Mr. De Sargues Universal way of dyaling, or, Plain and easie directions for placing the axeltree and marking the hours in sun-dyals, after the French, Italian, Babylonian, and Jewish manner together with the manner of drawing the lines of the signs, of finding out the height of the sun above the horizon, and the east-rising of the same, the elevation of the pole, and the position of the meridian ... / [edited] by Daniel King, Gent.
         Maniére universelle pour poser l'essieu. English
         Desargues, Gérard, 1591-1661.
      
       
         This text is an enriched version of the TCP digital transcription A35744 of text R17188 in the  English Short Title Catalog (Wing D1127). Textual changes  and metadata enrichments aim at making the text more  computationally tractable, easier to read, and suitable for network-based collaborative curation by amateur and professional end users from many walks of life.  The text has been tokenized and linguistically annotated with  MorphAdorner. The annotation includes standard spellings that support the display of a text in a standardized format that preserves archaic forms ('loveth', 'seekest'). Textual changes aim at restoring the text the author or stationer meant to publish.  This text has not been fully proofread 
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         EarlyPrint Project
         Evanston,IL, Notre Dame, IN, St. Louis, MO
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         A35744
         Wing D1127
         ESTC R17188
         13154958
         ocm 13154958
         98167
         
           
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         Early English books online.
      
       
         (EEBO-TCP ; phase 1, no. A35744)
         Transcribed from: (Early English Books Online ; image set 98167)
         Images scanned from microfilm: (Early English books, 1641-1700 ; 414:7)
      
       
         
           
             Mr. De Sargues Universal way of dyaling, or, Plain and easie directions for placing the axeltree and marking the hours in sun-dyals, after the French, Italian, Babylonian, and Jewish manner together with the manner of drawing the lines of the signs, of finding out the height of the sun above the horizon, and the east-rising of the same, the elevation of the pole, and the position of the meridian ... / [edited] by Daniel King, Gent.
             Maniére universelle pour poser l'essieu. English
             Desargues, Gérard, 1591-1661.
             King, Daniel, d. 1664?
             Bosse, Abraham, 1602-1676.
          
           [17], 108 p. : ill.
           
             Printed by Tho. Leach, and are to be sold by Isaac Pridmore ...,
             London :
             1659.
          
           
             Translation of: Maniére universelle pour poser l'essieu.
             Added illustrated t.p., engraved.
             The diagrams are reproductions of the engravings by Abraham Bosse who published the original French edition.
             Advertisement on p. [17].
             Reproduction of original in Cambridge University Library.
          
        
      
    
     
       
         eng
      
       
         
           Dialing.
           Sundials.
        
      
    
       A35744  R17188  (Wing D1127).  civilwar no Mr. De Sargues Universal way of dyaling. Or plain and easie directions for placing the axeltree, and marking the hours in sun-dyals, after t Desargues, Gérard 1659    29465 52 0 0 0 1 0 21 C  The  rate of 21 defects per 10,000 words puts this text in the C category of texts with between 10 and 35 defects per 10,000 words. 
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        2007-04 Robyn Anspach
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               Mr.
               DESARGVES
               .
               
                 vniversall
                 way
                 of
                 makeing
                 all
                 manner
                 of
                 Sun
                 dialls
                 ▪
                 Published
                 by
                 Daniell
                 king
                 ▪
                 &
                 Sold
                 by
                 Isaake
                 Pridmore
                 at
                 y
                 ,
                 golden
                 falcon
                 in
                 y
                 strand
                 ▪
                 A●
              
               1659
            
          
        
      
       
       
         
           Mr.
           
             De
             SAKGVES
          
           UNIVERSAL
           WAY
           OF
           DYALING
           .
        
         
           OR
           Plain
           and
           easie
           directions
           for
           placing
           the
           Axeltree
           ,
           and
           marking
           the
           hours
           in
           Sun-dyals
           ,
           after
           the
           
             French
             ,
             Italian
             ,
             Babylonian
          
           and
           
             Jewish
          
           manner
           .
        
         
           Together
           with
           the
           manner
           of
           drawing
           the
           lines
           of
           the
           signs
           ,
           of
           finding
           out
           the
           heighr
           of
           the
           Sun
           above
           the
           Horizon
           ,
           and
           the
           East
           rising
           of
           the
           same
           ,
           the
           Elevation
           of
           the
           Pole
           ,
           and
           the
           position
           of
           the
           Meridian
           .
        
         
           All
           which
           may
           be
           done
           in
           any
           superficies
           whatsoever
           ,
           and
           in
           what
           situation
           soever
           it
           be
           ,
           without
           any
           skill
           at
           all
           in
           Astronomy
           .
        
         
           By
           DANIEL
           KING
           Gent.
           
        
         
           
             LONDON
             ,
          
           Printed
           by
           
             Tho.
             Leach
          
           and
           are
           to
           be
           sold
           by
           
             Isaac
             Pridmore
          
           at
           the
           
             Golden
             Faulcon
          
           in
           the
           
             Strand
             ,
          
           near
           the
           
             New
             Exchange
             ,
          
           1659.
           
        
      
       
       
       
         
           TO
           THE
           ILLVSTRIOVS
           
             GEORGE
             VILLIERS
             ,
          
           Duke
           ,
           and
           Marquess
           of
           
             Buckingham
             ,
          
           Earl
           of
           
             Coventry
             ,
          
           Viscount
           
             Villiers
             ,
          
           Baron
           
             Whaddon
             ,
          
           and
           
             Ros
             ,
          
           Knight
           of
           the
           most
           noble
           Order
           of
           the
           
             Garter
             ,
          
           &c.
           
        
         
           
             Sir
             ,
          
        
         
           HAving
           had
           the
           honour
           to
           observe
           your
           Graces
           great
           affection
           ,
           and
           love
           to
           Sciences
           and
           Arts
           ,
           and
           your
           own
           excellency
           being
           most
           eminent
           therein
           ,
           together
           with
           your
           unparallel'd
           love
           and
           inclination
           to
           the
           splendour
           of
           your
           Native
           Country
           ,
           in
           promoting
           Learning
           and
           Ingenuity
           .
           These
           high
           merits
           with
           my
           own
           particular
           
           obligations
           and
           attendance
           ,
           encourage
           my
           endeavours
           of
           the
           patronage
           to
           a
           new
           birth
           never
           presented
           to
           the
           English
           Nation
           ;
           presuming
           by
           Gods
           assistance
           to
           bring
           forth
           something
           of
           worth
           that
           hathnot
           yet
           seen
           light
           ,
           and
           if
           your
           Grace
           shall
           please
           to
           pardon
           my
           observant
           presumption
           ,
           you
           will
           hereby
           more
           strictly
           engage
           him
           ever
           to
           honour
           your
           Heroick
           worth
           ,
           who
           is
           ,
        
         
           
             
               The
               very
               humblest
               of
               Your
               Servants
               ,
            
             Daniel
             King
             .
          
        
      
       
       
         
           The
           Preface
           .
        
         
           Concerning
           the
           particulars
           of
           this
           TREATISE
           .
        
         
           WHereas
           the
           Superficies
           or
           outsides
           whereon
           Dyals
           may
           be
           made
           ,
           may
           be
           either
           flat
           ,
           bowed
           ,
           or
           crooked
           ,
           plain
           or
           rugged
           ,
           &
           situated
           diversly
           ,
           the
           most
           part
           of
           the
           books
           treating
           of
           this
           matter
           ,
           contain
           severally
           the
           manner
           of
           making
           flat
           Dyals
           in
           all
           kinds
           of
           positions
           ,
           Horizontal
           ,
           Vertical
           ,
           Meridional
           ,
           Septentrional
           ,
           Oriental
           ,
           Occidental
           ;
           Declining
           ,
           Inclining
           ;
           Inclining
           ,
           and
           Declining
           ;
           and
           accordingly
           in
           all
           other
           kinds
           of
           superficies
           .
        
         
           They
           may
           also
           shew
           ,
           for
           those
           that
           are
           ignorant
           of
           it
           ,
           the
           way
           to
           find
           the
           elevation
           of
           the
           Pole
           ,
           the
           Meridian
           line
           ,
           the
           Declinings
           ,
           Inclinings
           ,
           and
           other
           particularities
           .
        
         
           But
           Monsieur
           
             de
             Sargues
          
           intention
           being
           to
           publish
           nothing
           ,
           if
           it
           be
           possible
           ,
           that
           is
           to
           be
           found
           in
           another
           Book
           ,
           and
           to
           give
           you
           only
           the
           general
           Rule
           to
           make
           ,
           and
           not
           to
           copy
           out
           a
           number
           of
           examples
           all
           differing
           one
           from
           another
           ;
           I
           will
           give
           you
           but
           one
           example
           only
           in
           this
           volume
           ,
           by
           this
           universal
           manner
           ,
           the
           discourse
           
           whereof
           may
           be
           applyed
           generally
           to
           all
           kinds
           of
           superficies
           ,
           and
           in
           what
           situation
           soever
           they
           be
           ,
           without
           having
           any
           knowledge
           of
           the
           Pole
           ,
           nor
           of
           the
           height
           of
           the
           Sun
           ,
           nor
           of
           the
           declining
           or
           inclining
           ,
           nor
           of
           the
           Meridian
           line
           ,
           nor
           of
           any
           other
           thing
           in
           Astronomy
           ,
           and
           without
           a
           needle
           touch'd
           ,
           nor
           of
           any
           kind
           of
           thing
           that
           may
           give
           a
           beginning
           to
           that
           ,
           as
           you
           shall
           see
           yet
           better
           when
           we
           shall
           treat
           of
           the
           practice
           .
        
         
           And
           in
           practising
           this
           general
           Rule
           ,
           you
           shall
           find
           at
           one
           and
           the
           same
           time
           ,
           the
           elevation
           of
           the
           Pole
           ,
           and
           the
           position
           of
           the
           Meridian
           ,
           you
           shall
           know
           how
           to
           place
           the
           needle
           of
           your
           Dyal
           ,
           and
           so
           you
           shall
           come
           to
           find
           the
           equal
           hours
           ,
           which
           are
           called
           hours
           after
           the
           
             French
          
           way
           ,
           
             alias
          
           Astronomical
           .
        
         
           The
           rest
           being
           more
           curious
           than
           necessary
           ,
           I
           thought
           to
           set
           down
           nothing
           else
           but
           those
           two
           things
           ;
           But
           I
           have
           been
           perswaded
           ,
           for
           the
           satisfaction
           os
           some
           ,
           to
           add
           also
           the
           manner
           of
           drawing
           upon
           the
           same
           superficies
           ,
           the
           lines
           of
           the
           signs
           ,
           the
           hours
           after
           the
           
             Italian
          
           and
           
             Babylonian
          
           way
           ,
           and
           of
           the
           Antients
           ,
           the
           height
           of
           the
           Sun
           ,
           and
           the
           situation
           thereof
           ,
           in
           respect
           of
           the
           Horizon
           .
        
         
           
             Of
             the
             Practice
             of
             Sun-Dyals
             .
          
           
             MAny
             diverse
             things
             are
             represented
             in
             Sun-Dyals
             by
             the
             shadow
             of
             the
             Sun
             ,
             to
             divers
             ends
             ,
             the
             hour
             is
             shewn
             by
             them
             ,
             and
             serves
             only
             
             for
             that
             purpose
             every
             day
             .
             Other
             things
             are
             represented
             also
             by
             it
             ,
             as
             the
             signs
             ,
             and
             other
             particularities
             ,
             whereby
             it
             may
             serve
             sometime
             for
             the
             divertisement
             of
             a
             few
          
           
             In
             antient
             time
             the
             hours
             were
             not
             counted
             as
             they
             are
             now
             a
             dayes
             ,
             and
             in
             
               Italy
            
             at
             this
             day
             they
             are
             counted
             otherwise
             than
             in
             
               France
            
          
           
             The
             manner
             that
             they
             count
             their
             hours
             in
             
               France
            
             is
             according
             to
             Astronomy
             ,
             and
             here
             is
             at
             length
             a
             generall
             way
             of
             framing
             and
             making
             Dyals
             with
             houres
             equal
             to
             the
             Sun
             ,
             according
             as
             the
             hours
             are
             now
             counted
             in
             
               France
               ,
            
             after
             which
             way
             one
             may
             come
             to
             shew
             if
             need
             be
             ,
             by
             the
             shadow
             of
             the
             Sun
             ,
             and
             also
             of
             the
             Moon
             ,
             whatsoever
             can
             be
             shewn
             concerning
             other
             circumstances
             to
             satisfie
             curiosity
             .
          
           
             There
             are
             two
             things
             which
             together
             do
             compose
             those
             kinds
             of
             Dyals
             of
             equal
             hours
             ,
             after
             the
             
               French
            
             way
             ,
             the
             one
             is
             as
             piece
             that
             shoots
             out
             or
             sallies
             out
             of
             the
             superficies
             of
             the
             Dyal
             ,
             the
             shadow
             whereof
             falling
             upon
             this
             superficies
             ,
             shews
             what
             a
             clock
             it
             is
             ,
             the
             other
             are
             the
             lines
             drawn
             upon
             the
             superficies
             of
             the
             Dyal
             ,
             each
             of
             them
             representing
             one
             of
             the
             hours
             after
             the
             
               French
            
             way
             .
          
           
             They
             make
             Dyals
             after
             the
             
               French
            
             way
             wherein
             there
             is
             only
             the
             shadow
             of
             one
             portion
             alone
             ,
             as
             might
             be
             a
             button
             of
             the
             piece
             that
             shoots
             out
             ,
             that
             shews
             what
             a
             Clock
             it
             is
             .
             But
             in
             this
             general
             way
             ,
             there
             is
             still
             the
             whole
             shadow
             of
             all
             the
             length
             ,
             in
             a
             direct
             line
             of
             this
             piece
             that
             shoots
             out
             ,
             shewing
             continually
             what
             a
             Clock
             it
             is
             ,
             of
             
             which
             piece
             or
             length
             ,
             you
             may
             take
             if
             you
             will
             a
             button
             ,
             and
             mark
             the
             hours
             with
             that
             button
             only
             ,
             together
             with
             all
             the
             other
             particularities
             that
             may
             be
             added
             to
             such
             Dyals
             .
             Some
             call
             by
             one
             and
             the
             same
             name
             these
             two
             kinds
             of
             pieces
             the
             shadow
             whereof
             shews
             the
             hour
             ,
             as
             well
             that
             same
             whose
             shadow
             shews
             continually
             the
             hour
             at
             length
             ,
             as
             that
             which
             hath
             but
             the
             shadow
             of
             a
             button
             to
             shew
             it
             .
          
           
             But
             to
             the
             end
             we
             may
             distinguish
             both
             kinds
             of
             pieces
             one
             from
             the
             other
             ,
             that
             same
             whose
             shadow
             shews
             the
             hour
             at
             length
             ,
             and
             is
             the
             original
             spring
             of
             all
             the
             others
             ,
             I
             call
             it
             the
             axeltree
             of
             the
             Dyal
             .
          
           
             This
             axeltree
             may
             be
             made
             as
             well
             with
             a
             straight
             ,
             round
             ,
             and
             smooth
             rod
             of
             yron
             or
             brasse
             ,
             as
             with
             a
             flat
             piece
             ,
             and
             cut
             of
             one
             side
             in
             a
             straight
             line
             .
          
           
             There
             are
             often
             other
             rods
             in
             the
             Dyals
             ,
             which
             serve
             to
             bear
             up
             the
             axeltree
             that
             shoots
             out
             ,
             and
             those
             kind
             of
             rods
             I
             call
             the
             supporters
             of
             the
             axeltree
             .
          
           
             The
             lines
             that
             are
             drawn
             upon
             the
             superficies
             of
             the
             Dyal
             ,
             and
             that
             shew
             each
             of
             them
             one
             of
             the
             hours
             after
             the
             French
             way
             ,
             I
             call
             them
             lines
             of
             the
             hours
             after
             the
             French
             way
             .
          
           
             In
             the
             innumerable
             number
             of
             such
             kinds
             of
             Dyals
             as
             may
             be
             made
             after
             the
             French
             way
             ,
             it
             happens
             that
             the
             superficies
             of
             the
             Dyal
             ,
             is
             either
             all
             flat
             ,
             or
             is
             not
             so
             altogether
             .
          
           
             When
             the
             superficies
             of
             the
             Dyal
             is
             all
             flat
             ,
             every
             line
             of
             the
             hours
             is
             a
             straight
             line
             .
          
           
           
             And
             when
             the
             superficies
             of
             the
             Dyal
             is
             not
             altogether
             flat
             ,
             it
             may
             be
             that
             every
             line
             of
             hours
             is
             not
             all
             straight
             also
             .
          
           
             To
             make
             one
             of
             those
             Dyals
             of
             equal
             hours
             after
             the
             French
             way
             ,
             by
             this
             universal
             way
             ,
             there
             are
             two
             things
             to
             be
             done
             one
             after
             another
             .
             The
             first
             is
             to
             place
             the
             axeltree
             as
             it
             ought
             to
             be
             ,
             that
             is
             ,
             shooting
             out
             of
             the
             superficies
             of
             the
             Dyal
             ;
             The
             second
             is
             ,
             to
             draw
             the
             lines
             of
             the
             hours
             as
             they
             must
             be
             upon
             the
             same
             superficies
             .
          
           
             And
             by
             means
             of
             this
             general
             way
             ,
             you
             shall
             do
             those
             two
             things
             without
             knowing
             in
             what
             day
             ,
             nor
             in
             what
             time
             of
             the
             year
             ,
             nor
             in
             what
             Country
             you
             are
             ,
             without
             knowing
             what
             the
             superficies
             of
             the
             Dyal
             is
             ,
             whether
             it
             is
             plain
             or
             rough
             ,
             nor
             which
             way
             it
             looks
             ,
             without
             knowing
             any
             thing
             concerning
             the
             making
             and
             the
             placing
             of
             the
             parts
             of
             the
             world
             ,
             or
             without
             any
             skill
             in
             Astronomy
             ,
             without
             any
             needle
             touch'd
             with
             the
             loadstone
             ,
             or
             any
             instrument
             or
             figure
             that
             may
             serve
             for
             a
             beginning
             towards
             the
             making
             of
             a
             Dyal
             :
             But
             by
             the
             means
             only
             of
             the
             Beams
             of
             the
             Sun
             ,
             by
             one
             general
             rule
             you
             shall
             place
             the
             axeltree
             ,
             and
             draw
             the
             lines
             of
             those
             hours
             upon
             one
             of
             those
             Dyals
             whatsoever
             the
             superficies
             may
             be
             ,
             and
             which
             way
             soever
             it
             looks
             ,
             with
             all
             the
             celerity
             and
             exactnesse
             that
             is
             possible
             in
             art
             ;
             and
             if
             you
             are
             equally
             exact
             in
             every
             operation
             ,
             you
             shall
             make
             by
             this
             means
             many
             Dyals
             upon
             different
             superficies
             ,
             and
             turned
             towards
             several
             parts
             of
             the
             world
             ,
             which
             shall
             agree
             plainly
             among
             themselves
             ,
             and
             if
             you
             do
             not
             do
             it
             ,
             you
             may
             be
             
             sure
             that
             the
             fault
             is
             on
             your
             part
             ,
             and
             not
             in
             the
             rules
             ,
             since
             that
             others
             do
             succeed
             well
             in
             it
             .
          
           
             There
             are
             some
             pieces
             that
             are
             requisite
             for
             the
             framing
             of
             a
             Dyal
             ,
             and
             whereof
             it
             is
             composed
             ,
             such
             are
             the
             axel-tree
             rod
             with
             its
             supporters
             .
          
           
             There
             are
             other
             pieces
             that
             must
             be
             used
             in
             the
             making
             of
             a
             Dyal
             ,
             as
             Rules
             ,
             Compasses
             ,
             a
             Squirt
             ,
             a
             lead
             with
             his
             two
             frames
             ,
             one
             to
             mark
             with
             ,
             and
             the
             other
             to
             level
             .
          
           
             There
             are
             some
             other
             things
             that
             you
             shall
             use
             also
             ,
             as
             pegs
             ,
             and
             rods
             ,
             either
             of
             yron
             ,
             or
             of
             brasse
             ,
             or
             of
             wood
             ,
             some
             sharp
             at
             both
             ends
             ,
             the
             others
             sharp
             at
             one
             end
             only
             ,
             a
             table
             ,
             either
             of
             wood
             ,
             or
             of
             slate
             ,
             or
             of
             any
             other
             stuff
             ,
             flat
             and
             solid
             ,
             to
             draw
             upon
             if
             need
             be
             ,
             some
             straight
             lines
             with
             the
             rule
             ;
             and
             in
             case
             the
             superficies
             of
             the
             Dyal
             were
             plain
             and
             even
             ,
             you
             must
             use
             some
             fine
             strings
             ,
             supple
             and
             strong
             ,
             some
             mastick
             ,
             cement
             ,
             or
             plaster
             ,
             or
             such
             like
             stuff
             fit
             to
             seal
             with
             ,
             
               &c.
            
             all
             which
             things
             you
             must
             have
             in
             readinesse
             ,
             whensoever
             you
             will
             go
             about
             the
             making
             of
             a
             Dyal
             .
          
           
             And
             though
             you
             would
             learn
             to
             make
             but
             one
             of
             these
             Dyals
             well
             ,
             it
             is
             fit
             you
             should
             have
             some
             models
             of
             all
             those
             pieces
             ,
             and
             when
             you
             are
             upon
             those
             chapters
             that
             concern
             them
             ,
             as
             you
             shall
             understand
             an
             Article
             ,
             it
             will
             be
             requisite
             that
             with
             the
             models
             of
             those
             pieces
             ,
             you
             work
             at
             the
             same
             time
             an
             actual
             model
             of
             the
             thing
             which
             that
             article
             shall
             teach
             you
             to
             do
             ,
             and
             so
             you
             must
             work
             from
             one
             end
             to
             another
             ,
             till
             you
             have
             at
             last
             every
             way
             compleated
             an
             actual
             model
             of
             
             this
             kind
             of
             Dyals
             ,
             and
             you
             shall
             need
             to
             make
             but
             few
             of
             such
             models
             of
             Dyals
             upon
             any
             superficies
             ,
             turned
             towards
             several
             parts
             of
             the
             world
             ,
             to
             bring
             you
             acquainted
             with
             the
             practice
             of
             making
             Dyals
             to
             the
             life
             ,
             or
             after
             the
             natural
             ,
             in
             what
             kind
             or
             odd
             situation
             of
             superficies
             soever
             they
             may
             be
             .
          
           
             Lastly
             ,
             you
             shall
             find
             the
             precepts
             and
             the
             descriptions
             to
             be
             more
             troublesome
             ,
             than
             the
             actual
             making
             or
             working
             ,
             study
             only
             to
             be
             as
             exact
             in
             every
             one
             of
             these
             operations
             of
             making
             of
             these
             Dyals
             ,
             as
             in
             the
             practice
             of
             other
             Arts
             .
          
        
      
       
       
         
           The
           Epistle
           to
           the
           READER
           .
        
         
           
             Courteous
             Reader
             ,
          
        
         
           THis
           Treatise
           being
           originally
           written
           in
           French
           ,
           and
           generally
           approved
           of
           all
           those
           that
           have
           any
           skill
           in
           the
           Art
           of
           Dyalling
           ,
           I
           have
           thought
           it
           my
           duty
           to
           lay
           hold
           upon
           this
           occasion
           ,
           to
           shew
           how
           desirous
           I
           have
           ever
           been
           to
           procure
           any
           good
           unto
           my
           Country
           .
           Therefore
           I
           have
           caused
           it
           to
           be
           carefully
           translated
           into
           English
           ,
           and
           have
           set
           it
           forth
           for
           the
           good
           and
           utility
           of
           all
           such
           ,
           as
           are
           curious
           ,
           and
           true
           lovers
           of
           that
           Art
           ;
           Reputing
           my self
           most
           happy
           to
           meet
           with
           any
           occasion
           ,
           whereby
           I
           may
           contribute
           any
           thing
           towards
           the
           advancement
           of
           learning
           ,
           and
           of
           the
           publick
           good
           ,
           —
           
             Non
             enim
             nobis
             solum
             nati
             sumus
             ;
          
           We
           are
           not
           meant
           to
           be
           wholely
           and
           soly
           for
           our selves
           .
           As
           for
           the
           work
           it self
           ,
           I
           am
           so
           confident
           it
           will
           so
           gain
           the
           attentive
           Readers
           approbation
           ,
           as
           that
           I
           shall
           forbear
           to
           say
           any
           more
           in
           commendation
           of
           it
           ,
           than
           that
           it
           is
           an
           expedite
           ,
           and
           sure
           way
           of
           obtaining
           the
           site
           of
           the
           Axis
           ,
           and
           of
           other
           requisites
           in
           the
           framing
           of
           all
           sorts
           of
           Dyals
           ,
           of
           no
           lesse
           curiosity
           ,
           than
           use
           ,
           performed
           without
           the
           ordinary
           rules
           and
           presupposals
           of
           
           the
           spiritual
           calculations
           and
           practice
           ;
           I
           need
           premise
           no
           more
           ,
           but
           advise
           to
           follow
           the
           directions
           that
           are
           set
           down
           through
           all
           the
           book
           ,
           for
           effecting
           that
           which
           is
           promised
           ,
           and
           thou
           shalt
           see
           the
           same
           plainly
           and
           readily
           performed
           .
           Accept
           then
           ,
           Courteous
           Reader
           ,
           this
           small
           labour
           ,
           the
           undoubted
           Testimony
           of
           my
           Love
           ,
           as
           kindly
           ▪
           as
           I
           offer
           it
           cordially
           unto
           thee
           ,
           hoping
           that
           God
           will
           enable
           me
           to
           give
           thee
           hereafter
           some
           thing
           of
           more
           consequence
           ,
        
         
           
             So
             Farewell
             .
          
           Vtere
           &
           fruere
           .
           
             
               Thine
            
             D.
             K.
             
          
        
      
       
       
         
           To
           all
           
             Lovers
          
           of
           Ingenious
           Practices
           .
        
         
           THe
           
             French
          
           have
           excelled
           all
           other
           Nations
           in
           the
           Art
           of
           
             Perspective
          
           for
           this
           last
           Age
           ,
           their
           many
           Books
           and
           curious
           Writings
           so
           excellently
           composed
           do
           witnesse
           for
           them
           .
        
         
           
             Dyalling
          
           I
           accompt
           one
           kind
           of
           Perspective
           ,
           for
           that
           glorious
           Body
           the
           
             Sun
             ,
          
           the
           Eye
           of
           the
           world
           ,
           traceth
           out
           the
           lines
           and
           hour-points
           by
           his
           Diurnal
           Course
           ,
           and
           upon
           the
           resubjected
           
             Plane
          
           by
           the
           laws
           of
           Picture
           ,
           
             Scenographically
          
           delineates
           the
           Dyal
           .
        
         
           Many
           have
           writ
           upon
           this
           subject
           of
           several
           Countryes
           ,
           in
           several
           Ages
           ,
           many
           are
           the
           Rules
           and
           Practices
           set
           down
           ;
           But
           among
           all
           those
           of
           forein
           Parts
           ,
           none
           hath
           performed
           the
           same
           with
           more
           ease
           ,
           and
           lesse
           trouble
           ,
           than
           
             Monsieur
             du
             Sargues
          
           the
           Author
           ;
           as
           wholy
           laying
           aside
           those
           tedious
           observations
           of
           Azimuth's
           ,
           Declination
           ,
           Reclination
           ,
           Inclination
           ,
           Meridian
           ;
           Substile
           ,
           
             &c.
          
           and
           performing
           the
           operation
           only
           by
           three
           observations
           of
           the
           Suns
           shadow
           from
           a
           Point
           .
        
         
           It
           will
           not
           be
           amisse
           to
           give
           the
           Reader
           a
           small
           consideration
           hereof
           ;
           the
           point
           B
           of
           the
           pin
           AB
           ,
           in
           all
           the
           figures
           is
           alwayes
           one
           part
           of
           the
           Axis
           ,
           
           or
           
             Gnomon
          
           of
           the
           
             Dyal
             ,
          
           and
           may
           be
           used
           to
           shew
           the
           hour
           :
           this
           point
           B
           ,
           you
           must
           imagine
           to
           be
           the
           Center
           of
           the
           Earth
           (
           for
           the
           vast
           distance
           to
           the
           Sun
           ,
           maketh
           the
           space
           betwixt
           the
           Center
           and
           superficies
           of
           the
           Earth
           to
           be
           insensible
           )
           and
           from
           it
           at
           all
           times
           of
           the
           year
           (
           excepting
           the
           Aequinoctial
           day
           )
           the
           Sun
           in
           its
           course
           forms
           two
           Cones
           ,
           whose
           Apex
           is
           the
           point
           B
           ,
           that
           next
           the
           Sun
           termed
           
             Conus
             luminosus
          
           or
           the
           light
           Cone
           ,
           the
           other
           whereof
           our
           Author
           makes
           use
           ,
           termed
           
             Conus
             umbrosus
          
           the
           dark
           Cone
           ,
           now
           in
           this
           dark
           Cone
           ,
           if
           by
           any
           three
           points
           equally
           distant
           from
           the
           Apex
           B
           ,
           the
           Cone
           be
           cut
           ,
           the
           Section
           will
           be
           a
           Circle
           parallel
           to
           the
           
             Equinoctial
             :
          
           And
           thereby
           ,
           as
           the
           Author
           shews
           many
           wayes
           ,
           the
           position
           of
           the
           Axis
           or
           Gnomon
           may
           be
           found
           out
           ,
           and
           the
           Dyal
           easily
           made
           .
        
         
           Now
           it
           rests
           ,
           courteous
           Countryman
           ,
           that
           we
           be
           very
           gratefull
           ,
           and
           every
           way
           forward
           to
           encourage
           Mr.
           
             D.
             King
             ,
          
           one
           very
           industrious
           in
           the
           studies
           of
           Antiquities
           and
           Heraldry
           ;
           who
           out
           of
           his
           desire
           to
           serve
           his
           Country
           ,
           hath
           caused
           this
           piece
           speak
           English
           ,
           hath
           been
           very
           carefull
           to
           see
           the
           Cutts
           well
           done
           ,
           and
           will
           (
           no
           doubt
           )
           proceed
           to
           cause
           some
           of
           those
           rare
           pieces
           of
           perspective
           in
           French
           to
           be
           translated
           .
        
         
           
             
               Then
               prosper
            
             King
             ,
             
               untill
               thy
               worthy
               hand
               ,
            
          
           
             
               The
            
             Gallick
             
               learning
               make
               us
               understand
               .
            
          
        
         
           
             JONAS
             MOORE
             
               Mathesios
               Professor
               .
            
          
        
      
       
       
         
           Books
           Printed
           for
           
             Isaac
             Pridmore
             ,
          
           and
           are
           to
           be
           sold
           at
           the
           Golden
           Faulcon
           near
           the
           
             New-Exchange
             .
          
        
         
           THE
           Rogue
           ,
           or
           the
           life
           of
           
             Gusman
             de
             Alpherache
          
           the
           witty
           Spaniard
           ,
           written
           in
           Spanish
           by
           
             Matthew
             Aleman
             ,
          
           Servant
           to
           his
           Catholick
           Majesty
           ;
           the
           fifth
           and
           last
           Edition
           Corrected
           .
        
         
           A
           Physical
           discourse
           ,
           exhibiting
           the
           cure
           of
           Diseases
           by
           signatures
           ,
           whereunto
           is
           annexed
           a
           Philosophical
           discourse
           ,
           vindicating
           the
           Souls
           prerogative
           in
           discerning
           the
           truths
           of
           Christian
           Religion
           with
           the
           eye
           of
           reason
           ,
           by
           
             R.
             Bunworth
             .
          
        
         
           Seif-Examination
           or
           Self-Preparation
           for
           the
           worthy
           receiving
           of
           the
           Lord
           ▪
           Supper
           ;
           delivered
           in
           a
           Sermon
           concerning
           the
           Sacrament
           ,
           by
           
             Daniel
             Cawdrey
             ,
          
           sometimes
           Preacher
           there
           ,
           with
           a
           short
           Chatechism
           :
           the
           third
           Edition
           .
        
         
           The
           Obstinate
           Lady
           ,
           a
           Comedy
           written
           by
           Sir
           
             Aston
             Cockaine
             .
          
        
         
           Sportive
           Elegies
           written
           by
           
             Samuel
             Holland
          
           Gent.
           
