun
                 enters
                 into
                 the
                 Sign
                 thereto
                 belonging
                 on
                 the
                 eighth
                 Day
                 of
                 the
                 said
                 Month
                 ,
                 as
                 in
                 the
                 Word
                 Paradise
                 ,
                 belonging
                 to
                 February
                 ,
                 in
                 that
                 Month
                 he
                 enters
                 Pisces
                 the
                 eighth
                 Day
                 ;
                 but
                 if
                 it
                 be
                 a
                 Vowel
                 ,
                 as
                 all
                 the
                 rest
                 are
                 ,
                 add
                 so
                 many
                 Days
                 unto
                 eight
                 ,
                 as
                 the
                 Vowel
                 denotes
                 ;
                 now
                 the
                 Vowels
                 are
                 but
                 five
                 in
                 Number
                 .
              
            
             
               
                 To
                 know
                 in
                 what
                 Degree
                 of
                 the
                 said
                 Sign
                 he
                 is
                 for
                 any
                 other
                 Day
                 .
              
               
                 If
                 the
                 Number
                 of
                 the
                 Day
                 of
                 the
                 given
                 Month
                 exceed
                 the
                 Number
                 of
                 that
                 Day
                 in
                 which
                 the
                 Sun
                 enters
                 into
                 any
                 Sign
                 ,
                 Substract
                 the
                 lesser
                 from
                 the
                 greater
                 ,
                 and
                 the
                 Remainder
                 is
                 the
                 Degree
                 .
              
               
                 
                   Example
                   .
                
                 
                   On
                   the
                   21
                   of
                   April
                   I
                   would
                   find
                   
                   the
                   Sun's
                   place
                   by
                   the
                   Verse
                   .
                   It
                   appears
                   the
                   Sun
                   enters
                   into
                   Taurus
                   on
                   the
                   ninth
                   of
                   that
                   Month
                   ,
                   which
                   taken
                   from
                   21
                   ,
                   there
                   remains
                   12
                   ,
                   shewing
                   that
                   the
                   Sun
                   is
                   in
                   the
                   12
                   Degree
                   of
                   Taurus
                   ,
                   the
                   second
                   Sign
                   .
                
                 
                   2.
                   
                   But
                   if
                   the
                   Number
                   of
                   the
                   Day
                   of
                   the
                   given
                   Month
                   be
                   less
                   than
                   the
                   Number
                   of
                   that
                   Day
                   in
                   which
                   the
                   Sun
                   enters
                   into
                   the
                   beginning
                   of
                   any
                   Sign
                   ,
                   the
                   Sun
                   is
                   not
                   entred
                   into
                   the
                   said
                   Sign
                   ,
                   but
                   is
                   still
                   in
                   the
                   Sign
                   belonging
                   to
                   the
                   former
                   Month.
                   In
                   this
                   Case
                   Substract
                   the
                   given
                   Day
                   from
                   the
                   Day
                   of
                   his
                   Entrance
                   into
                   the
                   next
                   Sign
                   ,
                   and
                   again
                   Substract
                   the
                   Remainder
                   from
                   30
                   ,
                   and
                   the
                   Remainder
                   shews
                   his
                   place
                   in
                   the
                   Sign
                   of
                   the
                   former
                   Month.
                   
                
              
               
                 
                   Example
                   .
                
                 
                   Let
                   it
                   be
                   required
                   to
                   know
                   the
                   Sun's
                   place
                   the
                   fifth
                   of
                   August
                   on
                   the
                   
                   thirteenth
                   day
                   of
                   the
                   Month
                   the
                   Sun
                   enters
                   into
                   Virgo
                   ,
                   5
                   from
                   13
                   rests
                   8
                   ,
                   and
                   that
                   taken
                   from
                   30
                   there
                   remains
                   22
                   ,
                   shewing
                   that
                   the
                   Sun
                   is
                   in
                   the
                   22
                   degree
                   of
                   Leo
                   ,
                   the
                   fifth
                   Sign
                   .
                
              
            
             
               FINIS
               .