Seven philosophical problems and two propositions of geometry by Thomas Hobbes of Malmesbury ; with an apology for himself and his writings.
         Hobbes, Thomas, 1588-1679.
      
       
         
           1682
        
      
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             Seven philosophical problems and two propositions of geometry by Thomas Hobbes of Malmesbury ; with an apology for himself and his writings.
             Hobbes, Thomas, 1588-1679.
          
           [6], 84 p., 1 folded leaf of plates.
           
             Printed for William Crook,
             London :
             1682.
          
           
             "Dedicated to the King in the year 1662."
             Also issued separately.
             Reproduction of original in the Harvard University Library.
          
        
      
    
     
       
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         eng
      
       
         
           Physics -- Early works to 1800.
           Geometry -- Early works to 1800.
        
      
    
     
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           SEVEN
           Philosophical
           Problems
           ,
           AND
           TWO
           PROPOSITIONS
           OF
           GEOMETRY
           .
        
         
           By
           Thomas
           Hobbes
           of
           Malmesbury
           .
        
         
           With
           an
           Apology
           for
           Himself
           ,
           and
           his
           WRITINGS
           .
        
         
           Dedicated
           to
           the
           KING
           ,
           in
           the
           year
           1662.
           
        
         
           LONDON
           :
           Printed
           for
           
             William
             Crook
          
           at
           the
           Green-Dragon
           without
           Temple-Bar
           ,
           1682.
           
        
      
       
         
         
         
           TO
           THE
           KING
           .
        
         
           THat
           which
           I
           do
           here
           most
           humbly
           present
           to
           Your
           Sacred
           Majesty
           ,
           is
           the
           best
           Part
           of
           my
           Meditations
           upon
           the
           Natural
           Causes
           of
           Events
           ,
           both
           of
           such
           as
           are
           commonly
           known
           ,
           and
           of
           such
           as
           have
           been
           of
           late
           artificially
           exhibited
           by
           the
           Curious
           .
        
         
           
             They
             are
             ranged
             under
             seven
             Heads
             .
          
           1.
           
           Problems
           of
           Gravity
           .
           2.
           
           Problems
           of
           Tides
           .
           3.
           
           Problems
           of
           Vacuum
           .
           4.
           
           Problems
           of
           Heat
           .
           5.
           
           Problems
           of
           Hard
           and
           Soft
           .
           6.
           
           Problems
           of
           Wind
           and
           Weather
           .
           7.
           
           Problems
           of
           Motion
           Perpendicular
           ,
           and
           Oblique
           ,
           
           
             &c.
             
             To
             which
             I
             have
             added
             ,
          
           Two
           Propositions
           of
           Geometry
           ;
           
             One
             is
          
           ,
           The
           Duplication
           of
           the
           Cube
           ,
           hitherto
           sought
           in
           vain
           ;
           
             The
             other
          
           ,
           A
           Detection
           of
           the
           absurd
           Use
           of
           Arithmetick
           ,
           as
           it
           is
           now
           applied
           to
           Geometry
           .
        
         
           The
           Doctrine
           of
           Natural
           Causes
           hath
           not
           infallible
           and
           evident
           Principles
           .
           For
           there
           is
           no
           Effect
           which
           the
           Power
           of
           God
           cannot
           produce
           by
           many
           several
           ways
           .
        
         
           But
           seeing
           all
           Effects
           are
           produced
           by
           Motion
           ,
           he
           that
           supposing
           some
           one
           or
           more
           Motions
           can
           derive
           from
           them
           the
           necessity
           of
           that
           Effect
           whose
           Cause
           is
           required
           ,
           has
           done
           all
           that
           is
           to
           be
           expected
           from
           Natural
           Reason
           .
           And
           though
           he
           prove
           not
           that
           the
           thing
           was
           thus
           produced
           ,
           yet
           he
           proves
           that
           thus
           it
           may
           be
           produced
           ,
           when
           the
           Materials
           ,
           and
           the
           power
           of
           Moving
           is
           in
           our
           hands
           ;
           which
           is
           as
           useful
           as
           if
           the
           Causes
           themselves
           were
           known
           .
           And
           notwithstanding
           the
           absence
           
           of
           rigorous
           Demonstration
           ,
           this
           Contemplation
           of
           Nature
           (
           if
           not
           rendred
           obscure
           by
           empty
           terms
           )
           is
           the
           most
           Noble
           Imployment
           of
           the
           Mind
           that
           can
           be
           ,
           to
           such
           as
           are
           at
           leisure
           from
           their
           necessary
           Business
           .
        