        
         
           A
           New
           discovery
           of
           the
           French
           Disease
           ,
           and
           running
           of
           the
           Reins
           ,
           with
           plain
           and
           easie
           directions
           for
           the
           perfect
           curing
           the
           same
           ,
           by
           
             R.
             Runworths
             .
          
        
         
           The
           Vnspotted
           high
           Court
           of
           Iustice
           ,
           erected
           and
           discovered
           in
           three
           Sermons
           Preached
           in
           
             London
          
           and
           other
           places
           ,
           by
           
             Thomas
             Baker
             ,
          
           Rector
           of
           St.
           
           
             Mary
             the
             More
          
           in
           
             Oxon.
             
          
        
         
           A
           Chain
           of
           Golden
           poens
           ,
           imbellished
           with
           wit
           ,
           Mirth
           ,
           and
           Eloquence
           ,
           together
           with
           two
           most
           exelent
           Comedies
           ,
           
             viz.
          
           the
           Obstinate
           Lady
           ,
           and
           
             Trapolin
          
           suppos'd
           a
           Prince
           ,
           by
           Sir
           
             Aston
             Cockaine
             .
          
        
         
           The
           Ascent
           to
           blisse
           by
           three
           steps
           ,
           
             viz.
          
           Philosophy
           ,
           History
           ,
           and
           Theology
           ,
           in
           a
           brief
           discourse
           of
           Mans
           felicity
           ,
           with
           many
           rem●●keable
           examples
           of
           divers
           Kings
           and
           Princes
           .
        
         
           The
           Heroical
           Loves
           ,
           or
           
             Anthcon
          
           &
           
             Fidelta
          
           a
           poem
           ,
           by
           
             Thomas
             Bancroft
             .
          
        
         
           Advice
           to
           
             Balams
          
           Asse
           ,
           or
           
             Momus
          
           Catechised
           ,
           in
           Answer
           to
           a
           certain
           scurrulous
           and
           abusive
           scribler
           by
           ,
           
             Iohn
             Heydon
          
           A●●hor
           of
           advice
           to
           a
           daughter
           ,
           by
           
             T.
             P.
          
           Gen●
           .
        
         
           The
           Analysis
           of
           all
           the
           Epistles
           of
           the
           new
           Testament
           ,
           wherein
           the
           chief
           things
           of
           every
           particular
           chapter
           are
           reduced
           to
           heads
           ,
           for
           the
           help
           of
           the
           Memory
           ,
           and
           many
           hard
           places
           explained
           ,
           for
           the
           help
           of
           the
           understanding
           ,
           by
           
             Iohn
             Dale
          
           Master
           of
           Arts
           ,
           and
           fellow
           of
           Magdal
           〈…〉
           in
           
             Oxford
             .
          
        
      
    
     
       
       
       
         
           
             
               1
            
          
        
         
         
           I
           Figure
           ,
           To
           all
           sorts
           of
           People
           .
        
         
           
             I
             come
             now
             to
             the
             first
             of
             those
             two
             things
             that
             you
             are
             to
             doe
             for
             to
             make
             one
             of
             those
             Dyals
             ,
             which
             is
             the
             manner
             how
             to
             find
             the
             position
             ,
             or
             the
             placing
             of
             the
             Axeltree
             .
          
        
         
           WHen
           you
           have
           a
           mind
           to
           find
           out
           the
           right
           placing
           of
           the
           Axeltree
           of
           one
           of
           those
           Dyals
           by
           this
           general
           way
           ,
           mark
           first
           which
           way
           the
           light
           of
           the
           Sun
           comes
           to
           the
           place
           where
           you
           will
           make
           your
           Dyal
           ,
           and
           which
           way
           it
           goes
           out
           again
           .
        
         
           Then
           make
           fast
           upon
           the
           place
           ,
           as
           the
           figure
           above
           doth
           shew
           ,
           with
           cement
           ,
           plaister
           ,
           mastick
           ,
           or
           the
           like
           ,
           a
           peg
           or
           pin
           ,
           AB
           ,
           by
           the
           great
           end
           A
           ,
           putting
           the
           other
           small
           or
           sharp
           end
           B
           as
           far
           out
           of
           the
           superficies
           of
           that
           place
           as
           you
           can
           ,
           In
           such
           sort
           that
           while
           the
           Sun
           doth
           shine
           upon
           that
           place
           ,
           the
           shadow
           of
           the
           end
           of
           the
           pin
           B
           may
           fall
           always
           upon
           this
           superficies
           ,
           and
           for
           the
           rest
           it
           is
           no
           matter
           how
           this
           pin
           or
           peg
           be
           framed
           ,
           or
           placed
           ,
           or
           turned
           ,
           you
           are
           only
           to
           look
           to
           the
           small
           end
           thereof
           ,
           that
           must
           be
           in
           such
           a
           manner
           ,
           that
           you
           may
           set
           or
           apply
           upon
           it
           one
           of
           the
           feet
           of
           the
           Compass
           .
        
         
           Then
           in
           a
           fair
           Sunshiny
           day
           ,
           when
           the
           light
           is
           very
           clear
           ,
           and
           the
           shadow
           very
           clean
           ,
           whilst
           it
           falls
           upon
           this
           superficies
           in
           the
           figure
           below
           ,
           mark
           in
           it
           ,
           as
           the
           figure
           shews
           ,
           in
           
           one
           and
           the
           same
           day
           ,
           at
           three
           several
           times
           as
           far
           asunder
           as
           you
           can
           ,
           three
           several
           points
           CDF
           ,
           each
           of
           them
           at
           the
           end
           of
           the
           shadow
           of
           this
           pin
           AB
           that
           answers
           to
           the
           small
           end
           of
           it
           B.
           
        
         
           You
           must
           nore
           that
           there
           is
           a
           certain
           time
           and
           place
           in
           which
           you
           cannot
           mark
           the
           points
           of
           the
           shadow
           ;
           That
           is
           when
           this
           superficies
           is
           flat
           ,
           and
           situated
           after
           such
           a
           manner
           ,
           that
           the
           ground
           plot
           thereof
           being
           stretch'd
           at
           length
           ,
           answereth
           and
           reacheth
           into
           the
           center
           of
           the
           Sun
           .
        
         
           For
           in
           that
           case
           how
           short
           soever
           the
           peg
           or
           pin
           B
           may
           be
           ,
           the
           shadow
           hereof
           cannot
           goe
           and
           fall
           in
           this
           superficies
           ,
           but
           at
           the
           end
           of
           an
           extreme
           length
           .
        
         
           Therefore
           when
           the
           days
           are
           equal
           with
           the
           nights
           ,
           or
           very
           near
           ,
           you
           cannot
           mark
           in
           this
           manner
           three
           points
           of
           shadow
           in
           a
           flat
           superficies
           ,
           which
           is
           situated
           in
           that
           manner
           called
           parallel
           to
           the
           Equator
           .
        
         
           When
           you
           have
           thus
           mark'd
           three
           points
           of
           shadow
           ,
           you
           have
           no
           more
           need
           of
           the
           light
           of
           the
           Sun
           ,
           and
           you
           may
           make
           an
           end
           of
           the
           rest
           in
           any
           other
           time
           and
           season
           ,
           as
           well
           by
           night
           as
           by
           day
           ,
           as
           I
           shall
           say
           three
           times
           together
           for
           one
           and
           the
           same
           manner
           ,
           in
           three
           several
           ways
           to
           be
           expressed
           ,
           after
           I
           have
           briefly
           satisfied
           the
           Theoriciens
           that
           take
           pleasure
           to
           see
           the
           reasons
           of
           the
           precepts
           ,
           or
           rules
           of
           the
           practice
           of
           the
           Arts
           ,
           before
           they
           see
           the
           precepts
           themselves
           .
        
         
           
             1
          
        
      
       
       
         
           To
           the
           Theoriciens
           .
        
         
           This
           Resolution
           will
           serve
           you
           .
        
         
           AFter
           you
           have
           conceived
           that
           the
           Sun
           in
           his
           full
           revolution
           of
           a
           natural
           day
           makes
           a
           Circle
           parallel
           to
           the
           Equator
           ,
           and
           the
           rest
           of
           this
           Hypothesis
           ,
           for
           Dyals
           .
        
         
           The
           three
           beams
           of
           the
           Sun
           or
           straight
           lines
           ,
           BC
           ,
           BD
           ,
           BF
           ,
           make
           in
           their
           point
           or
           common
           end
           B.
           some
           angles
           or
           corners
           equal
           one
           to
           another
           ;
           with
           an
           other
           straight
           one
           that
           makes
           the
           fourth
           ,
           which
           is
           the
           Axeltree
           of
           the
           Dyall
           .
        
         
           Now
           the
           position
           or
           placing
           of
           these
           three
           straight
           lines
           BC
           ,
           BD
           ,
           BF
           ,
           is
           given
           out
           ;
           Therefore
           the
           placing
           of
           this
           fourth
           which
           is
           the
           Axeltree
           of
           the
           Dyal
           is
           given
           also
           .
        
         
           You
           shall
           have
           hereafter
           in
           the
           fourth
           figure
           an
           other
           resolution
           of
           this
           kind
           ,
           before
           you
           have
           the
           way
           to
           compose
           some
           problemes
           ,
           or
           propositions
           about
           it
           .
        
         
           I
           said
           to
           the
           Theoriciens
           ,
           because
           if
           you
           were
           not
           at
           all
           versed
           in
           any
           kind
           of
           practice
           ,
           either
           of
           Geometry
           or
           Art
           ,
           you
           might
           hardly
           understand
           me
           at
           first
           concerning
           the
           2d
           .
           &
           third
           figures
           following
           ,
           because
           of
           the
           short
           &
           compendious
           way
           whereby
           I
           expresse
           my self
           unto
           those
           that
           are
           skilled
           in
           Geometry
           :
           but
           I
           can
           assure
           you
           ,
           that
           when
           you
           have
           understood
           what
           is
           written
           in
           order
           for
           all
           sorts
           of
           people
           ,
           if
           you
           come
           again
           to
           these
           second
           and
           third
           figures
           ,
           you
           shall
           know
           at
           the
           very
           first
           sight
           what
           they
           mean
           .
        
      
       
       
         
           For
           the
           Theoriciens
           ,
        
         
           And
           for
           those
           that
           are
           skilled
           in
           Geometry
           .
        
         
           THe
           I
           figure
           is
           a
           plate
           of
           some
           thin
           ,
           flat
           ,
           smooth
           ,
           and
           solid
           stuff
           ▪
           as
           Iron
           tinned
           ,
           or
           the
           like
           ,
           being
           round
           ,
           and
           having
           a
           hole
           just
           in
           the
           Center
           ,
           greater
           or
           lesser
           ,
           according
           to
           the
           occasion
           .
        
         
           The
           II
           figure
           is
           a
           straight
           rod
           ,
           round
           ,
           smooth
           ,
           and
           solid
           ,
           as
           of
           Iron
           ,
           or
           the
           like
           ,
           of
           the
           bigness
           of
           the
           hole
           in
           the
           plate
           .
        
         
           The
           III
           figure
           is
           as
           it
           were
           a
           whirl
           made
           of
           the
           plate
           ,
           and
           of
           the
           rod
           put
           thorow
           the
           plate
           ,
           in
           such
           sort
           that
           it
           is
           perpendicular
           to
           the
           said
           plate
           ,
           as
           the
           squire
           that
           turns
           round
           about
           doth
           represent
           unto
           you
           ,
           and
           is
           so
           fast
           that
           it
           cannot
           stir
           or
           move
           .
        
         
           In
           the
           V
           figure
           AB
           is
           the
           peg
           or
           pin
           that
           hath
           mark'd
           unto
           you
           the
           points
           of
           the
           shadow
           CDF
           ,
           the
           rods
           or
           sticks
           BC
           ,
           BD
           ,
           BF
           ,
           are
           solid
           and
           strong
           ,
           as
           of
           wood
           ,
           or
           the
           like
           ,
           having
           each
           of
           them
           a
           slope
           edge
           in
           a
           direct
           line
           all
           along
           ,
           going
           from
           the
           point
           of
           the
           peg
           B
           to
           each
           point
           of
           the
           shadow
           CDF
           ,
           and
           are
           so
           turned
           or
           ordered
           ,
           that
           in
           applying
           the
           whirl
           unto
           them
           ,
           the
           edge
           of
           the
           plate
           may
           goe
           andtouch
           the
           three
           slope
           edges
           of
           the
           rods
           all
           at
           once
           ;
           and
           the
           rods
           or
           sticks
           are
           made
           fast
           in
           this
           situation
           ,
           in
           such
           sort
           that
           they
           cannot
           move
           nor
           stir
           .
        
         
           The
           rule
           that
           crosseth
           over
           the
           three
           slope
           edges
           ,
           BC
           ,
           BD
           ,
           BF
           ,
           toucheth
           them
           all
           three
           ,
           or
           else
           two
           at
           the
           time
           only
           ,
           whereby
           it
           shews
           whether
           those
           slope
           edges
           are
           all
           three
           in
           one
           and
           the
           same
           situation
           ,
           or
           upon
           one
           and
           the
           same
           ground
           or
           no
           ,
           and
           on
           which
           side
           is
           their
           hollowness
           when
           there
           is
           any
           .
        
         
           The
           hand
           applies
           the
           whirl
           unto
           it
           ,
           and
           keeps
           it
           there
           till
           the
           Axeltree
           BO●
           come
           to
           touch
           the
           end
           of
           the
           peg
           or
           pin
           B
           ,
           and
           that
           at
           the
           same
           time
           the
           edge
           of
           the
           plate
           EDH
           touch
           the
           three
           slope
           edges
           of
           the
           rods
           .
        
         
           And
           when
           the
           whirl
           is
           placed
           or
           setled
           after
           this
           manner
           ,
           
           the
           rod
           is
           the
           Axeltree
           of
           the
           Dyal
           ,
           and
           placed
           as
           it
           ought
           to
           be
           ,
           and
           there
           remains
           nothing
           else
           but
           to
           make
           it
           fast
           in
           this
           situation
           or
           position
           .
        
         
           The
           IV
           figure
           doth
           shew
           ,
           that
           if
           you
           goe
           to
           make
           use
           of
           thin
           and
           supple
           strings
           in
           this
           practice
           or
           working
           ,
           in
           pulling
           those
           two
           mark'd
           with
           Ie
           ,
           and
           Ih
           ,
           to
           make
           them
           fast
           in
           direct
           lines
           ,
           they
           would
           make
           the
           two
           strings
           mark'd
           with
           bc
           ,
           bf
           to
           bend
           ,
           so
           that
           you
           can
           doe
           nothing
           exactly
           with
           them
           ,
           which
           is
           the
           reason
           that
           
             Monsieur
             Desargues
          
           hath
           not
           thought
           fit
           to
           make
           use
           of
           them
           for
           the
           Beams
           of
           the
           Sun
           ,
           but
           rather
           of
           the
           slope
           edges
           of
           the
           rods
           that
           are
           both
           stiff
           and
           strong
           .
        
         
           
             2
          
        
         
           
             3
          
        
      
       
       
         
           To
           the
           Theoriciens
           ,
        
         
           And
           others
           that
           are
           skill'd
           in
           Geometry
           .
        
         
           THis
           foregoing
           figure
           shews
           to
           the
           eye
           that
           all
           the
           pieces
           of
           the
           Instrument
           are
           made
           so
           strong
           and
           firm
           ,
           that
           they
           cannot
           bend
           .
        
         
           AB
           is
           the
           pin
           ,
           by
           whose
           point
           B
           ,
           you
           have
           had
           the
           points
           of
           shadow
           C
           ,
           D
           ,
           F.
           
        
         
           The
           three
           sticks
           or
           rods
           BC
           ,
           BD
           ,
           BF
           ,
           have
           each
           of
           them
           a
           slope
           edge
           in
           a
           direct
           line
           at
           length
           ,
           going
           from
           the
           point
           of
           the
           pin
           B
           to
           the
           three
           points
           of
           shadow
           ,
           C
           ,
           D
           ,
           F.
           
        
         
           The
           slope
           edges
           of
           the
           two
           longest
           sticks
           or
           rods
           ,
           BC
           ,
           BF
           ,
           have
           some
           portions
           made
           in
           them
           ,
           equal
           every
           one
           to
           the
           third
           and
           shortest
           stick
           BD.
           
        
         
           The
           three
           sticks
           IH
           ▪
           ID
           ,
           IE
           ,
           are
           every
           one
           longer
           than
           BD
           ,
           and
           all
           three
           made
           even
           ,
           then
           they
           are
           joyned
           all
           by
           the
           end
           to
           one
           of
           the
           points
           EDH
           ,
           of
           the
           slope
           edges
           of
           the
           other
           sticks
           ,
           BC
           ,
           BD
           ,
           BF
           ,
           and
           their
           other
           ends
           I
           ,
           are
           brought
           together
           in
           one
           and
           the
           same
           point
           ,
           I.
           
        
         
           The
           rod
           BI
           ▪
           is
           straight
           ,
           round
           ,
           smooth
           and
           strong
           as
           of
           yron
           or
           the
           like
           ,
           it
           hath
           a
           straight
           line
           BI
           ,
           drawn
           from
           one
           end
           to
           an
           other
           ,
           and
           one
           of
           the
           points
           B
           ,
           of
           this
           line
           of
           the
           said
           rod
           toucheth
           the
           point
           of
           the
           pin
           ;
           And
           with
           an
           other
           point
           I
           of
           the
           same
           it
           toucheth
           the
           point
           I
           of
           the
           three
           rods
           or
           sticks
           .
        
         
           This
           being
           so
           ,
           the
           rod
           BI
           comes
           to
           be
           the
           Axeltree
           of
           the
           Dyal
           rightly
           placed
           ,
           there
           remains
           nothing
           else
           but
           to
           make
           it
           fast
           in
           this
           position
           or
           situation
           .
        
         
           The
           figure
           shews
           in
           the
           rods
           that
           goe
           from
           the
           point
           of
           the
           pin
           B
           ,
           to
           the
           points
           of
           shadow
           CDE
           ,
           how
           one
           may
           make
           fast
           those
           rods
           at
           one
           end
           to
           the
           pin
           ,
           and
           also
           all
           together
           to
           one
           point
           ,
           by
           binding
           them
           to
           it
           ;
           And
           how
           they
           may
           be
           made
           f●●t
           at
           the
           otherend
           to
           one
           point
           of
           the
           superficies
           of
           the
           Dyal
           ,
           by
           fastning
           them
           to
           it
           with
           mastick
           ,
           plaster
           ,
           cement
           ,
           or
           thelike
           .
        
         
           This
           way
           is
           more
           sure
           than
           that
           with
           the
           strings
           ;
           But
           
           yet
           it
           is
           not
           the
           easiest
           ▪
           nor
           the
           least
           troublesome
           ,
           in
           my
           judgement
           .
        
      
       
         
           To
           the
           Theoriciens
           ,
        
         
           Another
           resolution
           of
           the
           same
           kind
           with
           the
           former
           .
        
         
           THe
           position
           or
           placing
           is
           given
           of
           the
           four
           points
           BC
           DF
           ,
           and
           the
           placing
           of
           the
           two
           straight
           lines
           BE
           ,
           BH
           ,
           that
           divide
           in
           two
           the
           angles
           CBD
           ,
           and
           DBF
           ,
           and
           of
           the
           two
           ground
           plots
           that
           passe
           unto
           those
           two
           straight
           lines
           BE
           ,
           and
           BF
           ,
           and
           that
           are
           perpendicular
           to
           the
           ground
           plots
           of
           those
           Angles
           CBD
           and
           DBF
           ,
           are
           given
           out
           ;
           Therefore
           the
           intersection
           or
           intercutting
           of
           these
           two
           ground
           plots
           so
           perpendicular
           is
           given
           .
        
         
           But
           this
           intercutting
           is
           the
           axeltree
           of
           the
           Dyal
           ,
           therefore
           the
           position
           of
           the
           axeltree
           of
           the
           Dyal
           is
           given
           .
        
         
           Any
           one
           may
           frame
           at
           his
           pleasure
           upon
           that
           which
           is
           granted
           concerning
           this
           composition
           ,
           many
           other
           resolutions
           ,
           and
           divers
           compositions
           of
           problemes
           ,
           and
           divers
           general
           ways
           of
           practice
           .
        
         
           In
           the
           mean
           time
           you
           shall
           have
           here
           three
           several
           ways
           one
           after
           another
           ,
           to
           see
           which
           is
           the
           most
           advantagious
           for
           the
           actual
           practizing
           of
           the
           Art
           ,
           and
           to
           induce
           you
           to
           seek
           or
           try
           if
           there
           is
           any
           other
           shorter
           .
        
         
           
             4
          
        
      
       
       
         
           For
           the
           Theoriciens
           .
        
         
           The
           Composition
           of
           the
           Probleme
           ,
           or
           Proposition
           ,
           in
           Consequence
           of
           the
           Resolution
           made
           upon
           the
           lowermost
           figure
           of
           the
           first
           draught
        
         
           THe
           first
           figure
           is
           the
           place
           of
           the
           Dyal
           ,
           with
           the
           pin
           and
           the
           points
           of
           shadow
           ,
           CDF
           .
        
         
           Make
           a
           ground
           plot
           of
           it
           ,
           II
           upon
           one
           straight
           line
           BD
           ,
           and
           with
           one
           point
           B
           ,
           three
           Angles
           DBN
           ,
           DBR
           ,
           DBH
           ,
           equal
           to
           the
           three
           Angles
           of
           the
           first
           figure
           ,
           that
           are
           between
           the
           beams
           of
           the
           Sun
           ,
           DBC
           ,
           DBF
           ,
           CBF
           ,
           every
           one
           to
           his
           own
           respectively
           .
        
         
           From
           the
           Center
           B
           ,
           II
           figure
           ,
           and
           from
           any
           space
           BD
           ,
           draw
           a
           half
           circle
           that
           may
           meet
           in
           the
           points
           ,
           DNRH
           ,
           the
           straight
           lines
           BD
           ,
           BN
           ,
           BR
           ,
           BH
           .
        
         
           Make
           in
           the
           third
           figure
           a
           triangle
           DGV
           ,
           with
           three
           spaces
           ,
           equal
           to
           the
           three
           spaces
           DH
           ,
           DR
           ,
           DN
           ,
           every
           one
           to
           his
           respectively
           ,
           as
           having
           the
           condition
           necessary
           for
           that
           purpose
           .
        
         
           Find
           the
           Center
           O
           of
           the
           circle
           EVGD
           ,
           drawn
           about
           this
           triangle
           VGD
           .
        
         
           Draw
           two
           Diametters
           DOE
           ,
           POB
           ,
           of
           this
           circle
           ,
           perpendicular
           one
           unto
           another
           .
        
         
           Lengthen
           one
           POB
           sufficiently
           of
           one
           side
           and
           on
           the
           other
           .
        
         
           From
           one
           of
           the
           ends
           D
           ,
           from
           the
           other
           EOD
           draw
           as
           far
           as
           that
           which
           is
           lengthened
           POB
           one
           straight
           line
           DB
           ,
           even
           with
           the
           straight
           line
           DB
           of
           the
           II
           figure
           ,
           for
           it
           must
           reach
           unto
           it
           ,
           viz.
           In
           the
           Equinoctial
           at
           the
           point
           O
           ,
           and
           in
           an
           other
           place
           at
           an
           other
           time
           ,
           lengthen
           sufficiently
           III
           figure
           this
           straight
           line
           BD.
           
        
         
           Make
           in
           it
           the
           segments
           or
           cuttings
           even
           with
           the
           beams
           of
           the
           Sun
           of
           the
           I
           figure
           BD
           ,
           BF
           ,
           BC.
           
        
         
           Take
           in
           the
           III
           figure
           ,
           in
           the
           straight
           line
           POB
           ,
           conveniently
           a
           point
           I
           other
           than
           B.
           
        
         
         
           Make
           in
           the
           IIII
           figure
           three
           rods
           or
           sticks
           CI
           ,
           DI
           ,
           FI
           ,
           each
           of
           them
           sharp
           at
           both
           ends
           ,
           and
           equal
           with
           the
           three
           spaces
           CI
           ,
           DI
           ,
           FI
           ,
           of
           the
           third
           figure
           .
        
         
           Draw
           a
           straight
           line
           along
           the
           Axeltree
           rod
           ,
           mark
           in
           this
           line
           of
           the
           Axeltree
           conveniently
           figure
           IIII
           ,
           one
           Cut
           BI
           equal
           with
           the
           space
           BI
           of
           the
           III
           figure
           .
        
         
           Set
           figure
           IIII
           one
           of
           the
           ends
           of
           the
           stick
           CI
           to
           the
           point
           of
           shadow
           ,
           C
           ,
           one
           of
           the
           ends
           of
           the
           stick
           DI
           to
           the
           point
           of
           shadow
           ,
           D
           ,
           and
           one
           end●
           of
           the
           stick
           FI
           to
           the
           point
           of
           shadow
           F.
           
        
         
           Let
           the
           ends
           of
           those
           sticks
           or
           rods
           be
           so
           well
           fastened
           to
           the
           points
           of
           shadow
           CDF
           ,
           that
           they
           cannot
           stir
           .
        
         
           Bring
           together
           the
           other
           ends
           I
           ,
           of
           those
           sticks
           in
           one
           point
           I.
           
        
         
           Put
           one
           of
           the
           point
           ▪
           B
           of
           the
           Axeltree
           rod
           to
           the
           point
           of
           the
           pin
           B
           ,
           and
           the
           other
           point
           I
           with
           the
           three
           ends
           of
           the
           sticks
           CI
           ,
           DI
           ,
           FI
           ,
           set
           or
           joyned
           together
           .
           And
           if
           you
           have
           been
           very
           exact
           in
           the
           work
           ,
           the
           point
           I
           of
           the
           pin
           will
           go
           and
           place
           it self
           with
           the
           three
           ends
           of
           the
           sticks
           set
           together
           in
           the
           point
           I
           ,
           if
           not
           ,
           you
           have
           not
           wrought
           exactly
           .
        
         
         
           
             6
          
        
      
       
       
         
           To
           the
           Theoriciens
           .
        
         
           It
           is
           no
           matter
           whether
           the
           Figures
           come
           right
           to
           the
           Compasses
           ,
           you
           are
           only
           to
           take
           notice
           what
           this
           insuing
           Discours
           ordains
           you
           to
           do
           .
        
         
           MAke
           figure
           I
           with
           three
           straight
           lines
           CQRD
           ,
           DIPE
           ,
           and
           CF
           ,
           a
           Triangle
           even
           and
           like
           unto
           the
           Triangle
           figure
           III
           ,
           of
           the
           three
           points
           of
           shadow
           CDF
           ,
           upon
           the
           straight
           line
           CQRD
           figure
           I.
           make
           a
           Triangle
           CBD
           ,
           both
           like
           and
           equal
           with
           the
           Triangle
           figure
           III.
           of
           the
           Sun-beams
           CBD
           ,
           and
           upon
           the
           straight
           line
           FPID
           figure
           I.
           make
           a
           Triangle
           FDB
           ,
           like
           to
           the
           Triangle
           figure
           III.
           of
           the
           Sun-beams
           FDB
           ,
           make
           longer
           if
           need
           be
           figure
           I.
           on
           the
           side
           of
           D
           the
           straight
           lines
           CQRD
           and
           FPID
           .
           By
           the
           points
           B
           and
           B
           draw
           a
           straight
           line
           BRAYH
           perpendicular
           to
           CQRD
           ,
           and
           a
           straight
           line
           BIAKL
           perpendicular
           to
           the
           straight
           line
           FPID
           ,
           find
           out
           the
           end
           or
           point
           A
           ,
           common
           to
           these
           two
           straight
           lines
           BRAYH
           ,
           BIAKL
           ,
           and
           by
           this
           end
           A
           draw
           a
           straight
           line
           AE
           perpendicular
           to
           the
           straight
           line
           BRAYH
           ,
           and
           a
           straight
           line
           AG
           ,
           perpendicular
           to
           the
           straight
           line
           BIAKL
           ,
           from
           the
           point
           R
           draw
           as
           far
           as
           the
           straight
           line
           AE
           a
           straight
           line
           RE
           even
           with
           RB
           ,
           from
           the
           point
           I
           draw
           as
           far
           as
           the
           straight
           line
           AG
           a
           straight
           line
           IG
           even
           with
           IB.
        
         
           From
           the
           point
           E
           carry
           to
           the
           straight
           line
           BRAIH
           a
           straight
           line
           EH
           ,
           perpendicular
           to
           the
           straight
           line
           RE
           ,
           from
           the
           point
           G
           ,
           carrry
           to
           the
           straight
           line
           BIAKL
           a
           straight
           line
           GL
           ,
           perpendicular
           to
           the
           straight
           line
           IG
           ,
           from
           the
           points
           B
           and
           B
           carry
           a
           straight
           line
           BQ
           that
           may
           divide
           in
           half
           the
           Angle
           CBD
           and
           a
           straight
           line
           BP
           that
           may
           divide
           in
           half
           the
           Angle
           DBF
           .
           By
           the
           points
           Q
           and
           H
           draw
           a
           straight
           line
           QOH
           ,
           and
           by
           the
           points
           P
           and
           L
           draw
           a
           straight
           line
           POL
           ,
           find
           the
           end
           or
           the
           point
           O
           common
           to
           the
           two
           straight
           lines
           QOH
           and
           POL
           ,
           and
           from
           the
           point
           A
           for
           center
           and
           space
           AO
           draw
           an
           half
           circle
           that
           may
           meet
           with
           the
           straight
           lines
           AL
           in
           K
           and
           AH
           in
           Y.
           
        
         
         
           Now
           make
           in
           some
           other
           place
           even
           or
           flat
           ,
           as
           in
           the
           second
           figure
           in
           one
           and
           the
           same
           line
           BDFC
           three
           cuts
           BC
           ,
           BD
           ,
           BF
           ,
           even
           with
           the
           Sun
           beams
           ,
           figure
           III.
           
           BC
           ,
           BD
           ,
           BF
           ,
           each
           of
           them
           to
           his
           own
           from
           the
           point
           B
           of
           this
           second
           figure
           for
           center
           ,
           and
           from
           the
           interval
           or
           space
           EY
           or
           GK
           ,
           of
           the
           first
           figure
           ,
           draw
           an
           half
           Circle
           O
           from
           the
           point
           C
           figure
           II
           for
           center
           ,
           and
           from
           the
           space
           CO
           ,
           of
           the
           first
           figure
           draw
           an
           other
           half
           Circle
           O
           from
           the
           point
           D
           of
           the
           II
           figure
           for
           center
           and
           space
           DO
           of
           the
           first
           figure
           ,
           draw
           an
           other
           half
           Circle
           O
           ,
           and
           from
           the
           point
           F
           also
           of
           the
           II
           figure
           for
           center
           and
           space
           FO
           of
           the
           I
           figure
           ,
           draw
           an
           other
           half
           Circle
           O
           ,
           and
           if
           you
           have
           done
           right
           ,
           all
           these
           half
           Circles
           will
           meet
           in
           the
           same
           point
           O
           ,
           if
           not
           ,
           you
           have
           not
           been
           exact
           in
           working
           .
        
         
           By
           the
           points
           B
           and
           O
           draw
           a
           straight
           line
           BO
           ,
           take
           in
           this
           line
           a
           point
           at
           discretion
           ,
           first
           make
           three
           rods
           even
           with
           the
           spaces
           CI
           ,
           DI
           ,
           FI
           of
           the
           second
           figure
           ,
           and
           every
           one
           sharp
           at
           both
           ends
           ,
           make
           in
           the
           length
           of
           the
           axeltree
           rod
           figure
           III
           the
           space
           BI
           ,
           even
           with
           the
           space
           BI
           of
           the
           II
           figure
           .
        
         
           Lastly
           set
           these
           rods
           to
           the
           axeltree
           figure
           III
           as
           I
           have
           said
           at
           the
           end
           of
           the
           fifth
           table
           ,
           and
           the
           axeltree
           of
           the
           Dyal
           is
           placed
           .
        
         
           There
           are
           some
           situations
           of
           superficies
           of
           Dyals
           ,
           where
           practising
           this
           manner
           of
           drawing
           one
           or
           the
           other
           of
           the
           points
           LH
           or
           O
           comes
           so
           far
           from
           the
           straight
           line
           CF
           ,
           that
           you
           should
           have
           need
           of
           too
           great
           a
           space
           to
           come
           to
           it
           .
        
         
           But
           in
           what
           manner
           soever
           the
           superficies
           of
           the
           Dyal
           may
           be
           situated
           ,
           and
           at
           all
           times
           or
           seasons
           of
           the
           year
           ,
           I
           mean
           ,
           in
           any
           strange
           or
           odd
           kind
           of
           example
           that
           may
           be
           found
           ,
           you
           may
           work
           or
           practise
           these
           kinds
           of
           draughts
           with
           as
           much
           ease
           as
           in
           the
           most
           easy
           pattern
           .
        
         
           
             5
          
        
         
           And
           by
           means
           of
           these
           three
           angles
           even
           with
           those
           in
           the
           air
           between
           the
           beams
           of
           the
           Sun
           ,
           you
           may
           chuse
           at
           pleasure
           within
           the
           lines
           that
           represent
           those
           beams
           ,
           other
           points
           CDF
           and
           otherwise
           disposed
           between
           them
           ,
           then
           those
           which
           the
           shadow
           of
           the
           point
           of
           the
           pin
           hath
           given
           upon
           the
           superficies
           of
           the
           Dyal
           ,
           and
           upon
           those
           three
           points
           chosen
           out
           at
           pleasure
           ,
           you
           may
           make
           an
           other
           triangle
           CDF
           ,
           and
           practise
           afterwards
           this
           manner
           of
           drawing
           as
           far
           as
           the
           triangle
           CBO
           figure
           II
           than
           in
           this
           triangle
           ;
           and
           in
           the
           straight
           line
           BC
           ,
           make
           BC
           ,
           BD
           ,
           BF
           ,
           even
           with
           the
           beams
           in
           the
           air
           ,
           BC
           ,
           BD
           ,
           BF
           ,
           of
           the
           third
           figure
           ,
           contained
           from
           the
           point
           of
           the
           pin
           B
           ,
           to
           the
           points
           of
           shadow
           CDF
           in
           the
           superficies
           of
           the
           Dyal
           each
           of
           them
           to
           his
           own
           ,
           and
           after
           you
           have
           taken
           ,
           as
           it
           is
           said
           ,
           the
           point
           I
           in
           the
           straight
           line
           BO
           ,
           you
           must
           make
           use
           of
           the
           points
           CDF
           ,
           last
           made
           in
           the
           triangle
           OCB
           ,
           for
           to
           set
           the
           rods
           CI
           ,
           DI
           ,
           FI
           ,
           to
           the
           axeltree
           BI
           then
           to
           work
           on
           as
           before
           .
        
         
           To
           make
           other
           points
           instead
           of
           those
           of
           the
           superficies
           of
           the
           Dyal
           ,
           you
           need
           only
           to
           make
           some
           at
           the
           two
           extremities
           or
           furthest
           ends
           CF
           ,
           and
           make
           BC
           ,
           and
           BC
           ,
           equal
           one
           to
           the
           other
           ,
           and
           unequal
           with
           the
           middlemost
           BD
           but
           a
           little
           bigger
           ,
           more
           or
           lesse
           according
           as
           the
           angles
           DBC
           ,
           DBF
           ,
           are
           more
           or
           lesse
           unequal
           among
           themselves
           ,
           and
           instead
           of
           making
           figure
           I
           the
           triangle
           CDF
           of
           the
           spaces
           between
           the
           points
           of
           shadow
           CDF
           of
           the
           superficies
           of
           the
           Dyal
           ,
           you
           shall
           make
           it
           of
           the
           spaces
           between
           the
           points
           that
           are
           set
           in
           the
           place
           of
           these
           points
           of
           shadow
           .
        
         
           
             6
          
        
      
       
       
         
           To
           the
           Theoriciens
           .
        
         
           MAke
           in
           one
           and
           the
           same
           plain
           ,
           as
           in
           the
           first
           figure
           ,
           vith
           three
           right
           lines
           CgkD
           ,
           CrtF
           ,
           DieF
           ,
           a
           triangle
           ,
           CDF
           equal
           and
           like
           to
           the
           triangle
           of
           the
           three
           points
           of
           shadow
           ,
           fig.
           IV.
           
           CDF
           make
           upon
           the
           said
           three
           straight
           lines
           CgkD
           ,
           CrtF
           ,
           DieF
           ,
           three
           other
           triangles
           CBD
           ,
           CbF
           ,
           DBF
           ,
           equal
           and
           like
           to
           the
           triangles
           in
           the
           air
           of
           the
           beams
           of
           the
           Sun
           ,
           III.
           fig.
           CBD
           ,
           CBF
           ,
           DBF
           every
           one
           to
           his
           own
           .
           By
           the
           points
           B
           and
           b
           I.
           fig.
           draw
           a
           straight
           line
           Bqg
           that
           may
           part
           in
           two
           the
           Angle
           DbF.
           
           Draw
           out
           of
           the
           point
           C
           at
           your
           discretion
           a
           straight
           line
           aqkty
           perpendicular
           to
           the
           straight
           line
           CgkD
           ,
           and
           out
           of
           the
           point
           F
           ,
           draw
           a
           straight
           line
           hPirx
           perpendicular
           to
           the
           straight
           line
           FeiD
           ,
           make
           in
           the
           triangle
           Fcb
           the
           section
           or
           cutting
           Cl
           ,
           equal
           with
           Ca
           ,
           of
           the
           triangle
           CBD
           ,
           and
           the
           section
           Fs
           ,
           with
           Fh
           ,
           of
           the
           triangle
           FbD
           ,
           from
           the
           point
           t
           center
           ,
           and
           space
           tl
           ,
           draw
           a
           bow
           lm
           ,
           from
           the
           point
           k
           ,
           center
           and
           space
           ka
           ,
           draw
           a
           bow
           am
           ,
           that
           may
           meet
           with
           the
           bow
           lm
           ,
           in
           m
           ▪
           and
           draw
           along
           the
           straight
           line
           km
           ,
           from
           the
           point
           r
           center
           and
           space
           rs
           ,
           draw
           a
           bow
           sn
           ,
           from
           the
           point
           i
           center
           and
           space
           i
           ,
           h
           ,
           draw
           a
           bow
           in
           (
           hn
           )
           that
           may
           meet
           with
           the
           bow
           (
           sn
           )
           in
           (
           n
           )
           draw
           along
           the
           straight
           line
           (
           in
           )
           :
           Make
           in
           the
           straight
           line
           (
           km
           )
           the
           section
           or
           cutting
           (
           ku
           )
           equal
           with
           kq.
           
           By
           the
           point
           (
           u
           )
           bring
           to
           the
           straight
           line
           aqkty
           ,
           a
           straight
           line
           (
           uy
           )
           perpendicular
           to
           the
           straight
           line
           (
           km
           )
           ;
           make
           in
           the
           straight
           line
           (
           in
           )
           a
           section
           (
           iz
           )
           equal
           with
           iP
           ;
           by
           the
           point
           (
           zx
           )
           carry
           to
           the
           straight
           line
           (
           hPirx
           )
           a
           straight
           line
           (
           zx
           )
           perpendicular
           to
           the
           straight
           line
           (
           in
           )
           finde
           out
           the
           butt
           end
           (
           y
           )
           common
           to
           the
           two
           straight
           lines
           (
           aqkty
           )
           and
           uy
           .
           And
           also
           the
           butt
           end
           x
           common
           to
           the
           straight
           lines
           hPirx
           and
           zx
           ,
           draw
           the
           straight
           lines
           goy
           ,
           and
           eox
           ▪
           find
           the
           butt
           end
           o
           common
           to
           these
           straight
           lines
           gov
           ,
           eox
           .
        
         
           Make
           in
           an
           other
           place
           figure
           II.
           a
           Triangle
           gqy
           ,
           of
           the
           three
           straight
           lines
           ,
           as
           ,
           gq
           ,
           gy
           ,
           and
           yu
           of
           the
           first
           
           
             
               7
            
          
           
           figure
           ;
           make
           in
           the
           II.
           fig
           ,
           and
           in
           the
           straight
           lines
           gy
           and
           gq
           ,
           the
           section
           (
           go
           )
           equal
           to
           go
           of
           the
           I.
           fig.
           And
           the
           section
           gb
           also
           equal
           to
           go
           of
           the
           I.
           figure
           ;
           draw
           if
           you
           will
           the
           straight
           line
           (
           bo
           )
           of
           the
           second
           figure
           .
           Make
           again
           in
           another
           place
           fig
           ,
           3.
           a
           Triangle
           (
           cbo
           )
           of
           the
           three
           straight
           lines
           (
           bo
           )
           of
           the
           Triangle
           (
           gbo
           )
           of
           the
           second
           figure
           .
           And
           of
           CB
           and
           CO
           of
           the
           first
           figure
           ;
           and
           upon
           bc
           fig.
           3.
           make
           the
           cuts
           bc
           ,
           bd
           ,
           bf
           ,
           equal
           to
           the
           lines
           BC
           ,
           BD
           ,
           bF
           ,
           of
           the
           first
           figure
           ,
           every
           one
           to
           his
           own
           respectively
           .
           And
           if
           you
           have
           done
           rightly
           ,
           the
           spaces
           fo
           ,
           do
           ,
           co
           of
           the
           Triangle
           cbo
           ,
           fig.
           3.
           are
           equal
           with
           the
           spaces
           FO
           ,
           DO
           ,
           CO
           of
           the
           first
           figure
           ,
           every
           one
           to
           his
           own
           respectively
           .
           Take
           fig.
           3.
           in
           the
           straight
           line
           (
           bo
           )
           according
           to
           your
           discretion
           the
           point
           (
           i
           )
           other
           then
           (
           b
           )
           make
           three
           sticks
           sharp
           at
           both
           ends
           ,
           and
           equal
           to
           the
           three
           spaces
           ci
           ,
           di
           ,
           si
           ,
           of
           the
           third
           figure
           :
           mark
           along
           upon`the
           rod
           or
           Axeltree
           the
           space
           (
           BI
           )
           equal
           to
           the
           space
           (
           bi
           )
           of
           the
           third
           figure
           :
           work
           as
           I
           have
           said
           ,
           and
           as
           the
           fourth
           figure
           doth
           shew
           you
           ,
           and
           you
           shall
           find
           the
           Axeltree
           of
           the
           Dial
           placed
           in
           his
           right
           place
           .
           You
           may
           after
           this
           manner
           ,
           as
           in
           others
           substitute
           ,
           or
           bring
           in
           other
           points
           CDF
           in
           stead
           of
           those
           of
           shadow
           of
           the
           superficies
           ,
           or
           face
           of
           the
           Dyal
           and
           work
           by
           this
           mean
           ,
           every where
           with
           the
           like
           ease
           .
        
      
       
       
         
           
             Figure
             8
             ,
          
           For
           those
           that
           have
           skill
           in
           Geometry
           .
        
         
           THe
           higher
           figure
           is
           the
           place
           of
           the
           Dyal
           with
           the
           face
           unequal
           to
           the
           pin
           AB
           ,
           and
           to
           the
           three
           points
           of
           shadow
           CDF
           ,
           all
           markt
           ,
           as
           it
           is
           said
           .
        
         
           Get
           a
           flat
           and
           solid
           thing
           ,
           as
           a
           slate
           ,
           a
           board
           ,
           paceboard
           ,
           or
           the
           like
           .
        
         
           Draw
           upon
           it
           in
           the
           lower
           figure
           a
           straight
           line
           BDFC
           ,
           make
           in
           that
           line
           three
           cuts
           BC
           ,
           BF
           ,
           BD
           ,
           equal
           with
           the
           three
           spaces
           BC
           ,
           BF
           ,
           BD
           ,
           of
           the
           place
           of
           the
           Dyal
           ,
           each
           of
           them
           to
           his
           own
           respectively
           ,
           then
           from
           the
           point
           B
           of
           the
           lower
           figure
           for
           the
           center
           ,
           and
           from
           the
           spaces
           BC
           ,
           BF
           ,
           BD
           ,
           draw
           some
           circles
           DH
           ,
           FE
           ,
           CG
           .
        
         
           By
           this
           means
           you
           see
           whether
           the
           spaces
           BC
           ,
           BD
           ,
           BF
           ,
           of
           the
           higher
           figure
           or
           Dyal
           ,
           are
           equal
           or
           unequal
           one
           unto
           another
           ,
           and
           when
           these
           spaces
           are
           unequal
           among
           themselves
           ,
           as
           it
           happens
           in
           this
           example
           ,
           you
           see
           which
           is
           the
           least
           ,
           and
           which
           is
           the
           biggest
           ,
           as
           in
           this
           example
           ,
           the
           space
           BD
           ,
           comes
           to
           be
           the
           shortest
           of
           the
           three
           .
        
         
           Now
           from
           the
           point
           C
           of
           the
           lower
           figure
           for
           the
           center
           ,
           and
           from
           the
           space
           between
           the
           two
           points
           of
           shadow
           C
           and
           F
           of
           the
           higher
           figure
           ,
           draw
           a
           circle
           E
           ,
           that
           may
           meet
           in
           one
           point
           E
           ,
           the
           circle
           of
           the
           space
           BF
           ,
           viz.
           the
           circle
           FE
           ,
           for
           it
           must
           meet
           with
           it
           ,
           then
           draw
           the
           straight
           line
           FB
           ,
           that
           may
           go
           and
           meet
           in
           one
           point
           H
           ,
           the
           circle
           of
           the
           shortest
           space
           BD
           ,
           viz.
           the
           circle
           DH
           .
        
         
           Again
           from
           the
           point
           C
           of
           the
           lower
           figure
           for
           center
           ,
           and
           space
           between
           the
           two
           points
           of
           shadow
           C
           and
           D
           of
           the
           higher
           figure
           ,
           draw
           a
           circle
           N
           ,
           that
           may
           go
           and
           meet
           in
           the
           point
           N
           ,
           the
           circle
           of
           the
           shortest
           space
           BD
           ,
           viz.
           the
           circle
           DH
           ,
           for
           it
           must
           meet
           with
           it
           .
        
         
           From
           the
           point
           F
           in
           the
           lower
           figure
           for
           center
           ,
           and
           from
           the
           space
           between
           the
           two
           points
           of
           shadow
           FD
           of
           the
           higher
           figure
           ,
           draw
           a
           circle
           that
           may
           meet
           in
           the
           point
           R
           ,
           the
           circle
           of
           the
           shortest
           space
           BD
           ,
           viz.
           the
           circle
           DH
           ,
           
           for
           it
           must
           meet
           with
           it
           ▪
           By
           this
           means
           the
           three
           spaces
           or
           straight
           lines
           DH
           ,
           DR
           and
           DN
           ,
           of
           the
           circle
           DH
           ,
           which
           is
           that
           of
           the
           shore●t
           space
           BD
           ,
           have
           the
           conditions
           that
           are
           requisite
           for
           the
           making
           of
           a
           triangle
           .
        
      
       
       
         
           
             Figure
             9
             ,
          
           For
           those
           that
           are
           skilled
           in
           Geometry
           .
        
         
           MAke
           in
           another
           place
           ,
           as
           in
           the
           lower
           figure
           ,
           a
           triangle
           DGV
           of
           three
           straight
           lines
           ,
           equal
           with
           the
           three
           spaces
           ,
           DH
           ,
           DR
           ,
           DN
           ,
           of
           the
           higher
           figure
           ,
           every
           one
           to
           its
           own
           .
        
         
           Find
           in
           the
           lower
           figure
           the
           center
           O
           of
           a
           circle
           ,
           the
           edge
           whereof
           may
           reach
           to
           the
           points
           VDG
           ,
           according
           as
           the
           lower
           figure
           doth
           declare
           .
        
         
           Draw
           a
           straight
           line
           DOE
           ,
           through
           the
           Diameter
           or
           midd'st
           of
           this
           circle
           .
        
         
           By
           the
           point
           O
           in
           the
           lower
           figure
           ,
           draw
           a
           straight
           line
           POQ
           ,
           perpendicular
           to
           this
           Diameter
           DOE
           .
        
         
           From
           the
           point
           D
           in
           the
           lower
           figure
           ,
           for
           the
           center
           and
           space
           BD
           of
           the
           higher
           figure
           ,
           draw
           a
           circle
           that
           may
           meet
           as
           in
           B
           ,
           the
           straight
           line
           QOP
           ,
           for
           it
           must
           meet
           with
           it
           in
           one
           or
           two
           points
           ,
           viz.
           In
           the
           times
           of
           the
           Equinoxe
           in
           one
           point
           only
           ,
           which
           is
           the
           point
           O
           ,
           and
           all
           the
           rest
           of
           the
           year
           ,
           in
           two
           points
           divided
           on
           both
           sides
           from
           the
           point
           O.
           
        
         
           And
           that
           you
           may
           be
           exact
           in
           working
           ,
           do
           as
           much
           on
           the
           other
           part
           ,
           and
           of
           E
           for
           center
           .
        
         
           Draw
           in
           the
           lower
           figure
           the
           straight
           line
           BD
           ,
           which
           in
           the
           times
           of
           the
           Equinoxe
           is
           joyned
           with
           the
           straight
           line
           OD
           ,
           and
           all
           the
           rest
           of
           the
           year
           is
           divided
           from
           it
           ,
           and
           draw
           along
           this
           straight
           line
           BD
           beyond
           the
           point
           D.
           
        
         
           Make
           in
           the
           straight
           line
           BD
           of
           the
           lower
           figure
           two
           Sections
           BC
           and
           BF
           ,
           equal
           to
           the
           two
           Sections
           BC
           ,
           &
           BF
           of
           the
           higher
           figure
           ,
           each
           of
           them
           to
           his
           own
           respectively
           .
        
         
           Take
           in
           the
           straight
           line
           QOP
           of
           the
           lower
           figure
           of
           one
           side
           or
           other
           of
           the
           point
           B
           ,
           at
           your
           discretion
           ,
           a
           point
           I
           ,
           besides
           the
           point
           B
           ,
           and
           that
           may
           stand
           as
           far
           from
           the
           point
           B
           ,
           as
           the
           occasion
           may
           give
           you
           leave
           .
        
      
       
       
         
           
             Figure
             10
             ,
          
           To
           those
           that
           are
           skilled
           in
           Geometry
           .
        
         
           THen
           according
           as
           the
           lower
           figure
           shews
           you
           ,
           cut
           three
           sticks
           CI
           ,
           FI
           ,
           DI
           ,
           sharp
           at
           both
           ends
           ,
           and
           equal
           to
           the
           three
           spaces
           CI
           ,
           FI
           ,
           DI
           ,
           of
           the
           higher
           figure
           ,
           each
           of
           them
           to
           its
           own
           space
           respectively
           ,
           and
           upon
           the
           rod
           below
           ,
           whereunto
           you
           mean
           to
           make
           the
           Axeltree
           of
           the
           Dyal
           ,
           make
           a
           Section
           BI
           ,
           equal
           with
           the
           space
           BI
           of
           the
           higher
           figure
           .
        
         
         
           
             
               8
            
          
        
         
         
           
             
               9
            
          
        
         
         
           
             
               10
            
          
        
      
       
       
         
           
             
               11
            
          
        
         
         
           
             Figure
             11
             ,
          
           For
           those
           that
           are
           skilled
           in
           Geometry
           .
        
         
           AFterwards
           as
           you
           see
           in
           the
           lower
           figure
           set
           to
           the
           points
           of
           shadow
           CDF
           upon
           the
           place
           of
           the
           Dyal
           ,
           the
           three
           ends
           CDF
           of
           the
           sticks
           CI
           ,
           DI
           ,
           FI
           ,
           each
           of
           them
           to
           his
           own
           point
           ;
           and
           the
           point
           B
           of
           the
           Axeltree
           rod
           to
           the
           point
           of
           the
           pin
           AB
           ,
           then
           bring
           into
           one
           point
           alone
           in
           the
           air
           I
           ,
           the
           three
           other
           ends
           I
           of
           these
           three
           sticks
           CI
           ,
           DI
           ,
           FI
           ,
           and
           set
           them
           to
           the
           point
           I
           of
           the
           Axeltree
           rod
           .
        
         
           For
           the
           ends
           of
           these
           three
           sticks
           ,
           and
           the
           point
           I
           of
           the
           Axeltree
           ought
           to
           meet
           all
           four
           together
           in
           one
           point
           in
           the
           air
           I
           ,
           and
           then
           you
           shall
           find
           the
           Axeltree
           rod
           placed
           as
           it
           must
           be
           in
           the
           Dyal
           .
           So
           that
           you
           need
           no
           more
           but
           to
           make
           it
           fast
           afterwards
           in
           this
           position
           or
           placing
           ,
           or
           else
           to
           place
           an
           other
           in
           an
           other
           place
           that
           may
           be
           a
           parallel
           to
           it
           .
        
         
           If
           the
           matter
           was
           only
           about
           that
           which
           is
           sufficient
           to
           shew
           Geometrically
           the
           truth
           of
           the
           proposition
           ,
           it
           were
           sufficient
           to
           have
           either
           the
           three
           sticks
           only
           without
           the
           spaceBI
           of
           the
           Axeltree
           rod
           ,
           or
           the
           spaceBI
           of
           the
           Axeltree
           rod
           with
           two
           sticks
           ,
           without
           a
           third
           .
           But
           to
           make
           the
           operation
           sure
           and
           effective
           ,
           you
           can
           not
           be
           confident
           that
           you
           have
           done
           rightly
           without
           a
           fourth
           stick
           that
           may
           serve
           for
           a
           proof
           ;
           This
           is
           that
           which
           
             Monsieur
             de
             Sargues
          
           had
           a
           mind
           to
           impart
           unto
           you
           .
        
      
       
       
         
           Figure
           8
           ,
           The
           same
           thing
           over
           again
           ,
           but
           in
           other
           Terms
           .
        
         
           To
           the
           workmen
           of
           many
           sorts
           of
           Arts
           .
        
         
           VVHen
           you
           have
           markt
           the
           three
           points
           of
           shadow
           CDF
           in
           the
           place
           where
           you
           mean
           to
           make
           one
           of
           these
           Dyals
           ,
           draw
           with
           the
           rule
           in
           some
           even
           or
           flat
           place
           ,
           as
           you
           see
           in
           the
           lower
           figure
           ,
           a
           line
           BD
           ,
           FC
           ,
           and
           make
           in
           that
           line
           a
           prick
           or
           point
           B
           where
           you
           shall
           think
           fit
           ,
           or
           at
           your
           discretion
           .
        
         
           Then
           go
           to
           the
           place
           of
           the
           Dyal
           in
           the
           higher
           figure
           ,
           take
           with
           the
           Compasses
           the
           space
           from
           the
           point
           B
           ,
           of
           the
           ●pin●●…
           B
           to
           the
           point
           of
           shadow
           C.
           And
           with
           that
           space
           come
           back
           to
           the
           line
           BD
           ,
           FC
           of
           the
           lower
           figure
           ,
           set
           one
           of
           the
           feet
           of
           the
           Compasses
           to
           the
           point
           B
           ,
           and
           with
           the
           other
           foot
           go
           and
           mark
           in
           that
           same
           line
           BD
           an
           an
           other
           point
           or
           prick
           C
           ,
           then
           with
           the
           same
           space
           ,
           give
           a
           stroak
           with
           the
           Compasse
           CG
           about
           the
           point
           B.
           
        
         
           Go
           back
           again
           to
           the
           place
           of
           the
           Dyal
           above
           ,
           take
           with
           your
           Compasses
           the
           space
           from
           the
           point
           B
           ,
           of
           the
           pin
           AB
           to
           the
           point
           of
           shadow
           F
           ,
           and
           with
           this
           space
           come
           back
           to
           the
           lower
           figure
           ;
           Set
           again
           one
           of
           the
           feet
           of
           the
           Compasse
           to
           the
           point
           B
           ,
           and
           with
           the
           other
           foot
           go
           and
           mark
           in
           that
           same
           line
           BC
           an
           other
           prick
           or
           stay
           F
           ,
           and
           draw
           again
           about
           the
           point
           B
           with
           the
           same
           space
           of
           the
           Compasse
           this
           half
           circle
           FE
           .
        
         
           
             8
          
        
         
           Then
           look
           in
           the
           lower
           figure
           which
           of
           the
           three
           stroaks
           CG
           ,
           FE
           ,
           DH
           ,
           is
           nearest
           the
           point
           B
           ,
           and
           which
           are
           the
           furthest
           off
           ,
           as
           in
           this
           example
           you
           see
           that
           the
           stroak
           DH
           is
           nearer
           to
           the
           point
           B
           than
           any
           of
           the
           two
           others
           FE
           and
           CG
           ,
           and
           if
           they
           were
           either
           two
           or
           three
           together
           it
           were
           no
           matter
           .
        
         
           When
           you
           know
           which
           of
           these
           stroaks
           of
           the
           lower
           figure
           CG
           FE
           and
           DH
           ,
           is
           the
           nearest
           to
           the
           point
           B
           ,
           and
           which
           are
           the
           farthest
           ,
           as
           here
           ,
           the
           stroak
           DH
           is
           the
           nearest
           ,
           and
           the
           two
           CG
           ,
           FE
           are
           the
           farthest
           off
           .
        
         
           Go
           to
           the
           higher
           figure
           to
           the
           points
           of
           shadow
           C
           ,
           and
           F
           ,
           which
           are
           even
           with
           the
           two
           stroaks
           below
           CG
           ,
           and
           FE
           ,
           which
           are
           the
           furthest
           from
           the
           point
           B
           ,
           and
           open
           your
           Compasses
           upon
           the
           points
           of
           shadow
           C
           and
           F
           ,
           and
           remember
           well
           the
           two
           letters
           or
           cotes
           upon
           which
           you
           have
           opened
           your
           Compasses
           ,
           and
           with
           this
           space
           come
           back
           to
           the
           lower
           figure
           ,
           and
           set
           one
           of
           the
           feet
           of
           the
           Compasses
           to
           the
           point
           C
           ,
           and
           with
           the
           other
           foot
           go
           and
           mark
           a
           point
           E
           ,
           upon
           the
           stroak
           of
           the
           Compasse
           FE
           ,
           for
           it
           must
           reach
           to
           it
           .
        
         
           Then
           draw
           with
           the
           rule
           by
           the
           two
           points
           E
           and
           B
           ,
           a
           line
           EB
           ,
           that
           may
           go
           and
           make
           a
           point
           H
           upon
           the
           stroak
           DH
           ,
           which
           is
           the
           nearest
           to
           the
           point
           B.
           
        
         
           Go
           back
           again
           to
           the
           higher
           figure
           ,
           and
           open
           your
           Compasses
           upon
           the
           points
           of
           shadow
           C
           and
           D
           ,
           and
           with
           this
           space
           come
           back
           to
           the
           lower
           figure
           ▪
           set
           one
           foot
           of
           the
           Compasse
           upon
           the
           point
           C
           ,
           and
           with
           the
           other
           foot
           go
           and
           mark
           a
           point
           N
           ▪
           upon
           the
           stroak
           DH
           ,
           which
           is
           the
           nearest
           to
           the
           point
           B
           ,
           for
           it
           must
           reach
           to
           it
           .
        
         
           Go
           back
           again
           to
           the
           higher
           figure
           ,
           and
           open
           your
           Compasses
           upon
           the
           point
           of
           shadow
           F
           and
           D
           ,
           and
           with
           this
           space
           come
           again
           to
           the
           lower
           figure
           ,
           and
           set
           one
           foot
           of
           the
           Compasse
           upon
           the
           point
           F
           ,
           and
           with
           the
           other
           foot
           go
           and
           make
           a
           point
           R
           upon
           the
           stroak
           DH
           ,
           which
           is
           the
           nearest
           to
           the
           point
           B
           ,
           for
           it
           must
           reach
           to
           it
           .
        
         
           After
           that
           ,
           you
           have
           no
           more
           to
           do
           upon
           the
           place
           of
           
           the
           Dyal
           ,
           till
           you
           place
           the
           Axeltree
           as
           it
           ought
           to
           be
           ,
           and
           you
           have
           in
           the
           lower
           figure
           upon
           the
           stroak
           DA
           ,
           which
           is
           the
           nearest
           to
           the
           point
           B
           ,
           four
           several
           points
           or
           stayes
           DNRH
           to
           make
           three
           point
           perdus
           with
           ,
           as
           you
           shall
           see
           ,
           in
           the
           mean
           time
           remember
           when
           you
           open
           the
           Compasse
           upon
           the
           points
           of
           shadow
           in
           the
           place
           of
           the
           Dyal
           ,
           to
           take
           great
           notice
           upon
           what
           letters
           you
           have
           opened
           your
           Compasse
           ,
           that
           you
           may
           apply
           the
           same
           space
           below
           upon
           the
           two
           stroaks
           which
           are
           equal
           with
           the
           two
           points
           of
           shadow
           upon
           which
           you
           have
           opened
           your
           Compasse
           ,
           and
           set
           one
           foot
           upon
           one
           of
           the
           stroaks
           ,
           and
           the
           other
           upon
           the
           other
           stroak
           .
           And
           moreover
           that
           the
           points
           NR
           ,
           may
           well
           come
           out
           from
           betwixt
           the
           points
           D
           and
           H
           ;
           and
           that
           I
           have
           caused
           them
           to
           come
           in
           so
           betwixt
           them
           ,
           by
           reason
           of
           the
           smallnesse
           of
           the
           place
           ,
           and
           what
           way
           soever
           they
           come
           to
           be
           disposed
           ,
           it
           is
           but
           one
           and
           the
           same
           thing
           still
           .
        
      
       
       
         
           
             Fig.
             9
             ,
          
           To
           the
           workmen
           of
           many
           sorts
           of
           Arts
           .
        
         
           SEt
           your
           Compasse
           upon
           the
           points
           D
           ,
           and
           H
           ,
           of
           the
           higher
           figure
           ,
           and
           with
           that
           space
           go
           to
           some
           flat
           or
           even
           place
           in
           the
           lower
           figure
           ,
           and
           make
           two
           points
           D
           ,
           and
           V
           ,
           so
           that
           the
           space
           DV
           below
           ,
           may
           be
           even
           with
           the
           space
           DH
           above
           .
        
         
           Then
           go
           to
           the
           figure
           above
           ,
           and
           set
           your
           Compass
           upon
           the
           points
           D
           and
           R
           ,
           and
           with
           this
           space
           come
           back
           to
           the
           figure
           below
           ,
           and
           set
           one
           foot
           of
           the
           Compasse
           to
           the
           point
           V
           ,
           and
           with
           the
           other
           foot
           draw
           a
           line
           from
           the
           point
           D
           ,
           to
           the
           point
           G
           ,
           so
           that
           the
           space
           VG
           below
           ,
           may
           be
           even
           with
           the
           space
           DR
           above
           .
        
         
           Go
           back
           again
           to
           the
           figure
           above
           ,
           and
           set
           your
           Compass
           to
           the
           points
           D
           &
           N
           ,
           and
           with
           this
           space
           come
           back
           to
           the
           lower
           figure
           ,
           &
           set
           one
           foot
           of
           the
           Compass
           to
           the
           point
           D
           ,
           and
           with
           the
           other
           foot
           draw
           a
           line
           from
           the
           point
           V
           ,
           to
           the
           point
           G
           ,
           so
           that
           the
           space
           DG
           below
           ,
           may
           be
           even
           with
           the
           space
           DN
           above
           ,
           and
           may
           meet
           in
           G
           the
           other
           circular
           line
           that
           you
           have
           drawn
           about
           the
           point
           V
           ,
           for
           it
           must
           meet
           with
           it
           .
        
         
           
           And
           so
           you
           have
           made
           in
           the
           lower
           figure
           three
           points
           VGD
           that
           will
           be
           perdus
           or
           lost
           .
           Now
           find
           a
           center
           O
           ,
           upon
           which
           having
           set
           one
           of
           the
           feet
           of
           the
           Compass
           ,
           and
           the
           other
           upon
           D
           ,
           let
           this
           foot
           in
           turning
           the
           Compass
           about
           ,
           go
           and
           passe
           by
           those
           three
           points
           perdus
           VGD
           ,
           then
           draw
           with
           the
           rule
           by
           the
           points
           ,
           as
           it
           were
           O
           and
           D
           ,
           a
           line
           DOE
           ,
           and
           setting
           again
           one
           foot
           of
           the
           Compass
           to
           the
           point
           O
           ,
           and
           turning
           the
           other
           foot
           to
           E
           ,
           make
           in
           the
           line
           DOE
           ,
           the
           side
           OE
           ,
           even
           with
           OD.
        