         
           This
           that
           I
           have
           done
           I
           know
           is
           anunworthy
           Present
           to
           be
           offered
           to
           a
           KING
           ,
           though
           considered
           (
           as
           God
           considers
           Offerings
           )
           together
           with
           the
           Mind
           and
           Fortune
           of
           the
           Offerer
           ,
           I
           hope
           will
           not
           be
           to
           Your
           Majesty
           unacceptable
           .
        
         
           But
           that
           which
           I
           chiefly
           consider
           in
           it
           is
           ,
           that
           my
           Writing
           should
           be
           tryed
           by
           Your
           Majesties
           Excellent
           Reason
           untainted
           with
           the
           Language
           that
           has
           been
           invented
           or
           made
           use
           of
           by
           Men
           when
           they
           were
           puzzled
           ;
           and
           who
           is
           acquainted
           with
           all
           the
           Experiments
           of
           the
           time
           ;
           and
           whose
           approbation
           (
           if
           I
           have
           the
           good
           Fortune
           to
           obtain
           it
           )
           will
           protect
           my
           reasoning
           from
           the
           Contempt
           of
           my
           Adversaries
           .
        
         
         
           I
           will
           not
           break
           the
           custom
           of
           joyning
           to
           my
           Offering
           a
           Prayer
           ;
           And
           it
           is
           ,
           
             That
             Your
             Majesty
             will
             be
             pleased
             to
             pardon
             this
             following
             short
             Apology
             for
             my
          
           Leviathan
           .
           Not
           that
           I
           rely
           upon
           Apologies
           ,
           but
           upon
           Your
           Majesties
           most
           Gracious
           General
           Pardon
           .
        
         
           That
           which
           is
           in
           it
           of
           Theology
           ,
           contrary
           to
           the
           general
           Current
           of
           Divines
           ,
           is
           not
           put
           there
           as
           my
           Opinion
           ,
           but
           propounded
           with
           submission
           to
           those
           that
           have
           the
           Power
           Ecclesiastical
           .
        
         
           I
           did
           never
           after
           ,
           either
           in
           Writing
           or
           Discourse
           ,
           maintain
           it
           .
        
         
           There
           is
           nothing
           in
           it
           against
           Episcopacy
           ;
           I
           cannot
           therefore
           imagine
           what
           reason
           any
           Episcopal-man
           can
           have
           to
           speak
           of
           me
           (
           as
           I
           hear
           some
           of
           them
           do
           )
           as
           of
           an
           Atheist
           ,
           or
           man
           of
           no
           Religion
           ,
           unless
           it
           be
           for
           making
           the
           Authority
           of
           the
           Church
           wholly
           upon
           the
           Regal
           Power
           ;
           which
           I
           hope
           Your
           Majesty
           will
           think
           is
           neither
           Atheism
           nor
           Heresie
           .
        
         
         
           But
           what
           had
           I
           to
           do
           to
           meddle
           with
           matters
           of
           that
           nature
           ,
           seeing
           Religion
           is
           not
           Philosophy
           ,
           but
           Law
           ?
        
         
           It
           was
           written
           in
           a
           time
           when
           the
           pretence
           of
           Christ's
           Kingdom
           was
           made
           use
           of
           for
           the
           most
           horrid
           Actions
           that
           can
           be
           imagined
           ;
           And
           it
           was
           in
           just
           Indignation
           of
           that
           ,
           that
           I
           desired
           to
           see
           the
           bottom
           of
           that
           Doctrine
           of
           the
           Kingdom
           of
           Christ
           ,
           which
           divers
           Ministers
           then
           Preached
           for
           a
           Pretence
           to
           their
           Rebellion
           ;
           which
           may
           reasonably
           extenuate
           ,
           though
           not
           excuse
           the
           writing
           of
           it
           .
        