         
           Then
           by
           the
           point
           O
           ,
           draw
           a
           line
           QOP
           ,
           that
           may
           cut
           the
           line
           DOE
           ,
           in
           two
           equal
           parts
           ;
           again
           set
           your
           compass
           to
           the
           points
           B
           ,
           and
           D
           ,
           of
           the
           figure
           above
           ,
           and
           with
           this
           space
           go
           to
           the
           figure
           below
           ,
           set
           one
           foot
           of
           the
           compass
           to
           the
           point
           D
           ,
           &
           with
           the
           other
           foot
           draw
           from
           the
           point
           E
           ,
           a
           line
           B
           ,
           that
           may
           meet
           as
           it
           were
           in
           the
           point
           B
           ,
           the
           line
           QOP
           ,
           and
           make
           with
           this
           other
           foot
           of
           the
           compass
           a
           point
           B
           ,
           in
           the
           line
           QOP
           ,
           for
           it
           must
           meet
           with
           it
           ,
           if
           you
           have
           done
           exactly
           .
        
         
           
             9
          
        
         
           
             9
          
        
         
         
           When
           the
           dayes
           and
           the
           nights
           are
           equal
           ,
           it
           meets
           with
           it
           in
           one
           point
           alone
           ,
           viz.
           O
           ,
           and
           at
           some
           other
           times
           it
           meets
           in
           two
           points
           ,
           one
           of
           one
           side
           of
           the
           O
           ,
           and
           the
           other
           on
           the
           other
           side
           ,
           as
           in
           the
           point
           E.
           Then
           remove
           your
           Compass
           out
           of
           his
           place
           ,
           and
           with
           the
           same
           space
           of
           the
           points
           B
           and
           D
           of
           the
           figure
           above
           ,
           set
           one
           foot
           of
           the
           Compass
           to
           the
           point
           E
           ,
           and
           with
           the
           other
           foot
           draw
           from
           the
           point
           D
           ,
           with
           your
           Compass
           another
           line
           B
           ,
           that
           may
           go
           and
           meet
           the
           line
           ▪
           QOP
           ,
           with
           the
           line
           that
           you
           have
           traced
           with
           the
           Compass
           about
           the
           point
           D
           ,
           and
           both
           of
           them
           in
           one
           and
           the
           same
           point
           B
           ,
           for
           it
           must
           do
           it
           if
           you
           have
           been
           exact
           :
           And
           that
           serves
           to
           mark
           more
           exactly
           this
           point
           B
           ,
           in
           the
           line
           QOP
           ,
           how
           neer
           soever
           it
           is
           to
           the
           Point
           O.
           After
           that
           ,
           Whether
           the
           Point
           B
           of
           the
           lower
           figure
           meets
           with
           the
           Point
           O
           or
           not
           ,
           draw
           with
           the
           rule
           by
           the
           points
           B
           and
           D
           ,
           the
           line
           BD
           ,
           and
           draw
           this
           line
           BD
           ,
           as
           you
           see
           beyond
           the
           point
           D.
           
        
         
           That
           being
           done
           ,
           open
           your
           Compass
           upon
           the
           points
           B
           and
           C
           ,
           of
           the
           higher
           figure
           ,
           and
           carry
           this
           space
           to
           the
           line
           BD
           of
           the
           lower
           figure
           ,
           and
           from
           B
           into
           C.
           
        
         
           Set
           your
           Compass
           again
           upon
           the
           points
           B
           and
           F
           of
           the
           higher
           figure
           ,
           and
           bring
           this
           space
           to
           the
           line
           BD
           of
           the
           lower
           figure
           ,
           and
           from
           B
           into
           F.
           
        
         
           And
           finally
           make
           in
           the
           line
           QOP
           ,
           a
           point
           I
           ,
           at
           your
           discretion
           of
           one
           side
           or
           other
           of
           the
           point
           B
           ,
           and
           let
           it
           be
           as
           far
           distant
           from
           the
           point
           B
           ,
           as
           occasion
           will
           give
           you
           leave
           .
           And
           so
           you
           have
           in
           this
           lower
           figure
           from
           the
           point
           I
           to
           every
           one
           of
           the
           points
           BDFC
           ,
           all
           the
           measures
           that
           are
           necessary
           for
           the
           placing
           of
           the
           axeltree
           or
           needle
           in
           your
           Dyal
           ,
           in
           the
           manner
           hereafter
           following
           .
        
      
       
       
         
           Figure
           10
           ,
        
         
           To
           the
           workmen
           of
           many
           sorts
           of
           Arts
           .
        
         
           CUt
           three
           rods
           or
           sticks
           sharp
           at
           both
           ends
           as
           you
           see
           below
           ,
           one
           CI
           of
           the
           length
           that
           is
           betwixt
           the
           point
           C
           ,
           and
           the
           point
           I
           of
           the
           figure●
           above
           ▪
           the
           other
           FI
           of
           the
           length
           that
           is
           betwixt
           the
           point
           F
           ,
           and
           the
           same
           point
           I
           of
           the
           higher
           figure
           ,
           the
           other
           DI
           of
           the
           length
           that
           is
           betwixt
           the
           point
           D
           ,
           to
           the
           same
           point
           I
           of
           the
           higher
           figure
           ,
           then
           open
           your
           compasse
           upon
           the
           points
           B
           and
           I
           of
           the
           higher
           figure
           ,
           and
           bring
           down
           this
           space
           upon
           the
           Axeltree
           rod
           ,
           and
           make
           in
           the
           same
           as
           you
           see
           ,
           two
           points
           B
           and
           I
           with
           this
           same
           space
           BI
           of
           the
           figure
           above
           .
        
         
         
           
             
               10
            
          
        
      
       
       
         
           
             
               11
            
          
        
         
         
           Figure
           11
           ,
        
         
           To
           the
           workmen
           of
           many
           sorts
           of
           Arts
           .
        
         
           GOe
           to
           the
           place
           of
           the
           Dyal
           below
           which
           I
           have
           expressed
           again
           ,
           a
           purpose
           to
           avoid
           the
           confusion
           of
           lines
           ,
           and
           put
           the
           end
           of
           the
           rod
           CI
           to
           the
           point
           of
           shadow
           C
           ,
           the
           end
           F
           of
           the
           rod
           FI
           to
           the
           point
           of
           shadow
           F
           ,
           and
           the
           end
           D
           of
           the
           rod
           DI
           to
           the
           point
           of
           shadow
           D
           ,
           and
           set
           the
           point
           B
           of
           the
           Axeltree
           rod
           to
           the
           point
           B
           of
           the
           pin
           AB
           .
        
         
           Then
           bring
           together
           into
           one
           point
           in
           the
           Air
           I
           ,
           the
           three
           other
           ends
           of
           the
           three
           rods
           CI
           ,
           DI
           ,
           FI
           ,
           for
           they
           must
           come
           in
           there
           together
           ,
           and
           bring
           the
           point
           I
           ,
           of
           the
           Axeltree
           rod
           ,
           to
           the
           same
           point
           I
           in
           the
           Air
           together
           with
           the
           three
           other
           ends
           of
           the
           rods
           I
           ,
           for
           these
           four
           things
           must
           come
           alltogether
           into
           one
           and
           the
           same
           point
           in
           the
           Air
           I
           ,
           if
           so
           be
           you
           have
           been
           exact
           in
           working
           .
           And
           when
           these
           three
           ends
           of
           the
           rods
           and
           the
           point
           I
           of
           the
           Axeltree
           rod
           ,
           are
           all
           four
           gathered
           together
           into
           one
           and
           the
           same
           point
           in
           the
           Air
           I
           ,
           the
           Axeltree
           rod
           will
           come
           to
           be
           placed
           directly
           as
           it
           must
           be
           in
           the
           Dyal
           ,
           and
           so
           you
           need
           no
           more
           but
           to
           make
           it
           fast
           in
           that
           place
           ,
           or
           to
           fasten
           an
           other
           either
           near
           it
           or
           farr
           from
           it
           ,
           that
           may
           be
           even
           with
           it
           ,
           or
           parallel
           to
           ,
           or
           equally
           distant
           from
           it
           .
        
         
           If
           the
           four
           points
           I
           should
           go
           and
           meet
           in
           the
           body
           of
           the
           Dyal
           ,
           you
           must
           but
           take
           in
           it's
           figure
           the
           point
           I
           nearer
           ,
           or
           in
           the
           other
           side
           of
           the
           point
           B
           ,
           and
           make
           an
           end
           of
           the
           rest
           as
           I
           have
           said
           .
        
      
       
       
         
           
             
               8
            
          
        
         
         
           Figure
           8
           ,
           I
           will
           say
           the
           same
           thing
           over
           again
           ,
           but
           more
           at
           large
           .
        
         
           To
           all
           sorts
           of
           People
           that
           have
           neither
           skill
           in
           Geometry
           nor
           in
           Arts
           ;
           but
           are
           apt
           and
           sit
           to
           learn
           them
           both
           ▪
        
         
           BEfore
           you
           undertook
           to
           make
           this
           Dyal
           ,
           you
           had
           nothing
           about
           you
           ,
           nor
           knew
           nothing
           wherewith
           to
           further
           you
           in
           it
           ,
           and
           going
           about
           it
           ,
           you
           have
           made
           use
           of
           the
           pin
           AB
           ,
           as
           it
           were
           at
           a
           venture
           .
        
         
           Now
           you
           must
           consider
           that
           having
           placed
           the
           pin
           AB
           ,
           in
           this
           manner
           ,
           you
           have
           given
           out
           of
           your self
           in
           the
           end
           thereof
           a
           point
           alone
           unmovable
           and
           fixed
           in
           the
           air
           .
        
         
           Then
           by
           means
           ,
           of
           this
           fixed
           point
           in
           the
           air
           B
           ,
           and
           of
           the
           Sun-beams
           ,
           you
           have
           found
           out
           three
           other
           unmovable
           and
           fixed
           points
           of
           shadow
           CDF
           ,
           on
           the
           outward
           face
           of
           the
           place
           where
           you
           have
           a
           mind
           to
           make
           your
           Dyal
           ▪
           So
           you
           see
           that
           by
           means
           of
           this
           end
           of
           pin
           B
           ,
           and
           of
           the
           Sun-beams
           ,
           you
           have
           established
           upon
           the
           place
           where
           you
           intend
           to
           make
           your
           Dyal
           four
           points
           fixed
           and
           divided
           one
           from
           another
           ,
           viz
           ,
           one
           in
           the
           Air
           ,
           which
           is
           the
           point
           or
           the
           end
           B
           of
           the
           pin
           AB
           ,
           and
           three
           in
           the
           superficies
           of
           the
           Dyal
           which
           are
           the
           three
           points
           of
           shadow
           CDF
           .
        
         
           Whereby
           you
           have
           found
           also
           six
           spaces
           ,
           that
           is
           to
           say
           ,
           the
           lengths
           of
           six
           straight
           lines
           unmoveable
           ,
           fixed
           ,
           distinct
           ,
           and
           divided
           one
           from
           the
           other
           .
        
         
           For
           if
           you
           consider
           well
           ,
           you
           shall
           see
           that
           you
           have
           found
           out
           by
           this
           means
           the
           spaces
           ,
           or
           lengths
           ,
           or
           distances
           that
           are
           from
           the
           point
           B
           of
           the
           pin
           AB
           ,
           to
           every
           one
           of
           the
           three
           points
           of
           shadow
           CDF
           ,
           viz.
           the
           space
           from
           the
           point
           of
           the
           pin
           B
           to
           the
           point
           of
           shadow
           C
           ,
           the
           space
           
           from
           the
           same
           point
           of
           the
           pin
           B
           to
           the
           point
           of
           shadow
           D
           ,
           and
           the
           space
           again
           from
           the
           same
           point
           of
           the
           pin
           B
           to
           the
           point
           of
           shadow
           F.
           
        
         
           And
           for
           your
           better
           instruction
           ,
           if
           you
           will
           make
           these
           three
           lines
           visible
           to
           the
           eye
           ,
           set
           unto
           every
           one
           of
           them
           either
           a
           ruler
           or
           a
           string
           stretch'd
           out
           in
           a
           direct
           line
           from
           the
           point
           of
           the
           pin
           B
           ,
           to
           every
           one
           of
           the
           points
           of
           shadow
           CDF
           ,
           as
           the
           points
           do
           shew
           it
           unto
           you
           ;
           And
           so
           you
           may
           see
           the
           three
           lines
           BC
           ,
           BD
           ,
           BF
           ,
           which
           otherwise
           are
           invisible
           in
           the
           Air
           .
        
         
           And
           besides
           these
           three
           spaces
           or
           lengths
           ,
           you
           have
           also
           found
           out
           the
           three
           spaces
           or
           lengths
           that
           are
           from
           every
           one
           of
           the
           three
           points
           of
           shadow
           CDF
           ,
           unto
           the
           other
           ,
           viz.
           the
           space
           from
           the
           point
           of
           shadow
           C
           ,
           to
           the
           point
           of
           shadow
           F
           ,
           the
           space
           from
           the
           point
           of
           shadow
           C
           ,
           to
           the
           point
           of
           shadow
           D
           ,
           and
           the
           spaces
           from
           the
           point
           of
           shadow
           F
           to
           the
           point
           of
           shadow
           D
           ,
           as
           you
           may
           see
           by
           the
           points
           that
           are
           there
           .
           So
           you
           have
           six
           spaces
           or
           lengths
           BC
           ,
           BD
           ,
           BF
           ,
           CF
           ,
           CD
           ,
           DF
           ,
           which
           you
           have
           already
           found
           unmovable
           ,
           and
           fixed
           to
           the
           place
           wherein
           you
           intend
           to
           make
           your
           Dyal
           ,
           which
           are
           so
           great
           a
           furtherance
           unto
           your
           work
           ,
           that
           there
           remains
           nothing
           else
           to
           do
           ,
           but
           by
           the
           help
           and
           means
           of
           the
           said
           six
           spaces
           or
           lengths
           ,
           to
           find
           also
           three
           or
           four
           more
           ,
           that
           you
           may
           have
           all
           that
           is
           requisite
           for
           the
           placing
           of
           the
           Axeltree
           rod
           of
           your
           Dyal
           as
           it
           ought
           to
           be
           .
        
         
           You
           must
           know
           that
           there
           are
           several
           wayes
           whereby
           these
           six
           spaces
           which
           you
           have
           found
           already
           ,
           viz
           ,
           BC
           ,
           BD
           ,
           BF
           ,
           CF
           ,
           CD
           ,
           DF
           ,
           are
           made
           use
           of
           to
           find
           out
           those
           three
           or
           four
           more
           ,
           which
           you
           must
           have
           to
           inable
           you
           to
           place
           the
           Axeltree
           rod
           of
           your
           Dyal
           as
           it
           must
           be
           .
        
         
           And
           that
           of
           all
           those
           several
           wayes
           a
           man
           may
           have
           a
           liking
           to
           one
           for
           one
           reason
           ,
           and
           another
           man
           to
           an
           other
           for
           some
           other
           reason
           ,
           and
           of
           those
           several
           wayes
           
             Monsieur
             de
             Sargues
          
           hath
           shewed
           me
           three
           or
           four
           at
           the
           most
           ,
           viz.
           that
           which
           he
           hath
           set
           down
           in
           the
           figure
           of
           his
           model
           or
           project
           page
           ,
           and
           of
           the
           others
           for
           which
           you
           must
           know
           how
           to
           make
           sometimes
           somekind
           of
           alteration
           ,
           and
           which
           I
           have
           set
           down
           in
           short
           ,
           there
           is
           one
           in
           the
           sixth
           figure
           ,
           and
           another
           in
           the
           seventh
           .
        
         
         
           As
           for
           this
           it
           is
           such
           ,
           that
           there
           is
           no
           occasion
           but
           you
           may
           practise
           it
           in
           effectually
           ,
           and
           with
           the
           like
           ease
           every where
           ,
           without
           you
           need
           either
           to
           add
           or
           alter
           any
           thing
           ,
           as
           you
           shall
           see
           presently
           .
        
         
           Draw
           with
           the
           rule
           ,
           as
           you
           see
           in
           the
           figure
           below
           in
           some
           flat
           or
           even
           place
           a
           straight
           line
           BD
           ,
           FC
           ,
           then
           go
           to
           the
           figure
           above
           ,
           and
           open
           your
           Compasse
           ,
           and
           set
           one
           of
           the
           feet
           to
           the
           point
           B
           of
           the
           pin
           AB
           ,
           and
           the
           other
           foot
           to
           the
           point
           of
           shadow
           C
           ,
           and
           by
           that
           means
           you
           shall
           take
           with
           your
           Compasse
           the
           space
           or
           the
           lengths
           that
           are
           from
           the
           point
           of
           the
           pin
           B
           ,
           to
           the
           point
           of
           shadow
           C
           ,
           whereof
           you
           will
           be
           pleased
           to
           remember
           ,
           to
           the
           end
           that
           when
           I
           shall
           bid
           you
           for
           brevity
           sake
           ,
           take
           after
           the
           same
           manner
           with
           your
           Compasse
           such
           a
           space
           ,
           you
           may
           be
           able
           to
           do
           with
           your
           Compasse
           even
           as
           I
           told
           you
           just
           now
           of
           the
           space
           BC
           in
           the
           figure
           above
           .
        
         
           Now
           with
           this
           space
           BC
           of
           the
           figure
           above
           ,
           come
           back
           to
           the
           figure
           below
           ,
           and
           set
           at
           your
           discretion
           one
           of
           the
           feet
           of
           the
           Compasse
           upon
           the
           straight
           line
           that
           you
           have
           drawn
           there
           ,
           as
           for
           example
           set
           it
           to
           the
           point
           B
           ,
           then
           turning
           the
           Compasse
           about
           upon
           this
           point
           B
           ,
           draw
           with
           the
           other
           foot
           a
           circular
           line
           CG
           ,
           which
           circle
           by
           this
           means
           shall
           have
           a
           space
           BC
           equal
           with
           the
           space
           BC
           of
           the
           higher
           figure
           ,
           and
           will
           meet
           the
           line
           BD
           for
           example
           in
           the
           point
           C.
           
        
         
           Go
           back
           again
           to
           the
           figure
           above
           ,
           take
           there
           after
           the
           same
           manner
           the
           space
           from
           the
           end
           or
           point
           of
           the
           pin
           B
           to
           the
           point
           of
           shadow
           D
           ,
           and
           with
           this
           space
           come
           back
           to
           the
           figure
           below
           ,
           and
           set
           again
           one
           of
           the
           feet
           of
           your
           Compasse
           to
           the
           point
           B
           ,
           and
           holding
           it
           still
           upon
           this
           point
           B
           draw
           with
           the
           other
           foot
           a
           second
           circular
           line
           DH
           ,
           that
           will
           be
           equal
           with
           the
           space
           above
           BD
           ,
           and
           that
           may
           meet
           the
           line
           BC
           ,
           for
           example
           in
           the
           point
           D.
           
        
         
           Go
           back
           again
           to
           the
           figure
           above
           ,
           and
           take
           with
           your
           Compasse
           the
           space
           betwixt
           the
           point
           of
           the
           pin
           B
           and
           the
           point
           of
           shadow
           F
           ,
           and
           with
           this
           space
           come
           back
           to
           the
           figure
           below
           set
           one
           of
           the
           feet
           of
           the
           Compasse
           to
           the
           point
           B
           ,
           and
           draw
           with
           the
           other
           foot
           a
           third
           circular
           line
           FE
           ,
           with
           the
           space
           BF
           of
           the
           figure
           above
           ,
           and
           that
           may
           
           meet
           the
           line
           BD
           for
           example
           in
           the
           point
           F.
           
        
         
           By
           this
           means
           you
           have
           set
           away
           and
           transported
           the
           three
           spaces
           BC
           ,
           BD
           ,
           BF
           ,
           from
           the
           rise
           or
           place
           which
           they
           had
           in
           the
           place
           of
           the
           Dyal
           above
           in
           a
           flat
           and
           even
           place
           below
           ;
           and
           all
           of
           them
           united
           together
           in
           one
           single
           line
           BDFC
           ,
           in
           which
           you
           may
           see
           whether
           those
           spaces
           be
           equal
           amongst
           themselves
           ,
           as
           they
           may
           be
           in
           some
           occasions
           which
           is
           indifferent
           ,
           or
           whether
           they
           be
           unequal
           ,
           by
           seeing
           whether
           the
           points
           CDF
           ,
           are
           united
           together
           two
           or
           three
           in
           one
           single
           point
           ,
           or
           whether
           they
           are
           disunited
           or
           divided
           one
           from
           another
           ,
           and
           when
           these
           three
           points
           CDF
           ,
           are
           disunited
           or
           divided
           one
           from
           the
           other
           which
           happens
           most
           commonly
           ,
           and
           that
           these
           three
           spaces
           BC
           ,
           BD
           ,
           BF
           ,
           are
           unequal
           amongst
           themselves
           ,
           as
           it
           falls
           out
           in
           this
           example
           ,
           you
           see
           which
           of
           these
           spaces
           are
           the
           greatest
           and
           which
           is
           the
           least
           ,
           considering
           which
           of
           these
           three
           points
           CDF
           is
           the
           nearest
           ,
           and
           which
           is
           the
           furthest
           from
           the
           point
           B
           ,
           that
           is
           to
           say
           also
           that
           by
           this
           means
           you
           see
           which
           of
           these
           circular
           lines
           CG
           ,
           EF
           ,
           DH
           ,
           is
           nearest
           to
           the
           point
           B
           ,
           and
           which
           are
           furthest
           as
           in
           this
           example
           you
           see
           that
           of
           the
           three
           spaces
           BC
           ,
           BD
           ,
           BF
           ,
           those
           two
           BC
           and
           BF
           ,
           are
           the
           greatest
           ,
           and
           BD
           is
           the
           least
           ;
           and
           of
           the
           three
           half
           circles
           CG
           ,
           FE
           ,
           DH
           ,
           you
           see
           that
           DH
           is
           the
           nearest
           to
           the
           point
           B
           ,
           and
           that
           the
           circle
           FB
           is
           nearer
           to
           it
           than
           the
           circle
           CG
           .
        
         
           When
           you
           have
           thus
           found
           out
           which
           of
           the
           three
           spaces
           BC
           ,
           BD
           ,
           BF
           is
           the
           least
           ,
           and
           which
           of
           the
           three
           circles
           CG
           ,
           FE
           DH
           is
           the
           nearest
           of
           the
           point
           B.
           Go
           back
           again
           to
           the
           higher
           figure
           to
           the
           points
           of
           shadow
           CDF
           ,
           and
           take
           with
           the
           compasse
           the
           space
           betwixt
           the
           points
           of
           shadow
           C
           and
           F
           ,
           which
           are
           at
           the
           ends
           of
           the
           two
           greatest
           spaces
           BC
           and
           BF
           ,
           and
           with
           this
           space
           CF
           of
           the
           higher
           figure
           ,
           go
           to
           the
           lower
           figure
           to
           the
           same
           point
           CF
           ,
           and
           set
           one
           foot
           of
           the
           compasse
           upon
           either
           of
           those
           points
           C
           and
           F
           ,
           that
           is
           the
           furthest
           from
           the
           point
           B
           ,
           viz.
           C
           ,
           and
           holding
           still
           the
           point
           of
           the
           compasse
           upon
           this
           point
           C
           ,
           go
           and
           mark
           with
           the
           other
           foot
           a
           point
           for
           example
           E
           ,
           in
           
           the
           circle
           of
           the
           other
           of
           these
           two
           points
           C
           and
           F
           ,
           viz.
           in
           the
           circle
           of
           the
           point
           〈◊〉
           which
           is
           the
           circle
           FE
           ,
           for
           this
           other
           foot
           of
           the
           compasse
           must
           reach
           to
           this
           circle
           of
           the
           point
           F
           ,
           as
           for
           example
           in
           the
           point
           E
           ;
           This
           being
           done
           ▪
           draw
           by
           this
           point
           E
           to
           the
           point
           B
           a
           straight
           line
           EB
           ,
           that
           may
           go
           and
           meet
           ,
           in
           one
           point
           H
           the
           circle
           of
           the
           point
           D
           which
           is
           the
           nearest
           to
           the
           point
           B
           ,
           and
           mark
           in
           it
           this
           point
           H.
           
        
         
           Then
           go
           to
           the
           figure
           above
           ,
           and
           take
           with
           the
           compasse
           the
           space
           betwixt
           the
           two
           points
           of
           shadow
           C
           and
           D
           ,
           and
           with
           this
           space
           CD
           of
           the
           figure
           above
           go
           to
           the
           figure
           below
           ,
           to
           the
           same
           points
           C
           and
           D
           set
           one
           foot
           of
           the
           compasse
           to
           that
           point
           of
           these
           two
           C
           and
           D
           ,
           which
           is
           the
           furthest
           from
           the
           point
           B
           ,
           viz.
           C
           ,
           and
           keeping
           this
           foot
           of
           the
           compasse
           upon
           this
           point
           C
           ,
           go
           and
           mark
           with
           the
           other
           a
           point
           ,
           for
           example
           N
           in
           the
           circle
           of
           the
           other
           of
           the
           two
           points
           C
           and
           D
           ,
           viz.
           in
           the
           circle
           of
           the
           point
           ▪
           D
           with
           the
           circle
           DH
           ,
           for
           this
           other
           foot
           of
           the
           compasse
           must
           reach
           to
           the
           circle
           of
           the
           point
           D
           ,
           for
           example
           in
           the
           point
           N.
           
        
         
           Go
           back
           to
           the
           figure
           above
           ,
           take
           with
           your
           compasses
           the
           space
           betwixt
           the
           two
           points
           of
           shadow
           F
           and
           D
           ,
           and
           with
           this
           space
           FD
           of
           the
           figure
           above
           ,
           come
           back
           to
           the
           figure
           below
           to
           the
           like
           points
           F
           and
           D
           set
           one
           foot
           of
           the
           compasse
           upon
           that
           point
           of
           these
           two
           F
           and
           D
           ,
           which
           is
           furthest
           from
           the
           point
           B
           ,
           viz.
           F
           and
           holding
           still
           the
           point
           of
           the
           compasse
           upon
           this
           point
           F
           ,
           go
           and
           mark
           with
           the
           other
           foot
           a
           point
           for
           example
           R
           ,
           in
           the
           circle
           of
           the
           other
           of
           these
           two
           points
           F
           and
           D
           to
           wit
           ,
           in
           the
           circle
           of
           the
           point
           D
           which
           is
           the
           circle
           DH
           ,
           for
           this
           other
           foot
           of
           the
           compasse
           must
           reach
           to
           the
           circle
           of
           the
           point
           D
           ,
           for
           example
           in
           the
           point
           R.
           This
           being
           done
           ,
           you
           have
           no
           more
           to
           do
           in
           the
           place
           of
           the
           Dyal
           ,
           till
           you
           go
           and
           place
           the
           Axeltree
           rod
           in
           it
           as
           it
           must
           be
           ,
           and
           in
           the
           figure
           below
           in
           the
           circle
           of
           the
           point
           D
           ,
           which
           is
           nearest
           to
           the
           point
           B
           ,
           you
           have
           found
           by
           this
           means
           four
           points
           DN
           ,
           RH
           ,
           different
           and
           divided
           one
           from
           the
           other
           ,
           and
           when
           the
           two
           points
           N
           and
           R
           should
           be
           found
           united
           together
           ,
           it
           were
           no
           matter
           .
           Now
           by
           the
           means
           of
           these
           four
           points
           you
           
           have
           three
           spaces
           amongst
           others
           from
           the
           point
           D
           ,
           to
           every
           one
           of
           the
           three
           points
           HR
           and
           N
           to
           wit
           ,
           the
           space
           from
           D
           to
           H
           ,
           the
           space
           from
           D
           to
           R
           ,
           and
           the
           space
           from
           D
           to
           N
           ,
           of
           which
           spaces
           you
           see
           which
           is
           the
           greatest
           and
           which
           is
           the
           least
           ,
           when
           they
           are
           all
           three
           unequal
           ,
           as
           in
           this
           example
           ,
           for
           it
           may
           happen
           that
           there
           will
           be
           two
           found
           equal
           amongst
           them
           .
        
         
           And
           with
           the
           help
           of
           these
           spaces
           DH
           ,
           DR
           ,
           DN
           ,
           you
           shall
           find
           presently
           those
           four
           that
           you
           must
           have
           for
           the
           placing
           of
           the
           Axeltree
           rod
           of
           your
           Dyal
           ,
           as
           it
           ought
           to
           be
           .
        
      
       
       
         
           
             Figure
             9
             ,
          
           To
           all
           sorts
           of
           People
           ▪
        
         
           TAke
           with
           the
           Compasse
           in
           the
           figure
           above
           ,
           of
           these
           three
           spaces
           DH
           ,
           DR
           DN
           ,
           that
           same
           that
           is
           the
           greatest
           of
           all
           ,
           as
           in
           this
           example
           here
           ,
           the
           space
           DH
           and
           with
           this
           space
           DH
           of
           the
           higher
           figure
           ,
           go
           to
           some
           place
           that
           is
           flat
           ,
           as
           in
           the
           figure
           below
           ,
           and
           set
           at
           the
           same
           time
           the
           two
           feet
           of
           the
           Compasse
           upon
           it
           ,
           as
           for
           example
           ,
           to
           the
           two
           points
           D
           and
           V
           ▪
           and
           mark
           these
           two
           points
           as
           it
           were
           D
           and
           V
           ,
           which
           by
           this
           means
           will
           be
           distant
           one
           from
           the
           other
           ,
           the
           length
           of
           the
           space
           DH
           of
           the
           figure
           above
           .
        
         
           Go
           back
           again
           to
           the
           figure
           above
           ,
           take
           there
           with
           the
           Compasse
           the
           space
           from
           D
           to
           R
           ,
           and
           with
           this
           space
           go
           to
           the
           figure
           below
           ,
           set
           one
           of
           the
           feet
           of
           the
           Compasse
           to
           the
           point
           V
           ,
           and
           from
           thence
           draw
           with
           the
           other
           foot
           towards
           the
           point
           D
           a
           circle
           G
           ,
           which
           by
           this
           means
           shall
           be
           made
           of
           the
           space
           DR
           of
           the
           figure
           above
           .
        
         
           Go
           back
           again
           to
           the
           figure
           above
           ,
           take
           with
           the
           Compasse
           the
           space
           from
           D
           to
           H
           ,
           and
           with
           this
           space
           go
           to
           the
           figure
           below
           ,
           set
           one
           of
           the
           feet
           of
           the
           Compasse
           to
           the
           point
           D
           ,
           and
           from
           thence
           with
           the
           other
           foot
           draw
           towards
           the
           point
           V
           another
           circular
           line
           that
           may
           meet
           ,
           for
           example
           ,
           in
           G
           the
           other
           circle
           ,
           which
           you
           have
           drawn
           about
           the
           point
           V
           ,
           for
           this
           other
           foot
           of
           the
           Compasse
           must
           meet
           the
           other
           circle
           in
           one
           or
           two
           points
           ,
           and
           for
           example
           ,
           in
           the
           point
           G
           for
           one
           .
        
      
       
       
         
           
             
               9
            
          
        
         
         
           
             Figure
             9
             ,
          
           To
           the
           workmen
           of
           many
           sorts
           of
           Arts
           .
        
         
           SEt
           your
           compasse
           upon
           the
           points
           D
           and
           H
           of
           the
           higher
           figure
           ,
           and
           with
           that
           space
           go
           to
           some
           flat
           or
           even
           place
           in
           the
           lower
           figure
           ,
           and
           make
           two
           points
           D
           and
           V
           ,
           so
           that
           the
           space
           DV
           below
           ,
           maybe
           even
           with
           the
           space
           DH
           above
           .
        
         
           Then
           go
           to
           the
           figure
           above
           ,
           and
           set
           your
           compasse
           upon
           the
           points
           D
           and
           R
           ,
           and
           with
           this
           space
           come
           back
           to
           the
           figure
           below
           ,
           and
           set
           one
           foot
           of
           the
           compasse
           to
           the
           point
           V
           ,
           and
           with
           the
           other
           foot
           ,
           draw
           a
           line
           from
           the
           point
           D
           to
           the
           point
           G
           ,
           so
           that
           the
           space
           VG
           below
           ,
           may
           be
           even
           with
           the
           space
           DR
           above
           .
        
         
           Go
           back
           again
           to
           the
           figure
           above
           ,
           and
           set
           your
           compasse
           to
           the
           points
           D
           and
           N
           ,
           and
           with
           this
           space
           come
           back
           to
           the
           lower
           figure
           ,
           and
           set
           one
           foot
           of
           the
           compasse
           to
           the
           point
           D
           ,
           and
           with
           the
           other
           foot
           draw
           a
           line
           from
           the
           point
           V
           to
           the
           point
           G
           ,
           so
           that
           the
           space
           DG
           below
           ,
           may
           be
           even
           with
           the
           space
           DN
           above
           ,
           and
           may
           meet
           in
           G
           the
           other
           circular
           line
           that
           you
           have
           drawn
           about
           the
           point
           V
           ,
           for
           it
           must
           meet
           with
           it
           .
        
         
           And
           so
           you
           have
           made
           in
           the
           lower
           figure
           three
           points
           VGD
           ,
           that
           will
           be
           perdus
           or
           lost
           .
        
         
           Now
           find
           a
           Center
           O
           ,
           upon
           which
           having
           set
           one
           of
           the
           feet
           of
           the
           compasse
           ,
           and
           the
           other
           upon
           D
           ,
           let
           this
           foot
           in
           turning
           the
           compasse
           about
           go
           and
           passe
           by
           those
           three
           points
           perdus
           VGD
           ,
           then
           draw
           with
           the
           rule
           by
           the
           points
           ,
           as
           it
           were
           ,
           O
           and
           D
           ,
           a
           line
           DOE
           ,
           and
           setting
           again
           one
           foot
           of
           the
           compasse
           to
           the
           point
           O
           ,
           and
           turning
           the
           other
           foot
           to
           E
           ,
           make
           in
           the
           line
           DOE
           ,
           the
           side
           OE
           ,
           even
           with
           OD.
        
         
           They
           by
           the
           point
           O
           ,
           draw
           a
           line
           QOP
           ,
           that
           may
           cut
           
           the
           line
           DOE
           in
           two
           equal
           ,
           parts
           .
           Again
           ,
           set
           your
           compasse
           to
           the
           points
           B
           and
           D
           of
           the
           figure
           above
           ,
           and
           with
           this
           space
           go
           to
           the
           figure
           below
           ,
           set
           one
           foot
           of
           the
           compasse
           to
           the
           point
           D
           ,
           and
           with
           the
           other
           foot
           draw
           from
           the
           point
           E
           a
           line
           B
           ,
           that
           may
           meet
           as
           it
           were
           in
           the
           point
           B
           the
           line
           QOP
           ,
           and
           make
           with
           this
           other
           foot
           of
           the
           compasse
           a
           point
           B
           in
           the
           line
           QOP
           ,
           for
           it
           must
           meet
           with
           it
           ,
           if
           you
           have
           done
           exactly
           .
        
         
           When
           the
           dayes
           and
           the
           nightes
           are
           equal
           ,
           it
           meets
           with
           it
           in
           one
           point
           alone
           ,
           viz.
           O
           ,
           and
           at
           some
           other
           times
           it
           meets
           in
           two
           points
           ,
           one
           of
           one
           side
           of
           the
           O
           ,
           and
           the
           other
           of
           the
           other
           side
           ,
           as
           in
           the
           point
           E
           ,
           then
           remove
           your
           compasse
           out
           of
           his
           place
           ,
           and
           with
           the
           same
           space
           of
           the
           points
           B
           and
           D
           ,
           of
           the
           figure
           above
           set
           one
           foot
           of
           the
           compasse
           to
           the
           point
           E
           ,
           and
           with
           the
           other
           foot
           draw
           from
           the
           point
           D
           with
           your
           compasse
           another
           line
           B
           ,
           that
           may
           go
           and
           meet
           the
           line
           QOP
           ,
           with
           the
           line
           that
           you
           have
           traced
           with
           the
           compasse
           about
           the
           point
           D
           ,
           and
           both
           of
           them
           in
           one
           and
           the
           same
           point
           B
           ,
           for
           it
           must
           do
           it
           if
           you
           have
           been
           exact
           ,
           And
           that
           serves
           to
           mark
           more
           exactly
           this
           point
           B
           in
           the
           line
           QOP
           ,
           how
           near
           soever
           it
           is
           to
           the
           point
           O.
           After
           that
           ,
           whether
           the
           point
           B
           of
           the
           lower
           figure
           meets
           with
           the
           point
           O
           or
           not
           ,
           draw
           with
           the
           rule
           by
           the
           points
           B
           and
           D
           the
           line
           BD
           ,
           and
           draw
           this
           line
           BD
           ,
           is
           you
           see
           ,
           beyond
           the
           point
           D.
           
        
         
           That
           being
           done
           ,
           open
           your
           compasse
           upon
           the
           points
           B
           and
           C
           of
           the
           higher
           figure
           ,
           and
           carry
           this
           space
           to
           the
           line
           BD
           of
           the
           lower
           figure
           ,
           and
           from
           B
           into
           C.
           
        
         
           Set
           your
           compass
           again
           upon
           the
           points
           B
           and
           F
           of
           the
           higher
           figure
           ,
           and
           bring
           this
           space
           to
           the
           line
           BD
           of
           the
           lower
           figure
           ,
           and
           from
           B
           into
           F.
           
        
         
           And
           finally
           make
           in
           the
           line
           QOP
           a
           point
           I
           ,
           at
           your
           discretion
           ,
           of
           one
           side
           or
           other
           of
           the
           point
           B
           ,
           and
           let
           it
           be
           as
           far
           distant
           from
           the
           point
           B
           ,
           as
           occasion
           will
           give
           you
           leave
           ;
           And
           so
           you
           have
           in
           this
           lower
           figure
           from
           the
           point
           I
           ,
           to
           every
           one
           of
           the
           points
           BD
           ,
           FC
           ,
           all
           the
           measures
           that
           are
           necessary
           for
           the
           placing
           of
           the
           axeltree
           or
           needle
           in
           the
           Dyal
           ,
           in
           the
           manner
           hereafter
           following
           .
        
      
       
       
         
           
             Figure
             9
             ,
          
           To
           all
           sorts
           of
           People
           .
        
         
           THat
           being
           done
           open
           your
           compasse
           at
           your
           discretion
           ,
           and
           the
           more
           that
           the
           occasion
           will
           permit
           you
           to
           open
           it
           ,
           it
           will
           be
           so
           much
           the
           better
           ,
           and
           with
           this
           opening
           ,
           set
           one
           of
           the
           feet
           of
           the
           compasse
           to
           the
           point
           G
           of
           the
           figure
           above
           ,
           then
           turning
           about
           this
           point
           of
           the
           compass
           upon
           this
           point
           G
           ,
           draw
           with
           the
           other
           foot
           four
           circles
           H
           ,
           L
           ,
           M
           ,
           S
           ,
           about
           the
           point
           G.
           viz.
           two
           H
           ,
           and
           L
           from
           the
           point
           D
           ,
           and
           two
           M
           and
           S
           from
           the
           point
           V
           ,
           then
           remove
           your
           compass
           ,
           and
           set
           one
           of
           the
           feet
           upon
           the
           point
           D
           ,
           and
           with
           the
           other
           foot
           draw
           from
           the
           point
           G
           ,
           two
           circles
           that
           may
           meet
           in
           two
           points
           ,
           viz.
           Land
           G
           ,
           those
           two
           circles
           that
           you
           have
           drawn
           about
           the
           point
           G
           ,
           from
           the
           point
           D
           ,
           if
           this
           same
           foot
           of
           the
           compass
           could
           not
           meet
           with
           these
           two
           circles
           HL
           ,
           that
           you
           have
           drawn
           about
           the
           point
           G
           &
           from
           the
           point
           D
           ,
           it
           is
           because
           you
           had
           not
           opened
           your
           compass
           enough
           ,
           before
           you
           did
           set
           it
           upon
           the
           point
           G
           ,
           and
           in
           such
           a
           case
           you
           shall
           open
           it
           more
           ,
           and
           set
           it
           again
           upon
           this
           point
           G
           ,
           and
           when
           this
           same
           foot
           meets
           these
           two
           first
           circles
           ,
           for
           example
           ,
           in
           H
           and
           in
           L
           ,
           matk
           these
           two
           points
           L
           ,
           and
           H.
           
        
         
           Afterwards
           remove
           the
           compass
           and
           keeping
           still
           the
           same
           open
           ,
           set
           one
           foot
           to
           the
           point
           V
           ,
           and
           turning
           the
           compass
           upon
           the
           point
           V
           ,
           draw
           with
           the
           other
           foot
           from
           the
           point
           G
           ,
           two
           circles
           that
           may
           meet
           likewise
           in
           two
           points
           as
           S
           ,
           and
           M
           ,
           the
           two
           circles
           that
           you
           have
           drawn
           about
           the
           point
           G
           ,
           from
           the
           point
           V
           ,
           and
           mark
           those
           two
           points
           S
           and
           M
           ,
           in
           which
           those
           two
           circles
           meet
           with
           the
           other
           two
           :
           And
           therefore
           note
           that
           before
           you
           make
           yout
           compass
           to
           turn
           upon
           the
           point
           G
           ▪
           you
           must
           open
           it
           in
           such
           a
           manner
           ,
           that
           when
           you
           shall
           set
           it
           afterwards
           upon
           the
           points
           D
           and
           V
           ,
           the
           other
           foot
           may
           meet
           with
           the
           circles
           that
           you
           have
           drawn
           about
           the
           point
           G.
           
        
         
           
             9
          
        
         
         
           Then
           draw
           by
           the
           two
           points
           H
           and
           L
           ,
           a
           long
           straight
           line
           H
           ,
           L
           ,
           O
           ,
           and
           by
           the
           two
           points
           S
           and
           M
           ,
           draw
           an
           other
           long
           line
           and
           as
           straight
           ,
           M
           ,
           S
           ,
           O
           ,
           and
           these
           two
           lines
           HL
           and
           MS
           ,
           being
           sufficiently
           drawn
           at
           length
           ,
           will
           meet
           in
           one
           and
           the
           same
           point
           O.
           
        
         
           By
           the
           two
           points
           D
           and
           O
           ,
           draw
           a
           straight
           line
           DO
           ,
           and
           draw
           it
           at
           length
           ,
           as
           you
           see
           from
           the
           point
           O
           ,
           then
           set
           one
           of
           the
           feet
           of
           the
           compass
           upon
           the
           point
           O
           ,
           and
           the
           other
           foot
           upon
           the
           point
           D
           ,
           and
           turn
           that
           foot
           of
           the
           compass
           which
           is
           upon
           the
           point
           O.
           The
           other
           foot
           which
           is
           upon
           the
           point
           D
           must
           go
           and
           touch
           every
           one
           of
           the
           points
           G
           and
           V
           ,
           and
           when
           this
           other
           foot
           hath
           gone
           over
           the
           point
           D
           ,
           G
           ,
           V
           ,
           go
           and
           mark
           at
           the
           very
           same
           time
           with
           it
           a
           point
           ,
           as
           E
           in
           the
           line
           DOE
           ,
           and
           so
           you
           shall
           make
           the
           portion
           OE
           of
           the
           line
           OD
           ,
           equal
           with
           the
           portion
           OD.
        
         
           Then
           open
           your
           compass
           at
           discretion
           more
           than
           from
           the
           space
           OD
           ,
           and
           as
           much
           as
           the
           occasion
           will
           give
           you
           leave
           ,
           the
           more
           the
           better
           ,
           and
           the
           compass
           being
           so
           open
           at
           discretion
           ,
           set
           one
           of
           the
           feet
           to
           the
           point
           D
           of
           the
           lower
           figure
           ,
           and
           turning
           that
           foot
           of
           the
           compass
           upon
           the
           point
           D
           ,
           draw
           with
           the
           other
           foot
           from
           the
           point
           O
           ,
           two
           circles
           ,
           as
           P
           and
           Q
           then
           remove
           the
           compass
           ,
           keeping
           still
           the
           same
           distance
           ,
           set
           one
           foot
           upon
           the
           point
           E
           ,
           and
           turning
           it
           about
           ,
           draw
           with
           the
           other
           foot
           from
           the
           point
           O
           ,
           two
           other
           circles
           ,
           that
           may
           meet
           in
           two
           points
           with
           the
           two
           circles
           that
           you
           have
           drawn
           about
           the
           point
           D
           ,
           and
           as
           for
           example
           in
           the
           two
           points
           Q
           and
           P
           ,
           and
           draw
           with
           the
           rule
           by
           these
           two
           points
           ,
           as
           Q
           and
           P
           ,
           a
           long
           straight
           line
           QP
           ,
           that
           must
           reach
           to
           the
           point
           O
           ,
           if
           you
           have
           been
           very
           exact
           in
           the
           working
           ;
           if
           it
           doth
           not
           reach
           to
           it
           you
           have
           not
           been
           very
           exact
           ,
           and
           I
           advise
           you
           to
           begin
           it
           again
           :
           If
           it
           reaches
           to
           it
           ,
           go
           back
           to
           the
           figure
           below
           ,
           and
           take
           with
           the
           compass
           the
           distance
           between
           B
           and
           D
           ,
           then
           with
           this
           space
           go
           to
           the
           figure
           below
           ,
           set
           one
           foot
           of
           the
           compass
           upon
           the
           point
           D
           ,
           and
           turning
           it
           about
           ,
           draw
           with
           the
           other
           foot
           from
           the
           point
           O
           ,
           a
           circle
           that
           may
           meet
           the
           line
           QOP
           ,
           as
           for
           example
           in
           the
           point
           B
           ,
           for
           this
           other
           foot
           of
           the
           compass
           must
           go
           and
           meet
           that
           straight
           line
           
           POQ
           either
           in
           one
           or
           in
           two
           points
           ,
           because
           the
           space
           from
           B
           to
           D
           of
           the
           higher
           figure
           ought
           never
           to
           be
           smaller
           or
           lesser
           than
           the
           space
           DO
           of
           the
           figure
           above
           .
        
         
           It
           is
           true
           that
           twice
           in
           the
           year
           ,
           viz.
           in
           
             Autumne
          
           and
           in
           the
           
             Spring
             ,
          
           when
           the
           dayes
           and
           nights
           are
           equal
           ,
           that
           space
           BD
           of
           the
           figure
           above
           comes
           to
           be
           equal
           with
           the
           space
           DO
           ,
           of
           the
           figure
           below
           ,
           and
           in
           those
           times
           that
           other
           foot
           of
           the
           Compasse
           that
           tutns
           about
           the
           point
           D
           of
           the
           figure
           below
           ,
           meets
           the
           line
           QOP
           just
           in
           the
           point
           O.
           But
           at
           all
           other
           times
           the
           space
           BD
           of
           the
           figure
           above
           is
           somewhat
           bigger
           than
           the
           space
           DO
           of
           the
           lower
           figure
           ;
           And
           then
           the
           other
           foot
           of
           the
           Compasse
           that
           turns
           about
           the
           point
           D
           ,
           meets
           the
           line
           QOP
           ,
           in
           two
           points
           ,
           one
           of
           each
           side
           of
           the
           point
           O
           ,
           as
           for
           example
           in
           B
           ,
           for
           one
           .
        
         
           And
           that
           you
           may
           be
           the
           more
           exact
           ,
           remove
           the
           Compasse
           from
           one
           part
           of
           the
           straight
           line
           BO
           unto
           the
           other
           ,
           and
           with
           the
           same
           opening
           of
           the
           space
           BD
           of
           the
           higher
           figure
           ,
           set
           one
           of
           the
           feet
           upon
           the
           point
           E
           of
           the
           figure
           below
           ,
           and
           turning
           this
           foot
           upon
           this
           point
           E
           ,
           draw
           with
           the
           other
           and
           from
           the
           point
           D
           an
           other
           circle
           that
           will
           meet
           (
           if
           you
           have
           been
           exact
           in
           the
           working
           )
           the
           straight
           line
           QOP
           ,
           and
           the
           circle
           also
           that
           you
           have
           drawn
           about
           the
           point
           D
           ,
           and
           both
           in
           one
           point
           ;
           as
           for
           example
           in
           the
           point
           B
           ,
           which
           will
           inable
           you
           to
           discern
           well
           the
           point
           B
           in
           the
           straight
           line
           POQ
           ;
           mark
           this
           point
           B
           in
           the
           line
           POQ
           ,
           whether
           you
           find
           it
           united
           with
           the
           point
           O
           ,
           and
           so
           both
           of
           them
           making
           but
           one
           and
           the
           same
           point
           ,
           as
           it
           falls
           out
           ,
           when
           the
           days
           and
           nights
           are
           equal
           ,
           or
           whether
           you
           find
           it
           divided
           from
           the
           point
           O
           ,
           as
           it
           falls
           out
           in
           other
           seasons
           ,
           and
           as
           you
           see
           in
           this
           example
           ▪
           Then
           draw
           with
           the
           rule
           by
           these
           two
           points
           B
           and
           D
           a
           straight
           line
           BD
           ,
           which
           you
           shall
           stretch
           out
           sufficiently
           beyond
           the
           point
           D.
           When
           the
           days
           and
           nights
           are
           equal
           ,
           as
           in
           
             Autumne
          
           and
           in
           the
           
             Spring
             ,
          
           and
           that
           the
           point
           B
           is
           found
           to
           be
           united
           with
           the
           point
           O
           ,
           the
           line
           BD
           comes
           likewise
           to
           be
           united
           with
           the
           line
           OD
           ,
           and
           both
           together
           make
           but
           one
           line
           ;
           But
           at
           any
           other
           time
           ,
           as
           the
           two
           points
           B
           and
           O
           are
           two
           several
           points
           and
           divided
           one
           from
           the
           other
           ,
           so
           the
           two
           
           lines
           BD
           and
           OD
           ,
           are
           two
           several
           lines
           ▪
           and
           divided
           one
           from
           the
           other
           ,
        
         
           This
           being
           done
           ,
           go
           to
           the
           figure
           above
           ,
           mea●ure
           with
           your
           Compasse
           the
           space
           from
           B
           to
           C
           ,
           and
           with
           this
           space
           go
           to
           the
           figure
           below
           ,
           set
           one
           foot
           of
           the
           Compasse
           upon
           the
           line
           BD
           ,
           to
           the
           point
           B
           ,
           and
           set
           the
           other
           foot
           in
           any
           place
           of
           the
           same
           line
           BD
           where
           it
           may
           light
           upon
           ;
           as
           for
           example
           in
           the
           point
           C
           ,
           by
           this
           means
           you
           shall
           make
           the
           portion
           BC
           ,
           of
           the
           line
           BD
           of
           the
           lower
           figure
           ,
           equal
           with
           the
           portion
           BC
           ,
           of
           the
           line
           BD
           of
           the
           higher
           figure
           ,
           make
           after
           the
           same
           manner
           with
           the
           Compasse
           ,
           the
           portion
           BF
           ,
           of
           the
           line
           BD
           of
           the
           lower
           figure
           ,
           equal
           to
           the
           Portion
           BF
           ,
           of
           the
           line
           BD
           of
           the
           figure
           above
           .
        
         
           Finally
           ,
           in
           the
           same
           figure
           below
           ,
           and
           in
           the
           line
           QOP
           ,
           mark
           at
           your
           discretion
           another
           point
           ,
           I
           ,
           of
           one
           side
           or
           other
           of
           the
           point
           B
           ,
           according
           as
           you
           shall
           find
           it
           most
           convenient
           for
           the
           place
           of
           the
           Dyal
           ,
           and
           as
           far
           from
           this
           point
           B
           ,
           as
           occasion
           will
           permit
           ,
           the
           further
           the
           better
           ,
           and
           so
           you
           have
           found
           the
           four
           spaces
           that
           you
           wanted
           for
           the
           perfect
           placing
           of
           the
           Axeltree
           of
           your
           Dyal
           .
        
         
           For
           in
           so
           doing
           ,
           you
           have
           found
           in
           this
           figure
           below
           the
           distances
           that
           are
           from
           every
           one
           of
           the
           four
           points
           BDF
           C
           ,
           to
           one
           and
           the
           same
           point
           I
           ,
           that
           is
           to
           say
           the
           space
           from
           B
           to
           I
           ,
           the
           space
           from
           D
           to
           I
           ,
           the
           space
           from
           F
           to
           I
           ,
           and
           the
           space
           from
           C
           to
           I
           ,
           which
           distances
           BI
           ,
           DI
           ,
           FI
           ,
           and
           CI
           ,
           will
           serve
           you
           to
           place
           the
           Axeltree
           of
           the
           Dyal
           in
           the
           manner
           following
           .
        
      
       
       
         
           
             Figure
             10
             ,
          
           To
           all
           sorts
           of
           People
           .
        
         
           CUt
           (
           as
           you
           see
           in
           the
           lower
           figure
           ,
           )
           three
           sticks
           sharp
           it
           both
           ends
           ,
           one
           CI
           of
           the
           length
           of
           the
           point
           C
           ,
           to
           the
           point
           I
           ,
           otherwise
           of
           the
           space
           CI
           of
           the
           figure
           above
           :
           The
           other
           FI
           ,
           of
           the
           length
           of
           the
           space
           FI
           of
           the
           higher
           figure
           ,
           and
           take
           with
           your
           Compasses
           the
           space
           BI
           of
           the
           figure
           above
           ,
           and
           being
           so
           open
           ,
           see
           both
           feet
           at
           once
           upon
           a
           straight
           line
           ,
           along
           the
           Axeltree
           rod
           of
           the
           lower
           figure
           ,
           for
           example
           ,
           in
           two
           points
           as
           B
           and
           I
           ,
           and
           mark
           these
           two
           points
           B
           ,
           I
           ,
           in
           the
           Axeltree
           rod
           .
        
         
         
           
             
               10
            
          
        
      
       
       
         
           
             
               11
            
          
        
         
         
           
             Figure
             11
             ,
          
           To
           all
           sorts
           of
           People
           .
        
         
           THat
           being
           done
           ,
           go
           to
           the
           place
           of
           the
           Dyal
           ,
           the
           which
           ,
           to
           avoid
           the
           confusion
           or
           multiplicity
           of
           lines
           ,
           I
           have
           set
           below
           in
           the
           lower
           figure
           ,
           set
           in
           this
           lower
           figure
           one
           of
           the
           ends
           of
           the
           stick
           CI
           ,
           to
           the
           point
           of
           shadow
           C
           ,
           one
           of
           the
           ends
           F
           ,
           of
           the
           stick
           FI
           ,
           to
           the
           point
           of
           shadow
           F
           ,
           and
           one
           of
           the
           ends
           D
           ,
           of
           the
           stick
           DI
           to
           the
           point
           of
           shadow
           D
           ,
           and
           one
           of
           the
           points
           B
           of
           the
           Axeltree
           rod
           ,
           set
           it
           to
           the
           point
           B
           ,
           of
           the
           pin
           AB
           .
        
         
           And
           holding
           thus
           the
           three
           ends
           CDF
           ,
           of
           the
           three
           sticks
           to
           the
           points
           of
           shadow
           CDF
           ,
           every
           one
           respectively
           to
           his
           own
           ,
           and
           the
           point
           B
           of
           the
           Axeltree
           rod
           ,
           to
           the
           point
           of
           the
           pin
           B
           ,
           bring
           together
           the
           three
           other
           ends
           I
           ,
           of
           the
           three
           sticks
           or
           rods
           CI
           ,
           DI
           ,
           FI
           ,
           into
           one
           point
           in
           the
           air
           I
           ,
           for
           they
           must
           meet
           there
           ▪
           then
           bring
           the
           point
           I
           of
           the
           Axeltree
           rod
           ,
           also
           to
           the
           point
           in
           the
           air
           I
           ,
           with
           the
           three
           ends
           I
           of
           the
           sticks
           ,
           for
           it
           must
           come
           and
           meet
           there
           exactly
           ,
           if
           you
           have
           done
           right
           ,
           or
           if
           the
           straightnesse
           of
           the
           place
           hath
           not
           hindered
           you
           .
        
         
           If
           the
           straightnesse
           of
           the
           place
           of
           the
           Dyal
           hinders
           the
           three
           ends
           I
           ,
           of
           the
           sticks
           from
           meeting
           together
           in
           one
           point
           in
           the
           air
           I
           ,
           take
           the
           point
           I
           in
           the
           figure
           below
           in
           the
           ninth
           cut
           ,
           or
           that
           above
           in
           the
           tenth
           figure
           in
           an
           other
           place
           ,
           than
           in
           that
           where
           you
           had
           taken
           it
           and
           according
           to
           the
           occasion
           ,
           then
           bring
           the
           sticks
           to
           it
           as
           before
           (
           for
           you
           may
           take
           it
           anywhere
           ,
           or
           in
           any
           place
           of
           the
           line
           POQ
           ,
           of
           one
           side
           or
           other
           of
           the
           point
           B
           ;
           )
           but
           the
           further
           you
           can
           take
           it
           from
           the
           point
           B
           ,
           will
           be
           better
           ,
           and
           take
           it
           in
           so
           many-places
           ,
           that
           having
           set
           the
           sticks
           of
           the
           points
           CDF
           ,
           to
           this
           point
           I
           ,
           and
           mark'ed
           the
           space
           BI
           upon
           the
           Axeltree
           rod
           ,
           the
           four
           points
           I
           ,
           may
           at
           last
           meet
           together
           in
           one
           point
           in
           the
           air
           I.
           
        
         
           And
           when
           the
           point
           B
           of
           the
           Axeltree
           rod
           ,
           is
           at
           the
           
           point
           B
           ,
           of
           the
           pin
           AB
           ,
           and
           when
           the
           three
           ends
           I
           ,
           of
           the
           sticks
           ,
           and
           the
           point
           I
           of
           the
           Axeltree
           rod
           are
           met
           ,
           as
           you
           see
           in
           the
           lower
           figure
           ,
           all
           four
           together
           in
           one
           and
           the
           same
           point
           in
           the
           air
           I.
           
        
         
           The
           Axeltree
           rod
           will
           come
           then
           to
           be
           placed
           ,
           just
           as
           it
           ought
           to
           be
           in
           the
           Dyal
           .
        
         
           That
           if
           you
           do
           not
           care
           to
           be
           sure
           that
           your
           Dyal
           must
           be
           as
           just
           ,
           as
           it
           is
           possible
           for
           art
           to
           do
           ,
           in
           such
           a
           case
           ,
           you
           may
           spare
           one
           of
           the
           four
           lengths
           CI
           ,
           DI
           ,
           FI
           ,
           BI
           ,
           and
           content
           your self
           with
           three
           only
           ,
           as
           being
           sufficient
           for
           the
           Theorie
           :
           But
           the
           fourth
           will
           serve
           you
           for
           a
           proof
           ,
           to
           see
           whether
           or
           no
           you
           have
           been
           very
           exact
           in
           working
           ,
           and
           will
           justifie
           the
           three
           others
           .
        
      
       
       
         
           
             Figure
             12
             ,
          
           To
           all
           sorts
           of
           People
           .
        
         
           THe
           figure
           above
           shews
           you
           how
           that
           which
           you
           have
           done
           with
           three
           sticks
           ,
           may
           be
           done
           either
           with
           many
           Compasses
           ,
           with
           the
           help
           of
           some
           body
           ,
           or
           else
           with
           other
           kinds
           of
           branches
           tyed
           or
           fastened
           one
           with
           another
           .
        
         
           The
           same
           figure
           above
           ,
           as
           also
           the
           figures
           below
           ,
           shew
           how
           every
           one
           of
           those
           branches
           may
           be
           of
           two
           several
           pieces
           ,
           which
           go
           in
           by
           couples
           into
           one
           hoop
           or
           ring
           ,
           and
           slide
           along
           one
           by
           another
           ,
           and
           are
           made
           fast
           with
           a
           screw
           to
           the
           measure
           where
           you
           will
           have
           them
           to
           stand
           upon
           ,
           and
           these
           pieces
           may
           be
           made
           of
           tinn'd
           yron
           ,
           or
           of
           yron
           ,
           if
           you
           are
           afraid
           that
           their
           points
           will
           grow
           dull
           by
           often
           using
           them
           .
        
         
           Or
           otherwise
           they
           shew
           you
           that
           insteed
           of
           one
           stick
           ,
           you
           may
           have
           two
           ,
           both
           sharp
           at
           one
           end
           ,
           which
           you
           shall
           fasten
           and
           bind
           together
           at
           the
           other
           end
           ,
           of
           what
           length
           or
           measure
           you
           please
           .
        
         
           The
           same
           figures
           do
           shew
           you
           also
           ,
           that
           two
           divers
           branches
           ,
           viz.
           CI
           ,
           and
           FI
           ,
           may
           be
           fastened
           together
           in
           the
           place
           where
           you
           will
           have
           them
           to
           stand
           together
           ,
           with
           a
           presse
           and
           a
           screw
           to
           fasten
           them
           with
           .
        
         
           The
           higher
           figure
           shews
           you
           besides
           ,
           that
           you
           may
           ●●●●en
           or
           bind
           with
           strings
           or
           threds
           ,
           the
           Axeltree
           rod
           with
           the
           point
           B
           ,
           of
           the
           pin
           AB
           ,
           and
           the
           two
           branches
           CI
           ,
           FI
           ,
           with
           the
           Axeltree
           rod
           ,
           to
           make
           them
           stand
           fast
           of
           themselves
           in
           their
           place
           .
        
         
           When
           you
           have
           found
           thus
           the
           placing
           of
           the
           Axeltree
           rod
           ,
           it
           is
           in
           your
           choice
           ,
           either
           to
           seal
           it
           and
           fasten
           it
           in
           that
           place
           ,
           or
           to
           place
           another
           insteed
           of
           it
           ,
           that
           may
           go
           the
           same
           way
           ,
           and
           that
           may
           be
           every
           way
           equally
           distant
           from
           it
           ;
           But
           that
           you
           may
           be
           the
           more
           exact
           ,
           it
           will
           be
           as
           good
           to
           seal
           or
           fasten
           that
           in
           the
           place
           ,
           where
           the
           practice
           of
           the
           Draught
           hath
           caused
           it
           to
           meet
           ,
           than
           to
           place
           another
           ,
           unlesse
           there
           was
           some
           occasion
           or
           necessity
           for
           it
           .
        
         
           
             12
          
        
      
       
       
         
           
             Figure
             3
             ,
          
           To
           those
           that
           have
           understood
           what
           hath
           been
           said
           before
           .
        
         
           HAving
           understood
           what
           I
           have
           said
           before
           ,
           concerning
           those
           many
           wayes
           of
           finding
           the
           position
           of
           the
           axeltree
           of
           the
           Dyal
           ,
           you
           may
           compose
           others
           besides
           ,
           making
           use
           partly
           of
           that
           of
           one
           figure
           ,
           and
           partly
           of
           that
           of
           an
           other
           .
        
         
           
             For
             example
             ,
             here
             is
             one
             way
             composed
             of
             two
             of
             those
             that
             are
             afore
             .
          
        
         
           OVt
           of
           the
           third
           or
           fifth
           figure
           ,
           you
           shall
           take
           in
           the
           Sun-beams
           or
           sticks
           BC
           ,
           BD
           ,
           BF
           ,
           three
           spaces
           equal
           each
           unto
           the
           other
           ;
           And
           out
           of
           the
           5
           and
           6
           figures
           ,
           you
           shall
           make
           a
           triangle
           of
           three
           lines
           equal
           to
           the
           three
           spaces
           HE
           ,
           DE
           ,
           DH
           of
           the
           third
           figure
           ,
           and
           you
           shall
           find
           the
           center
           O
           of
           the
           circle
           ,
           circumscribed
           about
           this
           triangle
           .
        
         
           You
           shall
           find
           also
           within
           the
           ground
           plot
           of
           the
           points
           HDE
           ,
           the
           points
           like
           to
           A
           &
           O
           of
           the
           6
           figure
           or
           cut
           ,
           which
           in
           this
           case
           come
           to
           be
           united
           together
           in
           one
           and
           the
           same
           point
           O.
           That
           is
           to
           say
           ,
           having
           found
           one
           of
           these
           two
           points
           A
           &
           O
           ,
           you
           have
           found
           also
           the
           other
           ,
           because
           they
           are
           united
           or
           gathered
           together
           into
           one
           .
        
         
           So
           you
           have
           in
           the
           second
           figure
           of
           the
           third
           cut
           ,
           the
           spaces
           DO
           ,
           and
           DI
           ,
           for
           two
           sides
           of
           a
           triangle
           with
           straight
           angles
           or
           corners
           ODI
           ,
           whose
           side
           DI
           ,
           holds
           up
           the
           straight
           angle
           ,
           and
           the
           sides
           DO
           ,
           and
           DI
           ,
           do
           contain
           or
           comprehend
           it
           .
        