         
           There
           is
           therefore
           no
           ground
           for
           so
           great
           a
           Calamny
           in
           my
           writing
           .
           There
           is
           no
           sign
           of
           it
           in
           my
           Life
           ;
           and
           for
           my
           Religion
           ,
           when
           I
           was
           at
           the
           point
           of
           Death
           at
           St.
           Germains
           ,
           the
           Bishop
           of
           Durham
           can
           bear
           witness
           of
           it
           ,
           if
           he
           be
           asked
           .
           Therefore
           ,
           I
           most
           humbly
           beseech
           Your
           Sacred
           Majesty
           not
           to
           believe
           so
           ill
           of
           me
           upon
           reports
           ,
           that
           proceed
           often
           (
           and
           may
           do
           so
           now
           )
           from
           the
           displeasure
           which
           commonly
           ariseth
           from
           difference
           in
           Opinion
           ;
           
           nor
           to
           think
           the
           worse
           of
           me
           ,
           if
           snatching
           up
           all
           the
           Weapons
           to
           fight
           against
           Your
           Enemies
           ,
           I
           lighted
           upon
           one
           that
           had
           a
           double
           edge
           .
        
         
           
             Your
             Majesties
             Poor
             and
             most
             Loyal
             Subject
             ,
             THOMAS
             ▪
             HOBBES
             .
          
        
      
       
         
         
         
           
        
      
    
     
       
         
         
         
           PHILOSOPHICAL
           PROBLEMS
           ▪
        
         
           CHAP.
           I.
           Problems
           of
           Gravity
           .
        
         
           
             A.
             
          
           
             WHat
             may
             be
             the
             cause
             ,
             think
             you
             ,
             that
             stones
             ,
             and
             other
             bodies
             ,
             thrown
             upward
             ,
             or
             carried
             up
             and
             left
             to
             their
             liberty
             ,
             fall
             down
             again
             (
             for
             ought
             a
             man
             can
             see
             )
             of
             their
             own
             accord
             ?
             I
             do
             not
             think
             (
             with
             the
             old
             Philosophers
             )
             that
             they
             have
             any
             love
             to
             the
             Earth
             ,
             or
             are
             sullen
             ,
             that
             they
             will
             neither
             go
             nor
             stay
             .
             And
             yet
             I
             cannot
             imagine
             what
             body
             there
             is
             above
             that
             should
             drive
             them
             back
             .
          
        
         
           
             B.
             
          
           
             For
             my
             part
             ,
             I
             believe
             the
             cause
             of
             their
             descending
             is
             not
             in
             any
             natural
             appetite
             of
             the
             bodies
             that
             descend
             ,
             but
             rather
             that
             the
             Globe
             of
             the
             Earth
             hath
             some
             special
             motion
             ,
             by
             the
             which
             it
             more
             easily
             casteth
             off
             the
             Air
             ,
             than
             it
             doth
             other
             bodies
             .
             And
             then
             this
             descent
             of
             those
             we
             
             call
             heavy
             bodies
             ,
             must
             of
             necessity
             follow
             ;
             unless
             there
             be
             some
             empty
             spaces
             in
             the
             world
             to
             receive
             them
             .
             For
             when
             the
             Air
             is
             thrown
             off
             from
             the
             Earth
             ,
             somewhat
             must
             come
             into
             the
             place
             of
             it
             ,
             (
             in
             case
             the
             world
             be
             full
             )
             and
             it
             must
             be
             those
             things
             which
             are
             hardliest
             cast
             off
             ,
             that
             is
             those
             things
             which
             we
             say
             are
             heavy
             .
          
        
         
           
             A.
             
          
           
             But
             suppose
             there
             be
             no
             place
             empty
             (
             for
             I
             will
             defer
             the
             Question
             till
             anon
             )
             how
             can
             the
             Earth
             cast
             off
             either
             the
             Air
             ,
             or
             any
             thing
             else
             ?
          
        
         
           
             B.
             
          
           
             I
             shall
             shew
             you
             how
             ,
             and
             that
             by
             a
             familiar
             Example
             .
             If
             you
             lay
             both
             your
             hands
             upon
             a
             Basen
             with
             water
             in
             it
             ,
             how
             little
             soever
             ,
             and
             move
             it
             circularly
             ,
             and
             continue
             that
             motion
             for
             a
             while
             ,
             and
             you
             shall
             see
             the
             water
             rise
             upon
             the
             sides
             ,
             and
             fly
             over
             ;
             by
             which
             you
             may
             be
             assured
             that
             there
             is
             a
             kind
             of
             circulating
             motion
             ,
             which
             would
             cast
             off
             such
             bodies
             as
             are
             contiguous
             to
             the
             body
             so
             moved
             .
          
        
         
           
             A.
             
          
           
             I
             know
             very
             well
             there
             is
             ;
             and
             it
             is
             the
             same
             motion
             which
             Country
             people
             use
             to
             purge
             their
             Corn
             ;
             For
             the
             Chaff
             and
             Straws
             ,
             by
             casting
             the
             Grain
             to
             the
             side
             of
             the
             Seive
             ,
             will
             come
             towards
             the
             middle
             .
             But
             I
             would
             see
             the
             Figure
             .
          
        
         
           
             B.
             
          
           
             Here
             it
             is
             .
             There
             is
             a
             Circle
             pricked
             out
             ,
             whose
             Center
             is
             A
             ,
             and
             three
             less
             Circles
             ,
             whose
             Centers
             are
             B
             ,
             C
             ,
             D
             ;
             let
             
             every
             one
             of
             them
             represent
             the
             Earth
             ,
             as
             it
             goeth
             from
             B
             to
             C
             ,
             and
             from
             C
             to
             D
             ,
             always
             touching
             the
             uttermost
             Circle
             ,
             and
             throwing
             off
             the
             Air
             ,
             as
             is
             marked
             at
             E
             and
             F.
             And
             if
             the
             world
             were
             not
             full
             ,
             there
             would
             follow
             by
             this
             scattering
             of
             the
             Air
             ,
             a
             great
             deal
             of
             space
             left
             empty
             .
             But
             supposing
             the
             world
             full
             ,
             there
             must
             be
             a
             perpetual
             shifting
             of
             the
             Air
             ,
             one
             part
             into
             the
             place
             of
             another
             .
          
        
         
           
             A.
             
          
           
             But
             what
             makes
             a
             stone
             come
             down
             ,
             suppose
             from
             G
             ?
          
        
         
           
             B.
             
          
           
             If
             the
             Air
             be
             thrown
             up
             beyond
             G
             ,
             it
             will
             follow
             ,
             that
             at
             the
             last
             ,
             if
             the
             motion
             be
             continued
             ,
             all
             the
             Air
             will
             be
             above
             G
             ,
             that
             is
             ,
             above
             the
             stone
             ;
             which
             cannot
             be
             ,
             till
             the
             stone
             be
             at
             the
             Earth
             .
          
        
         
           
             A.
             
          
           
             But
             why
             comes
             it
             down
             still
             with
             encreasing
             swiftness
             ?
          
        
         
           
             B.
             
          
           
             Because
             as
             it
             descends
             ,
             and
             is
             already
             in
             motion
             ,
             it
             receiveth
             a
             new
             impression
             from
             the
             same
             cause
             ,
             which
             is
             the
             Air
             ,
             whereof
             as
             part
             mounteth
             ,
             part
             also
             must
             descend
             ,
             supposing
             as
             we
             have
             done
             the
             plenitude
             of
             the
             world
             .
             For
             ,
             as
             you
             may
             observe
             by
             the
             Figure
             ,
             the
             motion
             of
             the
             Earth
             ,
             according
             to
             the
             Diameter
             of
             the
             uttermost
             Circle
             ,
             is
             progressive
             ;
             and
             so
             the
             whole
             motion
             is
             compounded
             of
             two
             motions
             ,
             one
             circular
             ,
             and
             the
             other
             progressive
             ;
             and
             consequently
             the
             
             Air
             ascends
             and
             circulates
             at
             once
             .
             And
             because
             the
             stone
             descending
             receiveth
             a
             new
             pressure
             in
             every
             point
             of
             its
             way
             ,
             the
             motion
             thereof
             must
             needs
             be
             accelerated
             .
          
        
         
           
             A.
             
          
           
             'T
             is
             true
             ;
             For
             it
             will
             be
             accelerated
             equally
             in
             equal
             times
             ;
             and
             the
             way
             it
             makes
             will
             encrease
             in
             a
             double
             proportion
             to
             the
             times
             ,
             as
             hath
             heretofore
             been
             demonstrated
             by
             Galileo
             .
             I
             see
             the
             solution
             now
             of
             an
             Experiment
             ,
             which
             before
             did
             not
             a
             little
             puzzle
             me
             .
             You
             know
             that
             if
             two
             plummets
             hang
             by
             two
             strings
             of
             equal
             length
             ,
             and
             you
             remove
             them
             from
             the
             perpendicular
             equally
             ,
             I
             mean
             in
             equal
             angles
             ,
             and
             then
             let
             them
             go
             ,
             they
             will
             make
             their
             turns
             and
             returns
             together
             ,
             and
             in
             equal
             times
             ;
             And
             though
             the
             arches
             they
             describe
             grow
             continually
             less
             and
             less
             ,
             yet
             the
             times
             they
             spend
             in
             the
             greater
             arches
             ,
             will
             still
             be
             equal
             to
             the
             time
             they
             spend
             in
             the
             lesser
             .
          