         
           Make
           this
           triangle
           ODI
           ,
           with
           three
           sticks
           ,
           or
           with
           any
           other
           thing
           that
           may
           be
           strong
           and
           small
           as
           you
           will
           ,
           so
           that
           you
           may
           at
           your
           need
           lengthen
           the
           side
           IO
           ,
           from
           the
           right
           angle
           O.
           
        
         
           
             3
          
        
         
         
           Set
           the
           point
           D
           ,
           of
           this
           triangle
           DIO
           ,
           to
           the
           point
           of
           shadow
           D
           ,
           and
           holding
           this
           point
           of
           triangle
           to
           this
           point
           of
           shadow
           D
           ,
           make
           the
           side
           IO
           ,
           of
           this
           triangle
           (
           drawn
           at
           length
           if
           need
           be
           )
           come
           and
           touch
           the
           point
           B
           ,
           of
           the
           pin
           AB
           for
           if
           you
           have
           been
           very
           exact
           in
           working
           ,
           it
           must
           touch
           it
           .
        
         
           Take
           a
           stick
           HI
           ,
           of
           the
           length
           of
           DI
           ,
           set
           one
           of
           the
           ends
           to
           the
           point
           H
           ,
           and
           bring
           the
           other
           end
           to
           the
           point
           I
           ,
           of
           the
           triangle
           ODI
           ,
           without
           the
           side
           IO
           ,
           leave
           the
           end
           B
           of
           the
           pin
           AB
           ,
           for
           it
           must
           be
           so
           ,
           if
           you
           have
           wrought
           exactly
           as
           you
           ought
           .
        
         
           You
           may
           have
           also
           an
           other
           stick
           EI
           ,
           of
           the
           length
           DI
           ,
           and
           set
           one
           end
           to
           the
           point
           E
           ,
           and
           bring
           the
           other
           likewise
           to
           the
           point
           I
           ,
           of
           the
           triangle
           DIO
           ,
           without
           the
           side
           OI
           ,
           leave
           the
           end
           B
           of
           the
           pin
           AB
           .
        
         
           That
           being
           done
           the
           rod
           BI
           ,
           comes
           to
           be
           the
           axeltree
           of
           the
           Dyal
           ,
           and
           placed
           as
           it
           ought
           to
           be
           ,
           and
           so
           of
           all
           the
           other
           wayes
           that
           you
           find
           besides
           .
        
         
           You
           may
           ,
           if
           you
           will
           make
           use
           of
           a
           triangle
           rectangular
           EOI.
           and
           of
           the
           stick
           HI
           ,
           content
           your self
           only
           with
           the
           three
           equal
           lengths
           EI
           ,
           DI
           ,
           HI
           ,
           to
           find
           out
           the
           point
           thereby
           ,
           that
           you
           may
           draw
           from
           thence
           a
           line
           to
           the
           point
           B
           ,
           without
           making
           use
           of
           any
           thing
           else
           to
           know
           if
           you
           have
           done
           exactly
           or
           no
           ,
           you
           can
           not
           be
           sure
           whether
           you
           have
           done
           well
           or
           ill
           .
        
         
           But
           when
           you
           have
           together
           with
           that
           ,
           either
           a
           fourth
           length
           BI
           ▪
           or
           the
           straight
           angle
           DOI
           ,
           that
           will
           serve
           you
           to
           try
           whether
           or
           no
           you
           have
           been
           exact
           in
           your
           operations
           ,
           for
           as
           concerning
           an
           effectual
           execution
           ,
           unlesse
           you
           have
           from
           time
           to
           time
           such
           a
           kind
           of
           proof
           ,
           to
           shew
           whether
           you
           have
           wrought
           exactly
           as
           you
           ought
           ,
           you
           cannot
           assure
           your self
           that
           your
           work
           is
           as
           well
           as
           it
           can
           be
           done
           .
        
         
           One
           thing
           I
           must
           tell
           you
           ,
           that
           in
           some
           certain
           occasions
           according
           to
           the
           times
           and
           the
           placing
           ,
           or
           according
           as
           the
           superficies
           of
           your
           Dyal
           is
           ,
           the
           shadow
           of
           the
           pin
           comes
           to
           be
           of
           such
           a
           length
           ,
           and
           the
           extremity
           or
           end
           thereof
           so
           weakned
           ,
           and
           so
           diminished
           in
           strength
           ,
           and
           so
           confuse
           in
           the
           superficies
           of
           the
           Dyal
           ,
           that
           it
           is
           very
           hard
           to
           find
           out
        
         
      
       
       
         
           
             Figure
             13
             ,
          
           To
           all
           sorts
           of
           People
           .
        
         
           
             I
             come
             now
             to
             the
             next
             and
             second
             thing
             that
             you
             are
             to
             do
             ,
             which
             is
             to
             trace
             out
             the
             lines
             of
             the
             hours
             .
          
        
         
           IN
           this
           example
           I
           suppose
           that
           the
           Axeltree
           rod
           doth
           not
           meet
           the
           superficies
           of
           the
           Dyal
           ,
           about
           the
           place
           that
           you
           work
           in
           ;
           and
           therefore
           I
           represent
           it
           suspended
           in
           the
           air
           ,
           with
           two
           or
           three
           supporters
           as
           you
           see
           ,
           I
           suppose
           also
           that
           the
           superficies
           of
           the
           Dyal
           is
           not
           smooth
           ,
           but
           rough
           and
           uneven
           as
           I
           have
           said
           .
        
         
           When
           you
           have
           placed
           the
           Rod
           BI
           ,
           which
           is
           the
           Axeltree
           of
           the
           Dyal
           ,
           as
           you
           see
           both
           in
           the
           higher
           and
           lower
           figure
           ,
           you
           have
           made
           an
           end
           then
           of
           the
           first
           of
           those
           two
           things
           that
           you
           were
           to
           do
           ,
           for
           the
           making
           of
           your
           Dyal
           :
           Now
           there
           remains
           but
           the
           second
           to
           be
           done
           ,
           which
           is
           the
           finding
           and
           the
           tracing
           out
           of
           the
           lines
           of
           the
           hours
           in
           the
           Dyal
           ;
           and
           for
           that
           purpose
           .
        
         
           Consider
           in
           your
           higher
           figure
           ,
           that
           the
           superficies
           and
           the
           axeltree
           of
           your
           Dyal
           are
           two
           divers
           things
           ,
           and
           differing
           one
           from
           an
           other
           ,
           and
           there
           is
           no
           such
           communication
           from
           the
           one
           to
           the
           other
           ,
           as
           that
           with
           them
           alone
           you
           may
           find
           out
           directly
           the
           place
           of
           the
           lines
           of
           the
           hours
           ,
           without
           making
           use
           of
           a
           third
           thing
           that
           may
           be
           a
           means
           betwixt
           those
           two
           .
        
         
           The
           meanest
           and
           the
           least
           thing
           that
           you
           can
           have
           to
           be
           a
           means
           betwixt
           the
           superficies
           and
           the
           axeltree
           of
           the
           Dyal
           ,
           is
           a
           Ruler
           .
        
         
           
             13
          
        
         
           To
           the
           end
           that
           this
           middle
           rule
           may
           serve
           you
           alike
           in
           all
           occasions
           ,
           it
           must
           have
           all
           the
           conditions
           that
           you
           see
           represented
           in
           the
           figure
           below
           .
           First
           it
           must
           be
           as
           long
           as
           the
           place
           will
           give
           you
           leave
           ,
           and
           it
           must
           crosse
           over
           if
           need
           be
           the
           whole
           superficies
           of
           the
           Dyal
           ,
           and
           reach
           over
           on
           both
           sides
           if
           it
           be
           possible
           .
        
         
           Secondly
           it
           must
           be
           in
           the
           air
           ,
           and
           suspended
           between
           the
           superficies
           and
           the
           axeltree
           of
           the
           Dyal
           .
        
         
           Thirdly
           it
           must
           be
           placed
           as
           far
           from
           the
           axeltree
           rod
           ,
           as
           possible
           may
           be
           .
        
         
           Fourthly
           it
           must
           be
           placed
           like
           a
           crosse
           ,
           in
           regard
           of
           the
           same
           axeltree
           rod
           .
        
      
       
       
         
           
             Figure
             14
             ,
          
           To
           all
           sorts
           of
           People
           .
        
         
           TO
           place
           this
           middle
           rule
           well
           ,
           and
           as
           it
           ought
           to
           be
           betwixt
           the
           superficies
           and
           the
           axeltree
           of
           the
           Dyal
           .
        
         
           Chuse
           along
           the
           axeltree
           rod
           BI
           ,
           of
           the
           higher
           figure
           ,
           some
           fit
           or
           convenient
           place
           ,
           as
           in
           the
           point
           O
           ,
           and
           make
           a
           round
           and
           fixed
           stay
           in
           that
           place
           ,
           by
           winding
           ,
           or
           tying
           some
           strong
           thing
           about
           this
           axeltree
           rod
           ,
           as
           the
           figure
           doth
           shew
           .
        
         
           Tye
           a
           string
           to
           the
           axeltree
           rod
           BI
           ,
           by
           the
           means
           of
           a
           ring
           that
           may
           be
           so
           big
           ,
           that
           you
           may
           turn
           the
           string
           with
           it
           about
           the
           axeltree
           rod
           easily
           ,
           as
           the
           lower
           figure
           shews
           you
           ;
           Then
           with
           the
           corner
           of
           a
           squire
           ED
           ,
           in
           the
           lower
           figure
           ,
           thrust
           on
           the
           ring
           where
           the
           string
           is
           ,
           and
           put
           it
           close
           to
           this
           stay
           O
           ,
           and
           holding
           the
           string
           fast
           between
           the
           stay
           O
           ,
           and
           the
           squire
           ED
           ,
           set
           the
           back
           of
           one
           of
           the
           sides
           OE
           of
           this
           squires
           length
           ,
           to
           the
           axeltree
           rod
           BI
           ,
           and
           by
           this
           means
           ,
           the
           other
           side
           DO
           ,
           of
           this
           squire
           ,
           will
           shoot
           out
           into
           the
           air
           like
           a
           wing
           from
           the
           axeltree
           rod
           BI
           ,
           then
           stretch
           out
           the
           string
           in
           a
           straight
           line
           from
           the
           stay
           O
           of
           the
           axeltree
           ,
           along
           the
           back
           of
           the
           other
           side
           OD
           of
           the
           squire
           .
           And
           holding
           still
           in
           this
           manner
           the
           ring
           close
           to
           the
           stay
           of
           the
           axeltree
           ,
           by
           means
           of
           the
           squire
           ,
           and
           the
           back
           of
           one
           of
           the
           sides
           joyned
           at
           length
           to
           the
           axeltree
           rod
           ,
           and
           the
           other
           side
           of
           the
           squire
           like
           a
           wing
           ,
           and
           the
           string
           stretcht
           out
           in
           a
           straight
           line
           along
           this
           wing
           ,
           turn
           both
           the
           squire
           and
           the
           string
           altogether
           still
           in
           this
           same
           manner
           about
           the
           axeltree
           rod
           ,
           as
           the
           lower
           figure
           doth
           shew
           .
        
         
           
             14
          
        
         
           When
           you
           have
           found
           out
           those
           two
           places
           that
           are
           farthest
           one
           from
           another
           ,
           in
           which
           this
           string
           turning
           in
           this
           manner
           with
           the
           squire
           along
           the
           side
           like
           a
           wing
           ,
           may
           go
           and
           meet
           the
           superficies
           of
           the
           Dyal
           ,
           as
           here
           the
           places
           G
           and
           H.
           
        
         
           Make
           with
           mastick
           ,
           or
           plaster
           ,
           or
           cement
           ,
           or
           such
           like
           stuff
           ,
           a
           little
           knob
           flat
           at
           the
           top
           in
           each
           of
           these
           places
           ,
           as
           for
           example
           ,
           one
           in
           G
           ,
           and
           another
           as
           in
           H
           ,
           which
           two
           knobs
           may
           shoot
           out
           of
           the
           superficies
           of
           the
           Dyal
           ,
           in
           such
           sort
           ,
           that
           you
           may
           lay
           a
           Ruler
           on
           the
           top
           of
           them
           ,
           going
           from
           one
           of
           the
           knobs
           to
           the
           other
           ,
           as
           you
           see
           here
           in
           the
           lower
           figure
           .
        
      
       
       
         
           
             
               15
            
          
        
         
         
           
             Figure
             15
             ,
          
           To
           all
           sorts
           of
           People
           .
        
         
           VVHen
           you
           have
           thus
           made
           those
           two
           knobbs
           G
           ,
           H
           ,
           in
           the
           lower
           figure
           ,
           take
           the
           squire
           again
           and
           the
           string
           ,
           and
           set
           them
           again
           close
           to
           the
           stay
           O
           ,
           of
           the
           axeltree
           rod
           ,
           as
           you
           know
           they
           were
           .
        
         
           And
           make
           them
           go
           about
           again
           as
           before
           ,
           both
           together
           about
           the
           axeltree
           BI
           ,
           and
           while
           you
           are
           turning
           about
           ,
           the
           string
           will
           fall
           right
           over
           against
           the
           two
           knobs
           ,
           shorten
           or
           lengthen
           it
           so
           ,
           that
           it
           may
           go
           and
           touch
           a
           point
           ,
           at
           the
           top
           of
           each
           one
           of
           the
           two
           knobs
           ,
           one
           after
           another
           ▪
           viz.
           a
           point
           as
           P
           ,
           at
           the
           top
           of
           the
           knob
           G
           ,
           and
           a
           point
           as
           Q
           ,
           at
           the
           top
           of
           the
           knob
           H
           ,
           and
           mark
           these
           two
           points
           Q
           and
           P
           ,
           upon
           these
           two
           knobs
           .
        
         
           When
           you
           have
           mark'd
           two
           points
           in
           this
           manner
           ,
           set
           a
           Ruler
           in
           the
           lower
           figure
           upon
           these
           two
           knobs
           ,
           and
           place
           it
           so
           ,
           that
           it
           may
           passe
           from
           one
           to
           the
           other
           ,
           by
           those
           two
           points
           Q
           and
           P
           ,
           and
           make
           the
           Ruler
           fast
           in
           this
           place
           with
           cement
           or
           plaster
           ,
           or
           the
           like
           ,
           in
           such
           wise
           that
           it
           may
           not
           stir
           any
           way
           .
        
         
           And
           this
           rule
           so
           placed
           ,
           is
           the
           third
           and
           middle
           piece
           between
           the
           superficies
           ,
           and
           the
           axeltree
           of
           the
           Dyal
           ,
           by
           means
           whereof
           you
           shall
           cause
           ,
           as
           I
           shall
           say
           hereafter
           ,
           this
           superficies
           and
           this
           axeltree
           to
           have
           what
           communication
           soever
           you
           please
           one
           with
           another
           .
        
         
           After
           you
           have
           placed
           this
           middle
           rule
           in
           this
           manner
           ,
           between
           the
           superficies
           and
           the
           axeltree
           of
           the
           Dyal
           .
        
         
           Consider
           that
           in
           
             France
          
           now
           they
           reckon
           34
           hours
           ,
           for
           one
           day
           and
           a
           night
           ,
           and
           that
           these
           24
           hours
           ,
           are
           divided
           in
           twice
           twelve
           hours
           ,
           and
           that
           every
           one
           of
           these
           12
           hours
           is
           subdivided
           in
           twice
           6
           hours
           .
        
         
           So
           that
           in
           the
           24
           hours
           of
           one
           day
           and
           one
           night
           ,
           as
           they
           are
           now
           reckoned
           in
           
             France
             ,
          
           there
           are
           two
           hours
           that
           are
           each
           of
           them
           of
           12
           ,
           that
           is
           to
           say
           ,
           one
           hour
           of
           12
           in
           the
           middest
           of
           the
           night
           ,
           and
           another
           hour
           of
           twelve
           in
           the
           
           middest
           of
           the
           day
           ,
           these
           two
           hours
           of
           12
           ,
           are
           called
           midnight
           and
           midday
           ,
           then
           there
           are
           two
           other
           hours
           ,
           each
           of
           them
           of
           6.
           viz.
           an
           hour
           of
           6
           in
           the
           evening
           ,
           and
           another
           of
           6
           in
           the
           morning
           .
        
         
           Where
           you
           must
           note
           ,
           that
           both
           the
           two
           hours
           of
           12
           ,
           and
           the
           two
           hours
           of
           6
           ,
           come
           alwayes
           to
           meet
           together
           in
           one
           and
           the
           same
           line
           ,
           though
           it
           may
           be
           lengthened
           if
           need
           be
           ,
           viz.
           the
           two
           of
           twelve
           in
           one
           line
           ,
           and
           the
           two
           of
           6
           in
           an
           other
           .
        
         
           And
           you
           shall
           know
           ,
           that
           it
           is
           an
           infallible
           thing
           ,
           that
           within
           the
           Compasse
           of
           the
           superficies
           of
           the
           Dyal
           where
           you
           work
           in
           ,
           if
           you
           have
           placed
           the
           axeltree
           pretty
           near
           it
           ,
           there
           must
           needs
           be
           either
           one
           of
           the
           hours
           of
           12
           ,
           or
           one
           of
           the
           hours
           of
           6
           ,
           and
           sometimes
           they
           meet
           there
           both
           at
           once
           ,
           that
           is
           to
           say
           ,
           one
           of
           the
           hours
           of
           12
           ,
           and
           one
           of
           the
           hours
           of
           6.
           
        
         
           There
           be
           many
           situations
           of
           superficies
           of
           Dyals
           ,
           in
           which
           ,
           within
           the
           Compasse
           ,
           where
           one
           may
           trace
           in
           the
           hours
           ,
           there
           is
           only
           the
           line
           of
           the
           hours
           of
           12
           ,
           and
           there
           is
           found
           not
           any
           one
           of
           the
           hours
           of
           6
           ,
           and
           others
           in
           which
           there
           is
           found
           only
           the
           line
           of
           the
           hours
           of
           6
           ,
           and
           not
           any
           one
           of
           the
           hours
           of
           12.
           
           But
           there
           is
           no
           Dyal
           in
           which
           ,
           within
           the
           Compasse
           where
           it
           is
           traced
           in
           ,
           but
           the
           hours
           of
           12
           ,
           and
           any
           one
           of
           the
           hours
           of
           6
           are
           found
           in
           it
           ,
           I
           mean
           that
           one
           may
           find
           in
           it
           ,
           either
           one
           or
           other
           of
           the
           hours
           of
           12
           ,
           and
           of
           the
           hours
           of
           6
           ,
           by
           setting
           the
           axeltree
           near
           enough
           to
           the
           superficies
           of
           the
           Dyal
           .
        
         
           And
           now
           since
           you
           are
           sure
           ,
           that
           there
           is
           without
           doubt
           in
           your
           Dyal
           ,
           either
           one
           of
           the
           hours
           of
           12
           ,
           or
           one
           of
           6.
           
        
         
           You
           shall
           begin
           to
           seek
           in
           it
           ,
           first
           the
           place
           of
           that
           sort
           of
           hours
           of
           twelve
           or
           of
           six
           ,
           that
           may
           be
           in
           it
           .
        
         
           And
           when
           you
           have
           found
           the
           point
           ,
           either
           of
           one
           of
           the
           hours
           of
           six
           ,
           or
           of
           one
           of
           twelve
           ;
           You
           shall
           find
           afterwards
           the
           points
           of
           the
           other
           hours
           ,
           that
           meet
           with
           it
           in
           the
           Dyal
           it
           is
           in
           your
           choice
           to
           begin
           to
           seek
           the
           point
           ,
           of
           which
           of
           the
           two
           sorts
           of
           hours
           of
           6
           ,
           or
           of
           12
           ,
           you
           will
           ,
           and
           I
           will
           show
           you
           two
           wayes
           of
           seeking
           them
           out
           ,
           both
           one
           after
           another
           ,
           that
           when
           they
           come
           to
           be
           both
           in
           the
           Dyal
           ,
           you
           may
           find
           them
           out
           both
           there
           if
           you
           will
           ,
           for
           
           they
           serve
           for
           a
           proof
           one
           unto
           another
           ,
           if
           you
           have
           been
           exact
           in
           your
           operation
           .
        
         
           That
           you
           may
           finish
           your
           Dyal
           as
           you
           ought
           ,
           seek
           in
           the
           middle
           rule
           the
           point
           which
           is
           there
           to
           be
           found
           ,
           either
           of
           the
           hours
           of
           twelve
           ,
           or
           of
           the
           hours
           of
           six
           ,
           for
           it
           is
           set
           there
           on
           purpose
           to
           serve
           for
           that
           chiefly
           .
        
         
           For
           example
           ,
           seek
           out
           first
           in
           it
           the
           point
           of
           one
           of
           the
           hours
           of
           six
           ,
           as
           I
           am
           going
           to
           shew
           ,
           then
           I
           will
           shew
           you
           the
           way
           to
           find
           out
           the
           point
           of
           one
           of
           the
           hours
           of
           12
           ,
           and
           afterwards
           I
           will
           shew
           you
           the
           way
           to
           find
           out
           the
           points
           of
           all
           the
           other
           hours
           of
           the
           Day
           .
        
      
       
       
         
           
             
               16
            
          
        
         
         
           
             Figure
             16
             ,
          
           To
           all
           sorts
           of
           People
           .
        
         
           TO
           seek
           out
           in
           the
           middle
           rule
           ,
           whether
           the
           point
           of
           one
           of
           the
           hours
           of
           6
           be
           there
           .
        
         
           Take
           the
           string
           that
           is
           made
           fast
           to
           the
           axeltree
           ,
           set
           it
           very
           close
           again
           to
           the
           point
           or
           stay
           O
           ,
           as
           it
           was
           when
           you
           made
           it
           turn
           about
           the
           axeltree
           ,
           then
           stretch
           it
           out
           in
           a
           straight
           line
           from
           the
           point
           O
           of
           the
           stay
           of
           the
           axeltree
           ,
           to
           the
           middle
           rule
           PQ
           ,
           and
           holding
           still
           this
           string
           so
           stretcht
           out
           ,
           make
           it
           turn
           about
           the
           point
           O
           ,
           carrying
           it
           from
           one
           to
           the
           other
           of
           the
           points
           Q
           and
           P
           ▪
           along
           the
           rule
           QP
           ,
           and
           making
           it
           longer
           or
           shorter
           if
           need
           be
           ,
           and
           set
           a
           Carpenters
           level
           or
           triangle
           over
           it
           ,
           to
           see
           ,
           while
           it
           turns
           thus
           ,
           stretch't
           out
           in
           a
           straight
           line
           about
           this
           point
           O
           ,
           keeping
           along
           the
           middle
           rule
           ,
           whether
           there
           is
           any
           place
           ,
           wherein
           it
           comes
           to
           be
           found
           levell
           ,
           as
           for
           example
           ,
           you
           see
           in
           the
           higher
           figure
           (
           over
           the
           leaf
           )
           and
           when
           you
           find
           it
           to
           be
           level
           ,
           you
           must
           make
           it
           fast
           there
           .
        
         
           And
           that
           your
           level
           may
           be
           more
           fast
           ,
           you
           may
           set
           it
           by
           the
           middle
           upon
           the
           axeltree
           rod
           close
           to
           the
           stay
           ,
           or
           you
           may
           set
           close
           to
           the
           stay
           a
           ruler
           notch't
           at
           one
           end
           ,
           as
           you
           see
           the
           ruler
           N
           ,
           is
           notcht
           ,
           then
           guide
           it
           with
           the
           string
           ,
           And
           it
           will
           serve
           to
           fasten
           the
           level
           upon
           it
           .
        
         
           Or
           to
           say
           it
           again
           otherwise
           ,
           you
           must
           ,
           as
           you
           know
           ,
           cause
           to
           go
           about
           the
           axeltree
           rod
           the
           squire
           and
           the
           string
           stretcht
           out
           ,
           as
           I
           have
           said
           ,
           in
           a
           straight
           line
           ,
           and
           made
           longer
           if
           need
           be
           ,
           this
           string
           will
           go
           and
           passe
           all
           along
           the
           ruler
           PQ
           .
        
         
           And
           if
           it
           happens
           that
           the
           string
           ,
           so
           guided
           or
           carryed
           along
           the
           middle
           rule
           PQ
           ,
           come
           to
           be
           found
           level
           ,
           as
           the
           higher
           figure
           shews
           ,
           mark
           in
           this
           middle
           rule
           the
           point
           6
           ,
           where
           this
           string
           toucheth
           or
           reacheth
           unto
           when
           it
           is
           so
           level
           ,
           and
           remember
           that
           this
           point
           6
           ,
           is
           the
           point
           of
           one
           of
           the
           hours
           of
           6
           ,
           either
           of
           the
           evening
           ,
           or
           of
           the
           morning
           .
           
           This
           is
           that
           which
           concerns
           one
           point
           of
           one
           of
           the
           hours
           of
           6
           ,
           that
           if
           the
           string
           in
           turning
           thus
           ,
           comes
           to
           passe
           from
           one
           end
           of
           the
           middle
           ●●…e
           to
           the
           other
           ,
           without
           falling
           to
           be
           level
           it
           is
           a
           sign
           ,
           that
           not
           one
           of
           the
           hours
           of
           6
           ,
           comes
           to
           be
           found
           in
           this
           Dyal
           ,
           to
           frame
           it
           from
           the
           point
           that
           you
           have
           taken
           for
           a
           rest
           or
           stay
           .
        
         
           Now
           that
           you
           may
           seek
           out
           the
           point
           of
           the
           hours
           of
           12
           ,
           in
           the
           lower
           figure
           .
        
         
           Fasten
           the
           center
           of
           a
           hanging
           plummet
           ,
           with
           a
           string
           S
           ,
           to
           the
           middle
           of
           the
           body
           of
           the
           axeltree
           rod
           ,
           above
           it
           or
           under
           ,
           as
           the
           lower
           figure
           shews
           ,
           it
           matters
           not
           ,
           and
           as
           the
           occasion
           will
           permit
           or
           require
           ,
           and
           set
           this
           plummet
           so
           ,
           that
           it
           may
           come
           and
           fall
           as
           near
           the
           middle
           rule
           as
           you
           can
           .
        
         
           Then
           tye
           to
           the
           axeltree
           rod
           ,
           as
           far
           as
           you
           can
           from
           the
           superficies
           of
           the
           Dyal
           ,
           another
           string
           I
           with
           a
           loose
           knot
           ,
           and
           when
           the
           plummet
           of
           the
           first
           string
           S
           ,
           comes
           to
           be
           at
           rest
           ,
           make
           it
           so
           fast
           that
           it
           may
           not
           stir
           ,
           then
           stretch
           out
           this
           second
           string
           I
           in
           a
           straight
           line
           ,
           in
           such
           sort
           ,
           that
           comming
           from
           the
           axeltree
           rod
           ,
           it
           may
           go
           and
           touch
           the
           string
           of
           the
           hanging
           plummet
           S
           ,
           without
           breaking
           (
           or
           stirring
           )
           the
           string
           nor
           the
           lead
           ,
           and
           so
           holding
           this
           second
           string
           I
           ,
           stretcht
           out
           close
           to
           the
           string
           with
           the
           plummet
           on
           S
           ,
           see
           whether
           this
           second
           string
           stretcht
           out
           in
           this
           manner
           can
           ,
           being
           made
           shorter
           or
           longer
           ,
           if
           need
           be
           ,
           go
           and
           meet
           the
           middle
           rule
           ,
           in
           a
           point
           ,
           or
           not
           .
        
         
           And
           when
           this
           second
           string
           so
           stretch'd
           out
           comes
           to
           meet
           the
           middle
           rule
           ,
           in
           one
           point
           ,
           as
           12
           ,
           mark
           in
           the
           middle
           rule
           this
           point
           12
           ,
           in
           which
           this
           string
           so
           stretcht
           out
           doth
           meet
           with
           it
           ,
           and
           note
           that
           that
           point
           12
           ,
           is
           the
           point
           of
           one
           of
           the
           hours
           of
           12.
           
        
         
           When
           you
           have
           found
           out
           and
           markt
           in
           the
           middle
           rule
           the
           point
           of
           one
           or
           other
           of
           the
           hours
           ,
           either
           of
           6
           ,
           as
           you
           see
           in
           the
           figure
           above
           ,
           or
           of
           12
           ,
           as
           you
           see
           in
           the
           figure
           below
           ,
           if
           you
           have
           them
           both
           ,
           they
           shall
           serve
           for
           a
           proof
           one
           to
           another
           ,
           if
           you
           have
           but
           one
           ,
           you
           may
           make
           use
           of
           that
           alone
           .
        
         
         
           Let
           us
           suppose
           first
           ,
           that
           it
           is
           the
           point
           of
           one
           of
           the
           hours
           of
           6
           ,
           as
           the
           point
           ,
           6
           ▪
           〈◊〉
           you
           shall
           go
           on
           in
           finding
           out
           the
           points
           of
           the
           other
           hours
           ,
           which
           may
           be
           found
           in
           your
           Dyal
           ,
           in
           this
           manner
           following
           .
        
      
       
       
         
           
             Figure
             17
             ,
          
           To
           all
           sorts
           of
           People
           .
        
         
           MArk
           at
           your
           discretion
           in
           the
           rule
           PQ
           .
           two
           several
           points
           MN
           ,
           and
           consider
           the
           point
           in
           the
           middle
           of
           the
           body
           of
           the
           axeltree
           ,
           close
           by
           the
           stay
           O
           ,
           that
           is
           the
           Point
           about
           which
           you
           have
           turned
           the
           string
           with
           the
           corner
           of
           the
           squire
           .
           You
           see
           there
           three
           several
           points
           unmoveable
           ,
           and
           fixed
           ,
           viz.
           the
           point
           M
           ,
           and
           the
           point
           N
           ,
           in
           the
           middle
           rule
           ,
           and
           the
           point
           O
           ,
           in
           the
           middle
           of
           the
           body
           of
           the
           axeltree
           rod
           ,
           close
           to
           the
           stay
           .
           And
           so
           having
           those
           three
           points
           fixed
           ,
           M
           ,
           N
           ,
           O
           ,
           you
           have
           by
           this
           means
           the
           three
           several
           distances
           ,
           viz.
           the
           measures
           of
           the
           distances
           that
           are
           from
           one
           of
           these
           three
           points
           ,
           to
           the
           two
           others
           ,
           viz.
           the
           space
           or
           distance
           from
           the
           point
           M
           ,
           to
           the
           point
           N
           ,
           the
           distance
           from
           the
           point
           M
           to
           the
           point
           O
           and
           the
           space
           from
           the
           point
           N
           ,
           to
           the
           point
           O.
           
        
         
           Remember
           two
           things
           ,
           one
           is
           ,
           that
           the
           point
           O
           ,
           is
           in
           the
           middle
           of
           the
           body
           ,
           that
           is
           to
           say
           of
           the
           bignesse
           ,
           and
           not
           in
           the
           out
           side
           of
           the
           axeltree
           rod
           .
           The
           other
           is
           ,
           that
           these
           two
           points
           MN
           ,
           that
           you
           have
           mark'd
           at
           discretion
           in
           the
           middle
           rule
           ,
           are
           not
           for
           all
           that
           certainly
           the
           points
           of
           hour
           ,
           and
           that
           they
           are
           to
           serve
           you
           to
           find
           out
           the
           points
           of
           hour
           ,
           and
           perhaps
           they
           may
           chance
           to
           be
           some
           of
           them
           ;
           and
           may
           be
           not
           ,
           and
           perhaps
           you
           must
           blot
           them
           out
           after
           you
           have
           found
           out
           the
           points
           of
           hour
           .
        
         
           This
           being
           done
           so
           ,
           take
           with
           your
           Compasse
           upon
           the
           middle
           rule
           ,
           the
           distance
           from
           the
           point
           M
           ,
           to
           the
           point
           N
           ,
           and
           with
           this
           space
           go
           to
           some
           place
           that
           is
           flat
           or
           smooth
           ,
           and
           set
           both
           the
           feet
           of
           your
           Compasse
           therein
           at
           once
           ,
           as
           in
           the
           figure
           below
           in
           the
           points
           M
           and
           N
           ,
           and
           by
           these
           two
           points
           ,
           draw
           a
           straight
           line
           MN
           ,
           as
           long
           at
           either
           end
           as
           the
           rule
           PQ
           .
        