        
         
           
             B.
             
          
           
             'T
             is
             true
             .
             Do
             you
             find
             any
             Experiment
             to
             the
             contrary
             ?
          
        
         
           
             A.
             
          
           
             Yes
             ;
             For
             if
             you
             remove
             one
             of
             the
             plummets
             from
             the
             perpendicular
             ,
             so
             as
             (
             for
             example
             )
             to
             make
             an
             angle
             with
             the
             perpendicular
             of
             80
             degrees
             ,
             and
             the
             other
             so
             as
             to
             make
             an
             angle
             of
             60
             degrees
             ,
             they
             will
             not
             make
             their
             turns
             and
             returns
             in
             equal
             times
             .
          
        
         
           
             B.
             
          
           
             And
             what
             say
             you
             is
             the
             cause
             of
             this
             ?
          
        
         
           
           
             A.
             
          
           
             Because
             the
             arches
             are
             the
             spaces
             which
             these
             two
             motions
             describe
             ,
             they
             must
             be
             in
             double
             proportion
             to
             their
             own
             times
             ;
             which
             cannot
             be
             ,
             unless
             they
             be
             let
             go
             from
             equal
             altitudes
             ,
             that
             is
             ,
             from
             equal
             angles
             .
          
        
         
           
             B.
             
          
           
             'T
             is
             right
             ;
             and
             the
             Experiment
             does
             not
             cross
             ,
             but
             confirm
             the
             equality
             of
             the
             times
             in
             all
             the
             arches
             they
             describe
             ,
             even
             from
             90
             degrees
             to
             the
             least
             part
             of
             one
             degree
             .
          
        
         
           
             A.
             
          
           
             But
             is
             it
             not
             too
             bold
             ,
             if
             not
             extravagant
             ,
             an
             assertion
             ,
             to
             say
             the
             Earth
             is
             moved
             as
             a
             man
             shakes
             a
             Basen
             or
             a
             Seive
             ?
             Does
             not
             the
             Earth
             move
             from
             West
             to
             East
             every
             day
             once
             ,
             upon
             his
             own
             Center
             ,
             and
             in
             the
             Ecliptick
             Circle
             once
             a
             year
             ?
             And
             now
             you
             give
             it
             another
             odd
             motion
             ;
             How
             can
             all
             these
             consist
             in
             one
             and
             the
             same
             body
             ?
          
        
         
           
             B.
             
          
           
             Well
             enough
             .
             If
             you
             be
             a
             Shipboard
             under
             sail
             ,
             do
             not
             you
             go
             with
             the
             Ship
             ?
             Cannot
             you
             also
             walk
             upon
             the
             Deck
             ?
             Cannot
             every
             drop
             of
             bloud
             move
             at
             the
             same
             time
             in
             your
             veins
             ?
             How
             many
             motions
             now
             do
             you
             assign
             to
             one
             and
             the
             same
             drop
             of
             bloud
             ?
             Nor
             is
             it
             so
             extravagant
             a
             thing
             to
             attribute
             to
             the
             Earth
             this
             kind
             of
             motion
             ;
             but
             that
             I
             believe
             if
             we
             certainly
             knew
             what
             motion
             it
             is
             that
             causeth
             the
             descent
             of
             bodies
             ,
             we
             should
             find
             it
             either
             the
             same
             ,
             or
             more
             extravagant
             .
             But
             seeing
             it
             can
             be
             nothing
             above
             that
             
             worketh
             this
             effect
             ,
             it
             must
             be
             the
             Earth
             it self
             that
             does
             it
             ;
             and
             if
             the
             Earth
             ,
             then
             you
             can
             imagine
             no
             other
             motion
             to
             do
             it
             withal
             ,
             but
             this
             ;
             And
             you
             will
             wonder
             more
             ,
             when
             by
             the
             same
             motion
             I
             shall
             give
             you
             a
             probable
             account
             of
             the
             causes
             of
             very
             many
             other
             works
             of
             Nature
             .
          
        
         
           
             A.
             
          
           
             But
             what
             part
             of
             the
             Heaven
             do
             you
             suppose
             the
             Poles
             of
             your
             pricked
             Circle
             point
             to
             ?
          
        
         
           
             B.
             
          
           
             I
             suppose
             them
             to
             be
             the
             same
             with
             the
             Poles
             of
             the
             Ecliptick
             .
             For
             ,
             seeing
             the
             Axis
             of
             the
             Earth
             in
             this
             Nation
             ,
             and
             in
             the
             annual
             motion
             keeps
             parallel
             to
             it self
             ,
             the
             Axis
             must
             in
             both
             motions
             be
             parallel
             as
             to
             sense
             .
             For
             ,
             the
             Circle
             which
             the
             Earth
             describes
             ,
             is
             not
             of
             visible
             magnitude
             at
             the
             distance
             it
             is
             from
             the
             Sun.
             
          
        
         
           
             A.
             
          
           
             Though
             I
             understand
             well
             enough
             how
             the
             Earth
             may
             make
             a
             stone
             descend
             very
             swiftly
             under
             the
             Ecliptick
             ,
             or
             not
             far
             from
             it
             ,
             where
             it
             throws
             off
             the
             Air
             perpendicularly
             ;
             yet
             about
             the
             Poles
             of
             the
             Circle
             methinks
             it
             should
             cast
             off
             the
             Air
             very
             weakly
             .
             I
             hope
             you
             will
             not
             say
             that
             bodies
             descend
             faster
             in
             places
             remote
             from
             the
             Poles
             ,
             than
             nearer
             to
             them
             .
          
        
         
           
             B.
             
          
           
             No
             ;
             but
             I
             ascribe
             it
             to
             the
             like
             motion
             in
             the
             Sun
             and
             Moon
             .
             For
             such
             motions
             meeting
             ,
             must
             needs
             cast
             the
             stream
             
             of
             the
             Air
             towards
             the
             Poles
             ;
             And
             then
             there
             will
             be
             the
             same
             necessity
             for
             the
             descent
             there
             ,
             that
             there
             is
             in
             other
             places
             ,
             though
             perhaps
             a
             little
             more
             slowly
             .
             For
             you
             may
             have
             observed
             that
             when
             it
             snows
             in
             the
             South
             Parts
             ,
             the
             flakes
             of
             Snow
             are
             not
             so
             great
             as
             in
             the
             North
             ;
             which
             is
             a
             probable
             sign
             they
             fall
             in
             the
             South
             from
             a
             greater
             height
             ,
             and
             consequently
             disperse
             themselves
             more
             ,
             as
             water
             does
             that
             falls
             down
             from
             a
             high
             and
             steep
             Rock
             .
          
        
         
           
             A.
             
          
           
             'T
             is
             not
             improbable
             .
          
        
         
           
             B.
             
          
           
             In
             natural
             causes
             all
             you
             are
             to
             expect
             is
             but
             probability
             ;
             which
             is
             better
             yet
             then
             making
             Gravity
             the
             cause
             ,
             when
             the
             cause
             of
             Gravity
             is
             that
             you
             desire
             to
             know
             ;
             and
             better
             then
             saying
             the
             Earth
             draws
             it
             ,
             when
             the
             Question
             is
             ,
             how
             it
             draws
             ?
          
        
         
           
             A.
             
          
           
             Why
             does
             the
             Earth
             cast
             off
             Air
             more
             easily
             than
             it
             does
             Water
             ,
             or
             any
             other
             heavy
             bodies
             ?
          
        
         
           
             B.
             
          
           
             It
             is
             indeed
             the
             Earth
             that
             casteth
             off
             that
             Air
             which
             is
             next
             unto
             it
             .
             But
             it
             is
             that
             Air
             which
             casteth
             off
             the
             next
             Air
             ;
             and
             so
             continually
             Air
             moveth
             Air
             ;
             which
             it
             can
             more
             easily
             do
             then
             any
             other
             thing
             ,
             because
             like
             bodies
             are
             more
             susceptible
             of
             one
             anothers
             motions
             ;
             as
             you
             may
             see
             in
             two
             Lute-strings
             equally
             strained
             ,
             what
             motion
             one
             
             string
             being
             stricken
             communicates
             to
             the
             Air
             ,
             the
             same
             will
             the
             other
             receive
             from
             the
             Air
             ;
             but
             strained
             to
             a
             differing
             note
             ,
             will
             be
             less
             ,
             or
             not
             at
             all
             moved
             .
             For
             there
             is
             no
             body
             but
             Air
             that
             hath
             not
             some
             internal
             ,
             though
             invisible
             motion
             of
             its
             parts
             .
             And
             it
             is
             that
             internal
             motion
             which
             distinguisheth
             all
             natural
             bodies
             one
             from
             another
             .
          