         
           Then
           go
           back
           to
           the
           Dyal
           above
           ,
           take
           with
           the
           Compasse
           the
           distance
           which
           is
           from
           the
           posnt
           M
           ,
           to
           the
           middle
           
           of
           the
           bigness
           of
           the
           axeltree
           close
           by
           the
           stay
           O
           ,
           or
           else
           otherwise
           ,
           take
           the
           distance
           which
           is
           from
           the
           point
           M
           ,
           to
           the
           axeltree
           towards
           the
           stay
           O
           ,
           and
           adde
           unto
           it
           half
           of
           the
           bigness
           of
           the
           Axeltree
           ;
           and
           with
           this
           space
           MO
           ,
           come
           back
           to
           the
           figure
           below
           ,
           set
           one
           of
           the
           feet
           of
           the
           Compasse
           to
           the
           point
           M
           ,
           and
           turning
           this
           foot
           about
           upon
           this
           point
           M
           ,
           trace
           with
           the
           other
           foot
           a
           line
           crooked
           like
           a
           bow
           O
           ,
           go
           back
           to
           the
           figure
           above
           ,
           take
           again
           with
           your
           Compass
           the
           distance
           which
           is
           from
           the
           point
           N
           ,
           to
           the
           middle
           of
           the
           bigness
           of
           the
           axeltree
           close
           by
           the
           stay
           O
           ,
           and
           with
           this
           space
           come
           back
           to
           the
           lower
           figure
           ,
           set
           one
           of
           the
           feet
           of
           the
           Compass
           to
           the
           point
           N
           ,
           and
           turning
           this
           foot
           upon
           this
           point
           N
           ,
           trace
           with
           the
           other
           foot
           another
           crooked
           line
           that
           may
           meet
           with
           the
           other
           in
           one
           point
           ,
           as
           O
           ,
           for
           it
           must
           meet
           with
           it
           .
        
         
           Then
           open
           yout
           Compass
           at
           discretion
           ,
           rather
           more
           than
           lesse
           ,
           and
           set
           one
           of
           the
           feet
           of
           the
           Compass
           so
           open
           at
           discretion
           to
           the
           point
           O
           ,
           and
           turning
           this
           foot
           of
           the
           Compass
           upon
           this
           point
           O
           ,
           trace
           with
           the
           other
           foot
           a
           round
           RGSH
           .
           Go
           back
           to
           the
           Dyal
           in
           the
           figure
           above
           ,
           take
           with
           your
           Compass
           upon
           the
           rule
           QP
           ,
           the
           distance
           which
           is
           from
           one
           of
           the
           points
           M
           or
           N
           ,
           to
           the
           point
           of
           6
           hours
           ,
           and
           with
           this
           space
           ,
           for
           example
           of
           M6
           ,
           come
           back
           to
           the
           lower
           figure
           ,
           set
           one
           of
           the
           points
           or
           feet
           of
           the
           Compass
           upon
           this
           point
           M
           ,
           go
           and
           mark
           with
           the
           other
           foot
           in
           the
           line
           M
           ,
           a
           point
           as
           6
           ,
           of
           the
           same
           side
           upon
           the
           rule
           .
        
         
           And
           so
           you
           have
           in
           the
           line
           MN
           ,
           one
           and
           the
           same
           thing
           as
           you
           have
           in
           the
           Dyal
           in
           the
           middle
           rule
           ,
           viz.
           the
           three
           points
           MN
           and
           6
           ,
           of
           the
           same
           distance
           ,
           in
           each
           of
           these
           two
           straight
           lines
           .
        
         
           This
           being
           done
           ,
           draw
           in
           the
           figure
           below
           by
           the
           two
           points
           O
           and
           6
           ,
           a
           straight
           line
           O
           ,
           6
           ,
           which
           may
           divide
           the
           round
           RGSH
           ,
           in
           two
           halfs
           RGS
           ,
           and
           RHS.
           
        
         
           Open
           the
           Compass
           at
           your
           discretion
           ,
           and
           as
           much
           as
           the
           space
           will
           give
           you
           leave
           ,
           and
           keeping
           your
           Compass
           so
           open
           at
           discretion
           ,
           set
           one
           of
           the
           feet
           to
           the
           point
           S
           ,
           and
           turning
           this
           foot
           upon
           this
           point
           S
           ,
           trace
           with
           the
           other
           
           foot
           ,
           two
           crooked
           lines
           L
           and
           D
           ,
           then
           with
           the
           same
           space
           ,
           remove
           your
           Compass
           out
           of
           his
           place
           ,
           and
           set
           one
           of
           the
           feet
           to
           the
           point
           R
           ,
           and
           turning
           this
           foot
           about
           upon
           this
           point
           R
           ,
           trace
           with
           the
           other
           foot
           two
           other
           crooked
           lines
           ,
           that
           may
           meet
           in
           two
           points
           L
           and
           D
           ,
           the
           two
           crooked
           lines
           that
           you
           have
           drawn
           about
           the
           point
           S
           ,
           and
           mark
           those
           two
           points
           L
           and
           D
           ,
           and
           draw
           by
           those
           two
           points
           a
           straight
           line
           LD
           ,
           which
           may
           passe
           by
           the
           point
           O
           ,
           if
           you
           have
           been
           exact
           in
           your
           operations
           .
        
         
           So
           you
           have
           divided
           this
           round
           ,
           into
           four
           quarters
           of
           a
           round
           ,
           with
           the
           two
           straight
           lines
           SOR
           ,
           LOD
           ,
           and
           if
           the
           straight
           line
           LOD
           ,
           drawn
           in
           length
           comes
           to
           meet
           the
           line
           MN
           ,
           in
           a
           point
           as
           12
           ,
           it
           shews
           that
           there
           is
           also
           the
           point
           of
           the
           hours
           of
           12
           ,
           in
           your
           Dyal
           ,
           viz.
           in
           the
           middle
           rule
           between
           the
           superficies
           and
           the
           axeltree
           ;
           now
           divide
           with
           your
           Compass
           every
           one
           of
           these
           quarters
           of
           the
           round
           ,
           into
           six
           parts
           equal
           ,
           as
           you
           see
           in
           the
           points
           that
           are
           upon
           the
           brim
           of
           the
           round
           RGSH
           ,
           and
           by
           the
           center
           or
           middle
           point
           of
           this
           round
           O
           ,
           and
           by
           every
           one
           of
           the
           points
           of
           these
           divisions
           of
           the
           edge
           or
           brim
           of
           the
           round
           ,
           draw
           some
           lines
           or
           beams
           ,
           as
           you
           see
           some
           drawn
           already
           ,
           that
           may
           go
           and
           meet
           the
           straight
           line
           MN
           ,
           as
           in
           the
           points
           ,
           5
           ,
           4
           ,
           3
           ,
           2
           ,
           1
           ,
           11.
           and
           these
           points
           are
           the
           points
           of
           the
           other
           hours
           ,
           that
           are
           to
           be
           found
           in
           your
           Dyal
           .
        
         
           
             18
          
        
      
       
       
         
           
             
               17
            
          
        
         
         
           
             Figure
             18
             ,
          
           To
           all
           sorts
           of
           People
           .
        
         
           NOw
           take
           with
           the
           Compass
           in
           the
           figure
           above
           ,
           the
           space
           from
           6
           to
           5
           ,
           and
           with
           this
           space
           go
           to
           the
           Dyal
           in
           the
           figure
           below
           ,
           set
           one
           of
           the
           feet
           of
           the
           Compass
           to
           the
           point
           6
           ,
           and
           keeping
           this
           foot
           of
           the
           Compass
           upon
           this
           point
           6
           ,
           go
           and
           mark
           with
           the
           other
           foot
           in
           the
           middle
           rule
           another
           point
           5
           ,
           and
           by
           this
           means
           you
           shall
           transport
           with
           your
           Compass
           the
           space
           6
           ,
           5
           ,
           ●●rom
           the
           line
           of
           the
           figure
           above
           ,
           which
           represents
           your
           table
           ,
           or
           the
           flat
           place
           in
           the
           Dyal
           of
           the
           figure
           below
           ,
           upon
           the
           middle
           rule
           MN
           ,
           &
           so
           accordingly
           take
           with
           your
           Compass
           every
           one
           of
           the
           other
           spaces
           ,
           5
           ,
           4
           ,
           4
           ,
           3
           ,
           3
           ,
           2
           ,
           2
           ,
           1
           ,
           1●
           ,
           12
           ,
           11
           ,
           from
           the
           higher
           figure
           ,
           and
           bring
           them
           in
           this
           manner
           to
           the
           Dyal
           upon
           the
           middle
           rule
           ,
           in
           the
           lower
           figure
           ,
           and
           so
           you
           have
           done
           in
           this
           middle
           rule
           in
           the
           Dyal
           of
           the
           lower
           figure
           ,
           all
           and
           the
           same
           spaces
           as
           those
           are
           ,
           that
           are
           upon
           the
           table
           of
           the
           lower
           figure
           :
           And
           those
           points
           of
           the
           middle
           rule
           of
           the
           lower
           figure
           ,
           are
           as
           many
           points
           of
           hours
           that
           will
           be
           in
           the
           Dyal
           ,
           among
           which
           you
           know
           that
           the
           point
           6
           ,
           is
           the
           point
           of
           one
           of
           the
           hours
           of
           six
           ,
           either
           of
           the
           evening
           ,
           or
           of
           the
           morning
           ,
           whereby
           you
           shall
           come
           to
           know
           which
           are
           the
           other
           hours
           ,
           whereof
           you
           have
           the
           points
           so
           mark'd
           in
           the
           rule
           of
           the
           Dyal
           .
        
         
           As
           for
           to
           let
           you
           know
           ,
           whether
           this
           point
           of
           6
           hours
           ,
           is
           either
           of
           those
           in
           the
           morning
           ,
           or
           of
           those
           of
           the
           evening
           ,
           I
           will
           not
           trouble
           this
           paper
           with
           it
           ,
           because
           that
           is
           plain
           enough
           of
           it self
           :
           And
           you
           see
           well
           enough
           ,
           whether
           the
           shadow
           of
           the
           axeltree
           rod
           will
           fall
           upon
           this
           point
           ,
           either
           in
           the
           morning
           about
           the
           beginning
           of
           the
           day
           ,
           or
           else
           in
           the
           evening
           about
           the
           shutting
           up
           of
           the
           day
           .
           By
           this
           means
           you
           may
           see
           well
           enough
           ,
           whether
           the
           hours
           of
           your
           Dyal
           are
           of
           those
           of
           the
           forenoon
           ,
           or
           of
           the
           afternoon
           ,
           for
           to
           mark
           them
           accordingly
           ,
           without
           
           speaking
           any
           further
           about
           it
           .
           If
           you
           have
           found
           upon
           the
           middle
           rule
           MN
           ,
           the
           point
           of
           one
           of
           the
           two
           hours
           of
           12
           ,
           and
           not
           the
           point
           of
           one
           of
           the
           hours
           of
           6
           ,
           you
           are
           but
           to
           do
           with
           that
           point
           of
           hour
           of
           twelve
           ,
           the
           same
           thing
           that
           I
           said
           you
           should
           do
           with
           the
           point
           of
           one
           of
           the
           hours
           of
           6.
           
        
         
           When
           you
           have
           so
           transported
           the
           points
           of
           the
           hours
           from
           the
           Table
           of
           the
           figure
           above
           ,
           to
           the
           Dyal
           in
           the
           lower
           figure
           upon
           the
           middle
           rule
           ▪
           That
           which
           remains
           to
           do
           ,
           is
           to
           transport
           those
           points
           of
           hours
           from
           the
           middle
           rule
           ,
           into
           the
           superficies
           of
           the
           Dyal
           in
           the
           manner
           following
           ,
           and
           to
           trace
           in
           it
           afterwards
           the
           line
           of
           the
           hours
           ,
           as
           I
           will
           shew
           you
           .
        
         
           You
           see
           ,
           there
           are
           two
           strings
           tyed
           to
           the
           axeltree
           rod
           ,
           in
           the
           figure
           below
           ,
           set
           the
           rings
           of
           these
           two
           strings
           ,
           as
           far
           as
           you
           can
           one
           from
           another
           ,
           and
           as
           from
           R
           in
           S
           ,
           then
           take
           one
           of
           these
           two
           strings
           ,
           as
           that
           which
           comes
           from
           the
           point
           R
           ,
           carry
           it
           stretcht
           out
           in
           a
           direct
           line
           from
           the
           axeltree
           rod
           ,
           to
           one
           of
           the
           points
           of
           hours
           that
           are
           mark'd
           in
           the
           middle
           rule
           ,
           for
           example
           in
           the
           point
           of
           hour
           12
           ,
           and
           cause
           this
           string
           comming
           so
           from
           the
           axeltree
           ,
           to
           passe
           to
           this
           point
           of
           hour
           12
           ,
           of
           the
           middle
           rule
           ,
           and
           to
           go
           altogether
           in
           a
           straight
           line
           as
           far
           as
           the
           superficies
           of
           the
           Dyal
           ;
           and
           mark
           in
           the
           superficies
           of
           the
           Dyal
           the
           point
           in
           which
           this
           string
           so
           carryed
           ,
           meets
           it
           ;
           By
           this
           means
           you
           shall
           transport
           this
           point
           or
           hour
           12
           ,
           from
           the
           middle
           rule
           into
           the
           superficies
           of
           the
           Dyal
           to
           the
           point
           XII
           .
        
         
           And
           after
           the
           same
           manner
           ,
           you
           shall
           transport
           one
           after
           another
           the
           points
           of
           hour
           11
           ,
           12.
           1
           ,
           2
           ,
           3
           ,
           4
           ,
           5
           ,
           6
           ,
           from
           the
           middle
           rule
           ,
           into
           the
           superficies
           of
           the
           Dyal
           to
           the
           points
           XI
           ,
           XII
           ▪
           I
           ,
           II
           ,
           III
           ,
           IV
           ,
           V
           ,
           VI
           .
        
      
       
       
         
           
             Figure
             19
             ,
          
           To
           all
           sorts
           of
           People
           .
        
         
           How
           to
           trace
           the
           lines
           of
           the
           hours
           upon
           the
           superficies
           of
           the
           Dyal
           .
        
         
           OF
           the
           two
           strings
           ,
           fig.
           above
           ,
           that
           are
           made
           fast
           to
           the
           axeltree
           rod
           ,
           stretch
           out
           one
           in
           a
           straight
           line
           ,
           from
           the
           axeltree
           rod
           ,
           as
           from
           the
           point
           R
           to
           a
           Point
           of
           hour
           of
           the
           middle
           rule
           ,
           as
           to
           the
           point
           of
           hour
           I
           ▪
           and
           holding
           this
           string
           so
           stretcht
           ,
           take
           the
           other
           or
           second
           string
           comming
           from
           the
           point
           S
           ,
           and
           stretching
           it
           likewise
           in
           a
           straight
           line
           ,
           make
           it
           crosse
           over
           the
           first
           string
           BI
           ▪
           and
           let
           it
           touch
           it
           without
           breaking
           his
           straight
           line
           ,
           and
           let
           it
           go
           in
           a
           straight
           line
           from
           thence
           ,
           to
           the
           superficies
           of
           the
           Dyal
           as
           to
           the
           point
           D
           ,
           and
           mark
           the
           point
           D
           ,
           in
           the
           superficies
           of
           the
           Dyal
           ,
           wherein
           this
           second
           string
           so
           carried
           ,
           comes
           to
           touch
           it
           ;
           then
           make
           this
           second
           string
           to
           go
           and
           touch
           again
           the
           first
           in
           another
           place
           ,
           and
           with
           this
           second
           string
           go
           and
           touch
           in
           the
           same
           manner
           ,
           another
           point
           E
           ,
           in
           the
           superficies
           of
           the
           Dyal
           E
           ,
           And
           so
           remove
           this
           second
           string
           along
           the
           first
           string
           ,
           as
           many
           times
           as
           you
           shall
           have
           need
           to
           mark
           any
           several
           points
           ,
           as
           D
           ,
           E
           ,
           L
           ,
           in
           the
           superficies
           of
           the
           Dyal
           ,
           to
           trace
           the
           line
           of
           that
           hour
           there
           ,
           then
           draw
           a
           line
           as
           fine
           and
           delicate
           as
           you
           can
           by
           all
           those
           points
           DEL
           ,
           in
           the
           superficies
           of
           the
           Dyal
           ,
           that
           line
           shall
           be
           the
           line
           of
           that
           hour
           I.
           
        
         
           And
           after
           this
           manner
           ,
           you
           shall
           trace
           in
           the
           superficies
           of
           the
           Dyal
           ,
           the
           lines
           of
           all
           the
           other
           hours
           that
           are
           in
           the
           middle
           rule
           ,
           and
           your
           Dyal
           will
           be
           finished
           .
        
         
           The
           lower
           figure
           shews
           you
           to
           the
           eye
           ,
           how
           that
           after
           you
           have
           transported
           as
           above
           said
           ,
           all
           the
           points
           of
           hour
           from
           the
           middle
           rule
           into
           the
           superficies
           of
           the
           Dyal
           ,
           you
           may
           take
           away
           this
           middle
           rule
           ,
           and
           the
           two
           knobs
           that
           
           hold
           it
           up
           ,
           and
           make
           an
           end
           of
           tracing
           the
           rest
           of
           the
           lines
           in
           the
           superficies
           of
           the
           Dyal
           ,
           as
           I
           have
           said
           ,
           with
           the
           strings
           comming
           from
           R
           and
           I
           ,
           and
           by
           means
           of
           the
           points
           of
           hours
           XI
           ,
           XII
           ,
           I
           ,
           II
           ,
           III
           ,
           IV
           ,
           V
           ,
           VI
           .
        
      
       
       
         
           
             Figure
             20
             ,
          
           To
           all
           sorts
           of
           People
           .
        
         
           AFter
           that
           you
           have
           placed
           the
           axeltree
           of
           the
           Dyal
           as
           it
           must
           be
           ,
           if
           you
           desire
           to
           find
           the
           points
           of
           the
           hours
           in
           the
           superficies
           ,
           with
           some
           extraordinary
           instruments
           ,
           that
           which
           is
           the
           plainest
           of
           all
           ,
           viz.
           a
           round
           flat
           plate
           ,
           and
           stiff
           ,
           as
           of
           tinn'd
           yron
           ,
           or
           the
           like
           ,
           and
           divided
           into
           24
           parts
           equal
           one
           unto
           another
           ,
           and
           set
           up
           in
           the
           manner
           of
           a
           rotunda
           or
           whirl
           ,
           by
           the
           squire
           ,
           or
           with
           right
           angles
           about
           the
           axeltree
           of
           the
           Dyal
           ,
           as
           the
           figure
           below
           doth
           shew
           ,
           is
           the
           most
           common
           and
           the
           shortest
           way
           of
           all
           .
        
         
           The
           figure
           H
           ,
           shews
           you
           this
           round
           alone
           ,
           and
           how
           it
           is
           open
           of
           one
           side
           ,
           that
           the
           center
           thereof
           may
           be
           placed
           with
           the
           center
           of
           the
           axeltree
           .
        
         
           The
           1.
           figure
           shews
           the
           neck
           that
           may
           be
           applyed
           unto
           this
           round
           about
           the
           center
           ,
           to
           the
           end
           that
           one
           may
           with
           this
           neck
           ,
           set
           the
           round
           to
           the
           axeltree
           of
           the
           Dyal
           by
           the
           squire
           ,
           or
           with
           angles
           straight
           between
           themselves
           ,
           as
           you
           see
           in
           the
           second
           figure
           .
        
         
           When
           you
           have
           thus
           set
           this
           round
           to
           the
           axeltree
           of
           the
           Dyal
           ,
           the
           lower
           figure
           shews
           you
           how
           you
           must
           place
           the
           string
           of
           the
           plummet
           ,
           hanging
           upon
           the
           axeltree
           by
           a
           point
           of
           one
           of
           the
           divisions
           of
           the
           edge
           of
           this
           round
           ,
           that
           it
           may
           give
           you
           the
           points
           of
           the
           hours
           in
           the
           superficies
           of
           the
           Dyal
           .
        
         
           The
           strings
           which
           comming
           from
           the
           axeltree
           passe
           afterwards
           to
           the
           points
           of
           the
           division
           of
           this
           round
           in
           it's
           24
           parts
           ,
           shew
           you
           ,
           how
           you
           must
           afterwards
           bring
           the
           strings
           from
           the
           axeltre
           ,
           by
           the
           points
           of
           the
           division
           of
           this
           round
           in
           24
           parts
           ,
           equal
           to
           the
           superficies
           of
           the
           Dyal
           ,
           that
           you
           may
           have
           the
           points
           of
           the
           hours
           in
           this
           superficies
           .
        
         
           The
           string
           LS
           ,
           XII
           ,
           that
           passeth
           to
           the
           string
           with
           the
           plummet
           RS
           ,
           gives
           the
           point
           of
           the
           hours
           of
           12.
           
           The
           
           string
           LVI
           ,
           that
           passeth
           to
           one
           of
           the
           points
           of
           this
           division
           in
           24
           ,
           and
           is
           found
           to
           be
           level
           ,
           gives
           the
           point
           of
           the
           hours
           of
           6.
           
        
         
           The
           other
           strings
           shew
           you
           ,
           that
           the
           way
           of
           tracing
           the
           points
           of
           the
           other
           hours
           is
           the
           same
           as
           above
           .
        
         
           
             20
          
        
      
       
       
         
           
        
         
         
           
             Figure
             21
             ,
          
           To
           all
           sorts
           of
           People
           .
        
         
           VVHen
           you
           have
           brought
           ,
           as
           I
           have
           said
           ,
           by
           means
           of
           this
           rotunda
           and
           the
           strings
           ,
           all
           the
           points
           of
           the
           hours
           ,
           into
           the
           superficies
           of
           the
           Dyal
           ;
           You
           may
           take
           away
           the
           rotunda
           if
           you
           will
           ,
           and
           make
           an
           end
           of
           tracing
           the
           lines
           of
           the
           hours
           as
           before
           with
           the
           strings
           ,
           and
           by
           means
           of
           the
           points
           of
           hours
           ,
           which
           you
           have
           brought
           into
           the
           superficies
           of
           the
           Dyal
           ,
           as
           you
           see
           in
           the
           figure
           below
           ,
           the
           line
           DELKPQSYIZG
           .
        
         
           And
           for
           this
           purpose
           by
           means
           of
           the
           said
           strings
           ,
           carry
           a
           string
           in
           a
           straight
           line
           from
           the
           axeltree
           to
           the
           point
           of
           hour
           ,
           for
           example
           I
           ,
           and
           holding
           it
           there
           stretcht
           in
           a
           straight
           line
           ,
           carry
           of
           one
           side
           or
           other
           according
           to
           the
           occasion
           ,
           an
           other
           string
           comming
           also
           from
           the
           axeltree
           ,
           as
           from
           I
           ,
           or
           from
           B
           ,
           that
           may
           go
           in
           a
           straight
           line
           as
           far
           as
           the
           superficies
           of
           the
           Dyal
           ,
           and
           let
           it
           go
           and
           touch
           ,
           and
           crosse
           over
           the
           string
           IR
           ,
           several
           times
           in
           several
           places
           ,
           and
           at
           every
           time
           go
           with
           this
           second
           string
           to
           touch
           and
           mark
           a
           point
           in
           the
           superficies
           of
           the
           Dyal
           ,
           until
           you
           have
           enough
           ,
           as
           you
           see
           the
           points
           D
           ,
           E
           ,
           L
           ,
           K
           ,
           P
           ,
           Q
           ,
           Y
           ,
           I
           ,
           Z
           ,
           G
           ,
           and
           carry
           by
           these
           points
           a
           line
           sweetned
           ,
           that
           shall
           be
           a
           line
           of
           hour
           ,
           do
           the
           like
           for
           the
           lines
           of
           the
           other
           hours
           ,
           and
           you
           have
           done
           .
        
         
           When
           you
           have
           mark'd
           in
           the
           superficies
           of
           the
           Dyal
           ,
           a
           point
           of
           every
           one
           of
           the
           hours
           that
           are
           to
           be
           found
           in
           it
           :
           If
           you
           desire
           to
           trace
           the
           lines
           of
           the
           hours
           every
           one
           at
           once
           ,
           without
           making
           use
           of
           the
           strings
           ,
           as
           in
           the
           figure
           above
           ,
           you
           may
           do
           it
           when
           it
           is
           dark
           ,
           as
           by
           night
           ,
           with
           the
           light
           of
           a
           candle
           ,
           in
           that
           manner
           as
           it
           is
           exprest
           in
           the
           lower
           figure
           .
        
         
           Set
           a
           light
           behind
           the
           axeltree
           rod
           of
           the
           Dyal
           ,
           and
           turn
           the
           same
           lightabout
           this
           axeltree
           ,
           untill
           the
           shadow
           of
           this
           axeltree
           come
           to
           one
           of
           the
           points
           of
           hour
           I
           ,
           and
           
           trace
           in
           the
           superficies
           of
           the
           Dyal
           a
           line
           DELKPQSYIZG
           ,
           all
           along
           this
           shadow
           of
           the
           axeltree
           ,
           that
           line
           shall
           be
           a
           line
           of
           hour
           ,
           do
           the
           like
           for
           every
           one
           of
           the
           other
           points
           of
           hour
           ,
           and
           you
           have
           finish'd
           your
           Dyal
           .
        
      
       
       
         
           
             
               22
            
             
               Instruments
               to
               work
               with
               all
               ,
            
          
        
         
         
           
             
               21
            
          
        
         
         
           
             Figure
             22
             ,
          
           Several
           Instruments
           to
           work
           withall
           in
           these
           occasions
           hereafter
           specified
           .
        
         
           I
           Did
           not
           intend
           to
           burden
           my
           memory
           with
           any
           thing
           in
           this
           matter
           ,
           but
           with
           
             Monsieur
             de
             Sargues
          
           universal
           rules
           for
           the
           placing
           of
           the
           axeltree
           ,
           and
           for
           the
           tracing
           in
           a
           Dyal
           the
           hours
           after
           the
           French
           way
           ,
           without
           medling
           with
           the
           rest
           ,
           which
           is
           more
           curious
           than
           useful
           .
        
         
           But
           to
           follow
           the
           advice
           of
           many
           considerable
           persons
           whom
           I
           do
           honour
           ,
           I
           have
           set
           down
           also
           the
           way
           to
           mark
           that
           which
           is
           commonly
           called
           the
           signs
           :
           The
           hours
           after
           the
           Italian
           or
           Babylonian
           way
           :
           The
           hours
           after
           the
           manner
           of
           the
           Ancients
           :
           The
           elevations
           of
           the
           Sun
           above
           the
           Horizon
           ;
           and
           the
           rising
           of
           the
           same
           .
        
         
           And
           for
           as
           much
           as
           none
           can
           do
           any
           of
           these
           things
           universally
           ,
           without
           using
           these
           instruments
           more
           or
           lesse
           ;
           This
           table
           following
           shews
           to
           the
           eye
           all
           the
           pieces
           that
           are
           used
           in
           those
           several
           occasions
           .
           These
           instruments
           are
           first
           a
           circle
           ,
           a
           half
           circle
           ,
           or
           the
           quarter
           of
           a
           circle
           ,
           which
           is
           all
           one
           which
           is
           made
           to
           turn
           about
           its
           Diameter
           set
           fast
           in
           it
           's
           due
           and
           convenient
           place
           ,
           or
           down
           right
           ,
           as
           in
           the
           fourth
           figure
           ,
           or
           level
           ,
           as
           in
           the
           second
           or
           third
           figure
           ,
           or
           else
           inclining
           or
           hanging
           downward
           ,
           as
           in
           the
           first
           figure
           .
        
         
           The
           way
           to
           make
           this
           circle
           to
           move
           in
           all
           kinds
           of
           positions
           ,
           is
           to
           set
           two
           rings
           in
           it's
           Diameter
           ,
           through
           which
           one
           may
           put
           in
           a
           stick
           straight
           ,
           round
           ,
           and
           smooth
           ,
           about
           which
           this
           circle
           may
           turn
           round
           like
           a
           weather
           cock
           about
           his
           needle
           or
           spear
           ,
           as
           in
           the
           second
           figure
           ,
           and
           there
           must
           be
           within
           those
           hoop
           rings
           ,
           a
           screw
           to
           fasten
           this
           circle
           in
           that
           place
           ,
           or
           which
           way
           soever
           you
           will
           have
           it
           to
           stand
           .
        
         
           The
           sticks
           or
           rods
           are
           represented
           by
           the
           7th
           .
           figure
           ,
           with
           a
           fork
           at
           the
           end
           of
           every
           one
           ,
           bored
           in
           the
           cheek
           ,
           to
           put
           a
           pin
           through
           ,
           as
           you
           see
           ,
           that
           one
           may
           be
           set
           plum
           or
           down
           right
           ,
           and
           the
           other
           level
           ,
           being
           made
           fast
           at
           one
           
           end
           to
           the
           axeltree
           rod
           as
           in
           the
           5th
           .
           figure
           .
           And
           for
           this
           purpose
           also
           the
           axeltree
           rod
           is
           bored
           in
           O.
           
        
         
           The
           8th
           .
           figure
           shews
           the
           axeltree
           rod
           by
           it self
           bored
           with
           O
           ,
           and
           the
           pin
           Q
           ,
           put
           through
           the
           hole
           ,
           to
           shew
           more
           plainly
           that
           which
           the
           5th
           figure
           represents
           ,
           viz.
           all
           the
           pieces
           set
           or
           joyned
           together
           being
           mark'd
           with
           qo
           .
        
         
           You
           see
           that
           the
           hoop
           rings
           are
           near
           the
           edge
           or
           brim
           of
           the
           circle
           ,
           a
           purpose
           to
           leave
           the
           center
           O
           ,
           and
           a
           space
           about
           it
           free
           ,
           having
           commonly
           a
           piece
           taken
           off
           ,
           that
           this
           circle
           may
           turn
           freely
           about
           the
           forked
           end
           ,
           that
           is
           to
           say
           about
           his
           center
           ,
           without
           any
           let
           or
           hinderance
           at
           all
           .
        
      
       
       
       
         
           
             
               23
            
             
               for
               the
               Signes
               .
            
          
        
         
         
           
             Figure
             23
             ,
          
           How
           to
           mark
           the
           Signs
           .
        
         
           GEt
           ,
           figure
           2
           below
           ,
           a
           half
           circle
           both
           thin
           and
           stiff
           ctsrd
           ,
           draw
           there
           a
           beam
           OZS
           ,
           perpendicular
           to
           the
           Diameter
           CPOQD
           ,
           take
           on
           both
           sides
           of
           this
           beam
           OS
           ,
           23
           degrees
           and
           half
           ,
           for
           example
           23
           degrees
           and
           half
           from
           s
           towards
           t
           ,
           and
           as
           much
           from
           s
           towards
           r
           ,
           draw
           the
           straight
           line
           r
           ,
           t
           ,
           make
           upon
           Diameter
           t
           ,
           r
           ,
           a
           half
           ,
           circle
           tzr
           ,
           divide
           the
           edge
           or
           brim
           of
           that
           half
           circle
           in
           six
           equal
           parts
           ,
           as
           in
           the
           points
           that
           you
           see
           there
           ;
           draw
           by
           those
           points
           as
           far
           as
           the
           half
           circle
           CtsrU
           ,
           some
           straight
           lines
           that
           may
           be
           perpendicular
           to
           the
           straight
           line
           r
           ,
           t
           ,
           bring
           from
           the
           center
           O
           ,
           by
           the
           points
           that
           those
           perpendicular
           have
           made
           upon
           the
           edge
           of
           the
           half
           circle
           CtsrD
           ,
           some
           straight
           lines
           ,
           as
           you
           see
           that
           the
           strings
           shew
           you
           ,
           and
           with
           those
           lines
           drawn
           out
           sufficiently
           ,
           you
           shall
           mark
           the
           signs
           in
           the
           Dyal
           ,
           as
           I
           shall
           say
           .
        
         
           You
           see
           that
           the
           half
           circle
           is
           cut
           thorow
           ,
           or
           made
           hollow
           from
           the
           point
           P
           ,
           to
           the
           point
           Q
           ,
           round
           about
           the
           center
           O
           ,
           according
           to
           the
           circumference
           PZQ
           ,
           which
           is
           notch'd
           also
           in
           the
           points
           that
           you
           see
           in
           it
           ,
           which
           are
           betwixt
           every
           degree
           of
           the
           half
           circle
           ;
           And
           the
           center
           O
           ,
           and
           these
           notches
           ,
           are
           there
           a
           purpose
           to
           fasten
           a
           string
           upon
           them
           ,
           insteed
           of
           bringing
           it
           from
           the
           center
           O.
           