        
         
           
             A.
             
          
           
             What
             is
             the
             cause
             why
             certain
             Squibs
             ,
             though
             their
             substance
             be
             either
             Wood
             or
             other
             heavy
             matter
             ,
             made
             hollow
             and
             filled
             with
             Gunpowder
             ,
             which
             is
             also
             heavy
             ,
             do
             nevertheless
             when
             the
             Gunpowder
             is
             kindled
             ,
             fly
             upwards
             ?
          
        
         
           
             B.
             
          
           
             The
             same
             that
             keeps
             a
             man
             that
             swims
             from
             sinking
             ,
             though
             he
             be
             heavier
             then
             so
             much
             water
             ;
             He
             keeps
             himself
             up
             ,
             and
             goes
             forward
             by
             beating
             back
             the
             water
             with
             his
             Feet
             ;
             and
             so
             does
             a
             Squib
             ,
             by
             beating
             down
             the
             Air
             with
             the
             stream
             of
             the
             fired
             Gunpowder
             ,
             that
             proceeding
             from
             its
             Tail
             makes
             it
             recoil
             .
          
        
         
           
             A.
             
          
           
             Why
             does
             any
             Brass
             or
             Iron
             Vessel
             ,
             if
             it
             be
             hollow
             ,
             flote
             upon
             the
             water
             ,
             being
             so
             very
             heavy
             ?
          
        
         
           
             B.
             
          
           
             Because
             the
             Vessel
             and
             the
             Air
             in
             it
             ,
             taken
             as
             one
             body
             ,
             is
             more
             easily
             cast
             off
             than
             a
             body
             of
             water
             equal
             to
             it
             .
          
        
         
           
             A.
             
          
           
             How
             comes
             it
             to
             pass
             ,
             that
             a
             Fish
             (
             especially
             such
             a
             broad
             Fish
             as
             a
             Turbut
             or
             
             a
             Plaice
             ,
             which
             are
             broad
             and
             thin
             )
             in
             the
             bottom
             of
             the
             Sea
             ,
             perhaps
             a
             mile
             deep
             ,
             is
             not
             press'd
             to
             death
             with
             the
             weight
             of
             water
             that
             lies
             upon
             the
             back
             of
             it
             ?
          
        
         
           
             B.
             
          
           
             Because
             all
             heavy
             bodies
             descend
             towards
             one
             point
             ,
             which
             is
             the
             Center
             of
             the
             Earth
             ,
             and
             consequently
             the
             whole
             Sea
             descending
             at
             once
             does
             arch
             it self
             so
             ,
             as
             that
             the
             upper
             parts
             cannot
             press
             the
             parts
             next
             below
             them
             .
          
        
         
           
             A.
             
          
           
             It
             is
             evident
             ;
             Nor
             can
             there
             be
             possibly
             any
             weight
             ,
             as
             some
             suppose
             there
             is
             ,
             of
             a
             Cylinder
             of
             Air
             ,
             or
             Water
             ,
             or
             of
             any
             other
             liquid
             thing
             ,
             while
             it
             remains
             in
             its
             own
             Element
             ,
             or
             is
             sustained
             and
             inclosed
             in
             a
             Vessel
             ,
             by
             which
             one
             part
             cannot
             press
             the
             other
             .
          
        
      
       
         
         
           CHAP.
           II.
           Problems
           of
           Tides
           .
        
         
           
             A.
             
          
           
             WHat
             makes
             the
             Flux
             and
             Reflux
             of
             the
             Sea
             twice
             in
             a
             natural
             day
             ?
          
        
         
           
             B.
             