        
         
           The
           two
           figures
           s32tgez
           ,
           s45rbcz
           ,
           both
           on
           the
           right
           and
           on
           the
           left
           side
           of
           the
           half
           circle
           CtsrD
           ,
           shew
           as
           you
           may
           judge
           by
           their
           letters
           or
           coats
           ,
           each
           of
           them
           one
           half
           of
           the
           figure
           tsrz
           ,
           of
           the
           half
           circle
           CtsrD
           ,
           which
           I
           have
           made
           thus
           bigger
           than
           each
           half
           of
           this
           figure
           ,
           that
           one
           may
           set
           in
           the
           letters
           ge
           ,
           cb
           ,
           and
           some
           figures
           ,
           2345
           ,
           about
           the
           edges
           of
           the
           two
           half
           circles
           ,
           and
           also
           the
           signs
           ,
           as
           you
           see
           ,
           which
           I
           could
           not
           do
           in
           the
           middle
           figure
           without
           confusion
           .
        
         
           The
           lines
           comming
           from
           the
           points
           t23s
           ,
           s45r
           ,
           
           towards
           the
           lowest
           past
           of
           the
           figure
           or
           plate
           ,
           comming
           near
           one
           an
           other
           ,
           go
           and
           seek
           the
           center
           of
           the
           half
           circle
           t23s45r
           ,
           Every
           one
           of
           the
           three
           saces
           between
           those
           straight
           lines
           is
           to
           hold
           two
           signes
           ,
           mark
           them
           there
           in
           the
           same
           order
           that
           you
           see
           them
           ,
           close
           by
           these
           straight
           lines
           ,
           one
           of
           one
           side
           ,
           and
           an
           other
           on
           
           th'other
           side
           .
        
         
           And
           by
           this
           meanes
           the
           straight
           line
           of
           the
           half
           circle
           t23s45r
           ,
           which
           from
           the
           center
           of
           the
           half
           circle
           passeth
           to
           the
           points
           ,
           is
           that
           of
           the
           signes
           of
           Aries
           ,
           and
           of
           Libra
           ;
           that
           which
           passeth
           to
           the
           point
           3
           ,
           is
           that
           of
           Taurus
           ,
           and
           of
           Virgo
           ;
           that
           which
           passeth
           to
           the
           point
           2
           ,
           is
           that
           of
           Gemini
           ,
           or
           the
           Twinnes
           ,
           and
           of
           Leo
           ;
           that
           which
           passeth
           to
           the
           point
           t
           ,
           is
           that
           of
           Cancer
           ;
           that
           which
           passeth
           to
           the
           point
           r
           ,
           is
           that
           of
           Capricornus
           ;
           that
           which
           passeth
           to
           the
           point
           5
           ,
           is
           that
           of
           Sagittarius
           and
           Aquarius
           ;
           that
           which
           passeth
           to
           the
           point
           4
           ,
           is
           that
           of
           the
           Scorpion
           ,
           and
           of
           the
           Fishes
           .
        
         
           The
           two
           figures
           s32cgez
           ,
           s45rbcz
           ,
           shew
           you
           also
           that
           with
           one
           quarter
           of
           circe
           mark'd
           on
           both
           sides
           with
           6
           signes
           in
           one
           part
           ,
           and
           6
           others
           in
           the
           other
           part
           ,
           you
           may
           do
           the
           same
           thing
           as
           well
           as
           with
           the
           half
           circle
           ,
           by
           turning
           this
           quarter
           of
           circle
           ,
           as
           you
           see
           in
           the
           said
           figures
           ,
           once
           of
           one
           side
           ,
           and
           once
           of
           
           th'other
           .
        
         
           I
           shall
           for
           all
           that
           speak
           to
           you
           alwayes
           as
           if
           you
           had
           the
           half
           circle
           in
           your
           hand
           .
        
         
           Therefore
           when
           you
           will
           mark
           the
           lines
           of
           the
           signes
           in
           the
           Superficies
           of
           the
           Dyall
           ,
           The
           first
           figure
           shewes
           you
           how
           you
           must
           set
           up
           your
           half
           circle
           with
           the
           axeltree
           ,
           for
           to
           turn
           it
           about
           the
           same
           ,
           without
           going
           up
           or
           down
           along
           the
           axeltree
           .
        
         
           The
           first
           figure
           above
           shewes
           how
           you
           must
           make
           your
           half
           circle
           ,
           
             viz.
          
           about
           the
           axeltree
           ,
           set
           then
           the
           half
           circle
           to
           the
           axeltree
           of
           the
           Dyall
           ,
           as
           you
           see
           in
           the
           figure
           that
           is
           under
           the
           first
           .
        
         
           Tye
           a
           string
           with
           a
           loose
           knot
           ,
           just
           in
           the
           center
           of
           the
           circle
           .
        
         
           Turn
           the
           half
           circle
           about
           the
           axeltree
           ,
           cause
           at
           the
           
           same
           time
           the
           string
           comming
           from
           the
           center
           ,
           to
           passe
           by
           one
           of
           the
           lines
           of
           the
           signes
           ,
           holding
           it
           longer
           or
           shorter
           as
           need
           shall
           require
           ,
           go
           and
           touch
           with
           the
           string
           many
           several
           points
           in
           the
           superficies
           of
           the
           Dyall
           one
           after
           an
           other
           .
        
         
           Draw
           a
           line
           sweetned
           ,
           by
           all
           those
           points
           ,
           and
           it
           is
           the
           line
           of
           the
           signes
           that
           are
           markt
           along
           the
           straight
           line
           of
           the
           half
           circle
           which
           the
           string
           doth
           cover
           ,
           in
           turning
           with
           it
           about
           the
           axeltree
           .
        
         
           Do
           the
           like
           for
           every
           line
           of
           the
           signes
           ,
           mark
           the
           signes
           in
           the
           Dyall
           by
           the
           lines
           so
           drawn
           according
           to
           the
           situation
           ,
           in
           regard
           of
           the
           Country
           and
           of
           the
           place
           of
           the
           Dyall
           ,
           and
           as
           the
           figure
           shews
           ,
           you
           have
           marked
           the
           signes
           in
           the
           Dyall
           .
        
         
           And
           if
           the
           strings
           could
           not
           come
           from
           the
           center
           ,
           fasten
           them
           with
           a
           knot
           to
           the
           beames
           ,
           comming
           from
           the
           center
           ,
           in
           the
           notches
           or
           clefts
           of
           the
           circumference
           PZQ
           .
        
         
           Set
           a
           button
           or
           an
           other
           mark
           in
           the
           axeltree
           ,
           in
           the
           place
           where
           the
           center
           of
           the
           half
           circle
           CtsrD
           hath
           been
           ,
           and
           the
           shadow
           of
           the
           button
           will
           go
           and
           mark
           the
           signe
           that
           the
           Sun
           is
           in
           .
        
      
       
       
         
           
             Figure
             24.
             
          
           To
           mark
           the
           houres
           after
           the
           Italian
           or
           Babylonian
           way
           .
        
         
           THE
           first
           figure
           shews
           how
           you
           must
           set
           on
           your
           half
           circle
           ,
           and
           how
           to
           make
           it
           turn
           about
           the
           axeltree
           .
        
         
           Moreover
           ,
           the
           line
           NO
           (
           shews
           you
           what
           kind
           of
           line
           comming
           from
           the
           center
           O
           of
           this
           half
           circle
           ,
           you
           must
           make
           use
           of
           ,
           in
           making
           the
           half
           circle
           to
           turn
           about
           .
        
         
           When
           you
           have
           drawn
           the
           lines
           of
           the
           houres
           after
           the
           French
           way
           at
           length
           ,
           in
           the
           superficies
           of
           the
           Dyall
           ,
           as
           the
           figure
           below
           doth
           shew
           .
        
         
           Set
           on
           ,
           as
           the
           same
           figure
           shewes
           you
           also
           ,
           the
           half
           circle
           O
           t
           rto
           the
           exeltree
           of
           the
           Dyall
           with
           a
           string
           ON
           in
           it's
           center
           .
        
         
           Let
           this
           half
           circle
           hang
           down
           right
           or
           Plum
           ,
           and
           when
           this
           half
           circle
           is
           just
           down
           and
           at
           rest
           ,
           draw
           the
           string
           ON
           ,
           in
           a
           straight
           line
           comming
           from
           the
           center
           O
           ,
           and
           closing
           with
           the
           half
           circle
           ,
           in
           such
           sort
           as
           it
           may
           go
           ,
           and
           touch
           it
           all
           at
           length
           ,
           turn
           this
           string
           as
           a
           beam
           of
           the
           half
           circle
           about
           the
           center
           O
           ,
           till
           it
           be
           very
           levell
           ,
           as
           the
           figure
           shewes
           by
           the
           setting
           on
           of
           the
           Carpenters
           levell
           A.
           
        
         
           When
           the
           string
           ON
           is
           stretcht
           out
           very
           levell
           close
           to
           the
           half
           circle
           ,
           mark
           exactly
           upon
           the
           edge
           of
           this
           half
           circle
           ,
           the
           point
           wherein
           the
           string
           ON
           toucheth
           it
           ,
           as
           doth
           the
           letter
           E.
           
        
         
           Then
           let
           the
           half
           circle
           turn
           about
           the
           axeltree
           .
        
         
           Make
           in
           the
           mean
           time
           the
           string
           ON
           ,
           to
           passe
           by
           the
           point
           t
           ,
           which
           you
           have
           markt
           upon
           the
           edge
           of
           the
           half
           circle
           ,
           and
           making
           it
           shorter
           or
           longer
           according
           as
           need
           shall
           require
           ,
           go
           and
           touch
           with
           this
           string
           many
           several
           
           points
           one
           after
           an
           other
           in
           the
           superficies
           of
           the
           Dyall
           in
           divers
           places
           ,
           1
           ,
           2
           ,
           3
           ,
           4
           ,
           5
           ,
           6.
           
        
         
           Draw
           an
           obscure
           line
           by
           those
           points
           ,
           as
           you
           see
           the
           line
           bowed
           or
           crooked
           ,
           23
           ,
           24
           ,
           1
           ,
           2
           ,
           3
           ,
           4
           ,
           5
           ,
           6
           ,
           and
           which
           reacheth
           beyond
           the
           axeltree
           towards
           h.
           
        
         
           This
           line
           crosseth
           over
           the
           superficies
           of
           the
           Dyall
           ,
           out
           of
           the
           Equinoctial
           line
           PQ
           ,
           and
           meets
           by
           the
           way
           all
           the
           lines
           of
           the
           houres
           after
           the
           French
           way
           ,
           as
           you
           see
           it
           doth
           in
           23
           ,
           24
           ,
           1
           ,
           2
           ,
           3
           ,
           4
           ,
           5
           ,
           6.
           
        
         
           There
           Remaines
           to
           trace
           the
           lines
           of
           these
           houres
           after
           the
           Italian
           or
           Babylonian
           way
           in
           the
           superficies
           of
           the
           Dyall
           and
           when
           you
           know
           how
           to
           trace
           one
           ,
           you
           shall
           be
           able
           also
           to
           trace
           the
           other
           .
        
         
           Therefore
           to
           trace
           a
           line
           of
           those
           kinds
           of
           houres
           ,
           It
           is
           no
           matter
           which
           you
           begin
           to
           trace
           first
           ;
           Count
           upon
           the
           Equinoctiall
           line
           PQ
           fixs
           paces
           of
           houres
           equall
           ,
           after
           the
           French
           way
           ,
           one
           after
           an
           other
           ,
           as
           from
           XII
           .
           to
           VI
           .
           Afterwards
           follow
           the
           lines
           of
           the
           houres
           ,
           after
           the
           French
           way
           ,
           that
           passe
           by
           the
           points
           XII
           .
           &
           VI
           the
           two
           extremities
           of
           these
           six
           spaces
           every
           one
           to
           the
           aforefaid
           line
           of
           which
           you
           have
           found
           the
           place
           ,
           by
           turning
           the
           string
           with
           the
           half
           circle
           about
           the
           axeltree
           by
           the
           point
           t
           ,
           as
           you
           see
           ,
           as
           farre
           as
           the
           points
           24.
           
           And
           6.
           
        
         
           Take
           conveniently
           in
           these
           two
           lines
           of
           hours
           after
           the
           French
           way
           ,
           In
           each
           of
           them
           one
           of
           the
           points
           wherein
           it
           meets
           with
           the
           Equinoctial
           line
           PQ
           ,
           or
           else
           the
           said
           line
           found
           with
           the
           string
           1
           ,
           2
           ,
           3
           ,
           4
           ,
           5
           ,
           6
           ,
           that
           is
           to
           say
           in
           one
           ,
           the
           point
           that
           the
           line
           placed
           with
           the
           string
           makes
           in
           it
           ,
           and
           in
           the
           other
           ;
           the
           point
           that
           the
           Equinoctial
           line
           makes
           in
           it
           ,
           for
           example
           ,
           In
           the
           line
           ,
           XII
           ,
           24
           ,
           take
           in
           it
           the
           point
           24.
           
           Wherein
           it
           meets
           with
           the
           line
           found
           with
           the
           string
           :
           and
           in
           the
           other
           ,
           VI
           ,
           take
           in
           it
           the
           point
           VI
           .
           wherein
           it
           meets
           with
           the
           Equinoctiall
           line
           .
        
         
           Set
           either
           a
           string
           or
           a
           rule
           by
           these
           two
           points
           so
           taken
           24.
           and
           VI
           ,
           as
           you
           see
           the
           line
           ,
           24.
           6.
           
        
         
           Then
           with
           the
           string
           comming
           from
           the
           center
           of
           the
           half
           circle
           Q
           go
           razing
           or
           laying
           even
           the
           string
           24.
           
           VI
           by
           making
           it
           longer
           or
           shorter
           as
           need
           requires
           ;
           as
           you
           see
           in
           O
           ,
           g
           ,
           mark
           many
           several
           points
           in
           the
           superficies
           of
           the
           
           Dyall
           one
           after
           an
           other
           ,
           as
           for
           example
           24
           ,
           g
           ,
           VI
           ,
           more
           or
           lesse
           ,
           according
           as
           the
           superficies
           of
           the
           Dyall
           is
           more
           or
           lesse
           uneven
           .
        
         
           Draw
           an
           obscure
           line
           by
           the
           points
           24
           ,
           g
           ,
           VI
           ,
           and
           it
           will
           be
           a
           line
           of
           houres
           after
           the
           Italian
           or
           Babylonian
           way
           ,
           and
           so
           of
           all
           the
           rest
           .
        
         
           The
           string
           h
           ,
           OH
           shews
           that
           you
           may
           if
           need
           be
           ,
           do
           the
           like
           both
           of
           one
           and
           of
           the
           other
           side
           of
           the
           center
           O
           ,
           to
           go
           and
           place
           of
           one
           part
           or
           other
           according
           to
           the
           occasion
           ,
           the
           line
           ,
           as
           2
           ,
           3
           ,
           4
           ,
           5.
           
        
         
           And
           if
           you
           have
           a
           straight
           line
           ,
           as
           might
           be
           O
           ,
           q
           ,
           which
           may
           turn
           about
           the
           center
           O
           ,
           and
           be
           perpendicular
           to
           the
           Axeltree
           BI
           ,
           and
           you
           hold
           the
           half
           circle
           with
           this
           straight
           line
           ,
           set
           one
           at
           a
           convenient
           or
           reasonable
           distance
           from
           the
           other
           :
           And
           let
           it
           be
           alwayes
           exactly
           of
           the
           distance
           of
           six
           hours
           after
           the
           French
           way
           :
           First
           of
           all
           ,
           this
           string
           describes
           the
           Equinoctial
           line
           in
           the
           superficies
           of
           the
           Dyall
           ,
           Secondly
           when
           one
           of
           the
           two
           ,
           either
           the
           half
           circle
           or
           the
           straight
           line
           O
           q
           ,
           is
           found
           in
           one
           of
           the
           points
           of
           the
           hours
           of
           the
           Equator
           ,
           
           th'other
           is
           likewise
           found
           in
           it
           ,
           in
           an
           other
           point
           of
           hour
           ,
           then
           drawing
           with
           a
           string
           coming
           from
           the
           center
           O
           ,
           a
           straight
           line
           that
           may
           go
           from
           the
           point
           ,
           as
           t
           ,
           to
           the
           end
           of
           the
           straight
           line
           O
           q
           which
           you
           shall
           go
           drawing
           with
           this
           string
           made
           shorter
           or
           longer
           ,
           as
           need
           requires
           ,
           and
           mark
           some
           points
           of
           line
           of
           hour
           ,
           after
           the
           Italian
           or
           Babylonian
           way
           in
           the
           superficies
           of
           the
           Dyall
           .
        
         
           And
           for
           this
           purpose
           there
           is
           nothing
           so
           easie
           as
           to
           have
           a
           circle
           of
           Equator
           ,
           that
           may
           be
           fitted
           to
           the
           half
           circle
           ,
           and
           where
           you
           may
           have
           alwayes
           a
           space
           ready
           made
           for
           it's
           hour
           .
        
         
           
             25
          
           
             To
             mark
             the
             houres
             after
             the
             Manner
             of
             the
             Iewes
             .
          
        
      
       
       
         
           
             
               24
            
             
               for
               the
               houres
               after
               the
               Italian
               way
               .
            
          
        
         
         
           
             Figure
             25
             ,
          
           To
           mark
           the
           hours
           after
           the
           manner
           of
           the
           Ancients
           or
           the
           Jewes
           .
        
         
           YOu
           must
           know
           first
           that
           it
           would
           be
           very
           troublesome
           to
           draw
           in
           the
           superficies
           of
           the
           Dyall
           ,
           the
           lines
           of
           this
           kind
           of
           hours
           in
           such
           a
           manner
           as
           that
           they
           might
           be
           alwayes
           just
           and
           right
           in
           theory
           ,
           all
           the
           year
           long
           .
        
         
           And
           therefore
           it
           is
           sufficient
           to
           draw
           them
           just
           by
           demonstration
           in
           three
           points
           onely
           ,
           
             viz
             ,
          
           in
           their
           points
           of
           both
           ends
           ,
           and
           of
           the
           middle
           ,
           which
           are
           the
           points
           of
           those
           circles
           that
           appear
           the
           greatest
           above
           the
           Horizon
           being
           parallel
           to
           the
           Equator
           ,
           and
           of
           the
           Equator
           it self
           .
        
         
           The
           rest
           goes
           as
           it
           may
           ,
           and
           therefore
           it
           may
           be
           said
           ,
           that
           the
           lines
           of
           such
           hours
           traced
           in
           this
           manner
           are
           false
           in
           the
           rest
           of
           their
           length
           ,
           yet
           Curiositie
           makes
           them
           passe
           for
           current
           .
        
         
           Wherefore
           to
           mark
           this
           kind
           of
           lines
           of
           hours
           .
        
         
           The
           higher
           figure
           4
           shewes
           which
           way
           you
           must
           make
           this
           half
           Circle
           to
           turn
           about
           ,
           
             viz.
          
           about
           a
           straight
           axeltree
           line
           placed
           levell
           in
           the
           center
           of
           the
           Axel-tree
           of
           the
           Dyall
           .
        
         
           And
           to
           be
           short
           ,
           set
           up
           and
           make
           very
           fast
           a
           rod
           in
           a
           straight
           line
           passing
           to
           the
           center
           O
           ,
           and
           let
           it
           be
           first
           within
           the
           joynt
           of
           the
           axeltree
           rod
           ,
           secondly
           let
           it
           be
           level
           ,
           as
           the
           figures
           do
           shew
           of
           a
           plummet
           P.
           and
           of
           a
           level
           A
           ,
           this
           being
           done
           ,
           tye
           some
           strings
           with
           a
           loose
           knot
           to
           this
           rod
           so
           levelled
           NL
           as
           you
           see
           NR
           ,
           and
           LT.
           
        
         
           Take
           the
           string
           from
           about
           the
           center
           O
           ,
           stretch
           it
           out
           in
           a
           direct
           or
           straight
           line
           from
           the
           center
           O
           to
           one
           of
           the
           
           points
           of
           hour
           ,
           after
           the
           French
           way
           ,
           of
           the
           Equinoctial
           line
           of
           the
           Dyall
           ,
           for
           example
           to
           the
           point
           of
           1
           hour
           ,
           as
           you
           see
           the
           string
           OI
           .
        
         
           This
           string
           being
           thus
           strecht
           out
           ,
           take
           the
           other
           strings
           of
           one
           or
           
           th'other
           end
           NL
           ,
           and
           Crosse
           over
           this
           string
           OI
           with
           them
           ,
           and
           so
           go
           and
           mark
           many
           points
           in
           the
           superficies
           of
           the
           Dyall
           ,
           as
           TIR
           .
        
         
           Draw
           an
           obscure
           line
           by
           those
           points
           as
           TIR
           ,
           it
           is
           a
           line
           of
           hours
           after
           the
           manner
           of
           the
           Ancients
           or
           the
           Jews
           ,
           do
           the
           like
           with
           the
           other
           hours
           and
           half
           hours
           of
           the
           Equinoctial
           line
           .
        
         
           If
           you
           leave
           a
           rod
           in
           the
           Dyall
           ,
           as
           NOL
           ,
           the
           shadow
           thereof
           will
           go
           and
           shew
           these
           hours
           continually
           at
           length
           ,
           if
           you
           will
           not
           leave
           it
           in
           ,
           the
           button
           or
           center
           O
           of
           the
           axeltree
           of
           the
           Dyall
           will
           shew
           them
           .
        
      
       
       
         
           
             
               26
            
             
               for
               the
               hight
               of
               the
               sun
               .
            
          
        
         
         
         
           
             Figure
             26.
             
          
           How
           to
           mark
           the
           Elevation
           of
           the
           Sun
           above
           the
           Horizon
           .
        
         
           THE
           higher
           fig.
           3.
           shews
           which
           way
           you
           must
           turn
           the
           half
           circle
           ,
           
             viz.
          
           about
           a
           straight
           axel-line
           hanging
           down
           right
           .
        
         
           Set
           up
           your
           half
           circle
           ,
           so
           that
           it
           may
           turn
           like
           a
           weather-cock
           about
           a
           rod
           hanging
           down
           right
           ,
           or
           plum
           ,
           above
           or
           below
           the
           axeltree
           of
           the
           Dyal
           ,
           it
           matters
           not
           which
           .
        
         
           VVhilest
           you
           turn
           it
           thus
           as
           it
           is
           above
           said
           ,
           cause
           in
           the
           mean
           time
           the
           string
           comming
           from
           the
           center
           O
           to
           passe
           by
           one
           of
           the
           degrees
           of
           the
           edge
           of
           the
           circle
           ;
           and
           make
           the
           string
           shorter
           or
           longer
           as
           need
           shall
           require
           ,
           mark
           with
           it
           many
           several
           points
           in
           the
           superficies
           of
           the
           Dyal
           ,
           according
           as
           you
           see
           them
           rankt
           one
           by
           an
           other
           ,
           in
           four
           places
           .
        
         
           Draw
           a
           small
           or
           obscure
           line
           through
           all
           these
           points
           ,
           and
           this
           will
           be
           one
           of
           the
           lines
           of
           the
           Elevation
           of
           the
           Sun
           .
        
         
           Count
           the
           Degrees
           in
           the
           edge
           of
           the
           circle
           ,
           beginning
           at
           the
           first
           of
           the
           beam
           which
           is
           level
           ,
           and
           ending
           at
           the
           90.
           
           Beam
           which
           is
           down
           right
           or
           plum
           .
        
         
           Mark
           in
           the
           line
           of
           the
           Dyal
           ,
           the
           number
           of
           the
           Degrees
           of
           the
           border
           of
           the
           circle
           ,
           where
           the
           string
           passes
           that
           hath
           mark't
           the
           points
           of
           that
           line
           ,
           and
           so
           of
           all
           the
           others
           ,
           and
           the
           shadow
           of
           the
           button
           of
           the
           axeltree
           which
           is
           in
           the
           center
           of
           the
           circle
           ,
           will
           shew
           the
           Elevation
           of
           the
           Sum
           above
           the
           Horizon
           .
        
      
       
       
         
           
             Figure
             27
             :
          
           How
           to
           mark
           the
           Sun
           rising
           ,
           or
           East
           rising
           of
           the
           Sun
           .
        
         
           THE
           figure
           2
           above
           shews
           how
           you
           must
           place
           the
           half
           circle
           ,
           
             viz.
          
           parallel
           unto
           the
           Horizon
           ,
           I
           would
           not
           put
           a
           levell
           to
           it
           to
           avoid
           confusion
           .
           It
           shews
           also
           that
           one
           of
           the
           Diameters
           of
           the
           circle
           must
           be
           set
           within
           the
           center
           of
           the
           Dyal
           ,
           that
           is
           to
           say
           ,
           thar
           it
           must
           go
           directly
           from
           the
           south
           to
           the
           North
           ,
           and
           accordingly
           the
           Diameter
           which
           is
           perpendicular
           to
           it
           ,
           will
           go
           from
           East
           to
           West
           .
        
         
           When
           your
           circle
           is
           set
           fast
           in
           this
           position
           ,
           let
           a
           plummet
           op
           in
           the
           lower
           figure
           hang
           from
           the
           center
           O.
           
        
         
           This
           being
           done
           ,
           from
           each
           point
           of
           Degree
           of
           the
           edge
           of
           the
           circle
           ,
           as
           from
           x
           and
           from
           z.
           mark
           with
           a
           string
           XT
           or
           ZR
           .
           many
           points
           in
           the
           superficies
           of
           the
           Dyal
           .
        
         
           Draw
           a
           small
           or
           obscure
           line
           through
           these
           points
           ,
           as
           TY
           or
           SR.
           it
           is
           a
           line
           of
           the
           Suns
           Eastrising
           -
        
         
           Mark
           in
           it
           the
           number
           of
           Degrees
           of
           the
           point
           of
           the
           circle
           from
           whence
           the
           string
           comes
           ,
           according
           as
           you
           will
           count
           them
           ,
           to
           begin
           either
           from
           the
           East
           ,
           or
           from
           the
           South
           .
           And
           so
           of
           all
           the
           other
           Degrees
           accordingly
           .
        
         
           And
           the
           shadow
           of
           the
           button
           O
           will
           shew
           which
           way
           the
           sight
           of
           the
           Sun
           comes
           upon
           the
           Dyal
           .
        
         
           I
           will
           take
           here
           occasion
           to
           tell
           you
           ,
           that
           if
           for
           some
           reason
           or
           other
           ,
           you
           could
           observe
           ,
           in
           one
           and
           the
           same
           day
           ,
           but
           two
           shadows
           of
           the
           Sun
           in
           stead
           of
           three
           ,
           as
           we
           have
           said
           in
           the
           placing
           of
           the
           axeltree
           in
           the
           Dyal
           ,
           the
           declining
           of
           the
           Sun
           in
           that
           day
           ,
           will
           serve
           you
           for
           a
           third
           shadow
           ,
           or
           else
           two
           other
           shadows
           observed
           in
           an
           other
           day
           .
           I
           mean
           you
           may
           find
           equally
           the
           placing
           of
           the
           axeltree
           by
           one
           or
           other
           of
           those
           ways
           above
           mentioned
           ,
           and
           with
           3
           shadows
           ;
           and
           with
           2
           shadows
           ,
           and
           the
           declining
           of
           the
           Sun
           in
           that
           day
           ,
           and
           with
           4
           shadows
           ,
           two
           of
           one
           day
           ,
           and
           two
           of
           an
           other
           ,
           which
           are
           three
           wayes
           that
           come
           all
           to
           one
           .
        
         
           
             27
          
           
             for
             the
             Eastrising
             of
             the
             sun
             .
          
        
      
       
       
         
           
             
               28
            
          
        
         
         
           Figure
           28.
           
        
         
           I
           do
           not
           specifie
           in
           this
           volum
           these
           kinds
           of
           flat
           Dyals
           ,
           wherein
           you
           may
           work
           without
           knobs
           or
           middle
           rule
           :
           And
           where
           you
           may
           draw
           the
           Equinoctial
           line
           ;
           trace
           out
           and
           divide
           the
           circle
           Equator
           :
           in
           a
           word
           ,
           where
           you
           may
           do
           all
           :
           yea
           and
           in
           the
           very
           superficies
           of
           the
           Dyal
           ,
           you
           may
           easily
           come
           to
           know
           them
           you
           self
           ,
           by
           putting
           this
           universall
           way
           into
           practice
           .
        
         
           Here
           is
           onely
           a
           way
           how
           to
           trace
           out
           all
           the
           twelue
           lines
           of
           the
           hours
           equal
           ,
           after
           the
           French
           way
           ,
           in
           the
           flat
           Dyals
           where
           the
           axeltree
           meets
           the
           superficies
           athwart
           in
           the
           space
           that
           you
           work
           in
           ,
           so
           that
           you
           shall
           have
           no
           need
           of
           a
           greater
           place
           .
           And
           what
           I
           have
           already
           said
           ,
           and
           what
           I
           am
           now
           going
           to
           say
           again
           ,
           will
           serve
           to
           find
           out
           the
           way
           to
           do
           the
           like
           in
           all
           kinds
           of
           Dyals
           universally
           .
        
         
           When
           you
           have
           drawn
           upon
           your
           Dyal
           the
           Equinoctial
           line
           M
           12
           M
           ,
           drawn
           conveniently
           and
           divided
           the
           circle
           Equator
           Q
           12
           Q
           bring
           to
           the
           Equinoctial
           line
           ,
           the
           beam
           of
           the
           12
           hours
           Q
           ,
           12.
           
           Draw
           of
           both
           sides
           of
           the
           Equator
           ,
           and
           from
           the
           Equinoctial
           line
           a
           straight
           line
           MQ
           parallel
           to
           the
           beam
           of
           12.
           hours
           O
           12.
           bring
           the
           beams
           of
           the
           other
           hours
           to
           the
           first
           ,
           which
           they
           shall
           find
           of
           the
           Equinoctial
           in
           rt
           :
           and
           of
           MQ
           in
           c
           ,
           d●g
           ,
           Q
           ,
           Bring
           in
           the
           Dyal
           the
           line
           of
           the
           twelve
           hours
           B.
           12.
           draw
           by
           the
           point
           M
           ,
           of
           the
           Equinoctial
           line
           ,
           and
           from
           the
           center
           of
           the
           Dyal
           B
           a
           straight
           line
           ML
           parallel
           to
           the
           line
           of
           twelve
           hours
           B
           12
           ;
           make
           upon
           this
           line
           ML
           and
           upon
           the
           point
           M
           a
           triangle
           LMN
           like
           to
           the
           triangle
           in
           the
           aire
           OB
           12.
           and
           let
           the
           angles
           of
           these
           triangles
           in
           the
           points
           L
           and
           B
           be
           equal
           one
           unto
           an
           other
           ,
           Carry
           the
           spaces
           Mq
           ,
           Mg
           ,
           Md
           ,
           Mc
           ,
           from
           the
           straight
           line
           MQ
           into
           the
           straight
           line
           MN
           ,
           
             viz.
          
           from
           M
           into
           N
           ,
           into
           u
           ,
           into
           i
           ,
           into
           o
           ,
           bring
           by
           the
           points
           
           N
           ,
           u
           ,
           i
           ,
           o
           ,
           some
           straight
           lines
           NL
           ,
           ub
           ,
           if
           ,
           oh
           ,
           parallel
           to
           the
           side
           ,
           NL
           of
           the
           triangle
           LMN
           :
           Carry
           from
           the
           center
           of
           the
           Dyal
           B
           by
           the
           points
           r
           ,
           t
           ,
           h
           ,
           f
           ,
           o
           ,
           L
           ,
           Some
           straight
           lines
           ,
           BL
           ,
           Bh
           ,
           Bf
           ,
           Bh
           ,
           Bt
           ,
           Br
           ;
           These
           are
           such
           lines
           of
           hours
           as
           you
           may
           continue
           beyond
           the
           center
           B
           ,
           and
           mark
           them
           according
           to
           their
           orders
           .
        
         
           THE
           END
           .
        
         
      
    
     
       
         Notes, typically marginal, from the original text
         
           Notes for div A35744e-3300
           
             i.e.
             
               That
               are
               made
               without
               any
               aim
               ,
               or
               heed
               .