          
           
             We
             must
             come
             again
             to
             our
             Basen
             of
             water
             ;
             wherein
             you
             have
             seen
             ,
             whilst
             it
             was
             moved
             ,
             how
             the
             water
             mounteth
             up
             by
             the
             sides
             ,
             and
             withal
             goes
             circling
             round
             about
             .
             Now
             if
             you
             should
             fasten
             to
             the
             inside
             of
             the
             Basen
             some
             bar
             from
             the
             bottom
             to
             the
             top
             ,
             you
             would
             see
             the
             water
             ,
             instead
             of
             going
             on
             ,
             go
             back
             again
             from
             that
             bar
             ,
             ebbing
             ,
             and
             the
             water
             on
             the
             other
             side
             of
             the
             bar
             to
             do
             the
             same
             ,
             but
             in
             counter-time
             ;
             and
             consequently
             to
             be
             highest
             where
             the
             contrary
             streams
             meet
             together
             ,
             and
             then
             return
             again
             ,
             marking
             out
             four
             quarters
             of
             the
             Vessel
             ,
             two
             by
             their
             meeting
             ,
             which
             are
             the
             high
             waters
             ,
             and
             two
             by
             their
             retiring
             ,
             which
             are
             the
             low
             waters
             .
          
        
         
           
             A.
             
          
           
             What
             bar
             is
             that
             you
             find
             in
             the
             Ocean
             ,
             that
             stops
             the
             current
             of
             the
             water
             ,
             like
             that
             you
             make
             in
             the
             Basen
             ?
          
        
         
           
             B.
             
          
           
             You
             know
             that
             the
             main
             Ocean
             lies
             East
             and
             West
             ,
             between
             India
             and
             the
             
             Coast
             of
             America
             ;
             and
             again
             ,
             on
             the
             other
             side
             ,
             between
             America
             and
             India
             .
             If
             therefore
             the
             Earth
             have
             such
             a
             motion
             as
             I
             have
             supposed
             ,
             it
             must
             needs
             carry
             the
             current
             of
             the
             Sea
             East
             and
             West
             ;
             In
             which
             course
             ,
             the
             bar
             that
             stoppeth
             it
             is
             the
             South
             part
             of
             America
             ,
             which
             leaves
             no
             passage
             for
             the
             water
             ,
             but
             the
             narrow
             Streight
             of
             Magellan
             .
             The
             Tide
             rises
             therefore
             upon
             the
             Coast
             of
             America
             ;
             And
             the
             rising
             of
             the
             same
             in
             this
             part
             of
             the
             world
             proceedeth
             from
             the
             swelling
             chiefly
             of
             the
             water
             there
             ;
             and
             partly
             also
             from
             the
             North
             Sea
             ,
             which
             lieth
             also
             East
             and
             West
             ,
             and
             has
             a
             passage
             out
             of
             the
             South
             Sea
             by
             the
             Streight
             of
             Anian
             ,
             between
             America
             and
             Asia
             .
          
        
         
           
             A.
             
          
           
             Does
             not
             the
             
             Mediterranean-Sea
             lie
             also
             East
             and
             West
             ?
             why
             are
             there
             not
             the
             like
             Tides
             there
             ?
          
        
         
           
             B.
             
          
           
             So
             there
             are
             ,
             proportionable
             to
             their
             lengths
             ,
             and
             quantity
             of
             water
             .
          
        
         
           
             A.
             
          
           
             At
             Genoa
             ,
             at
             Ancona
             there
             are
             none
             at
             all
             ,
             or
             not
             sensible
             .
          
        
         
           
             B.
             
          
           
             At
             Venice
             there
             are
             ,
             and
             in
             the
             bottom
             of
             the
             Streights
             ;
             and
             a
             current
             all
             along
             both
             the
             
             Mediterranean-Sea
             ,
             and
             the
             Gulf
             of
             Venice
             ;
             And
             it
             is
             the
             current
             that
             makes
             the
             Tides
             unsensible
             at
             the
             sides
             ▪
             but
             the
             check
             makes
             them
             visible
             at
             the
             bottom
             .
          
        
         
           
           
             A.
             
          
           
             How
             comes
             it
             about
             that
             the
             Moon
             hath
             such
             a
             stroke
             in
             the
             business
             ,
             as
             so
             sensibly
             to
             encrease
             the
             Tides
             at
             Full
             and
             Change
             ?
          
        
         
           
             B.
             
          
           
             The
             motion
             I
             have
             hitherto
             supposed
             but
             in
             the
             Earth
             ,
             I
             suppose
             also
             in
             the
             Moon
             ,
             and
             in
             all
             those
             great
             Bodies
             that
             hang
             in
             the
             Air
             constantly
             ,
             I
             mean
             the
             Stars
             ,
             both
             fixed
             and
             errant
             .
             And
             for
             the
             Sun
             and
             Moon
             ,
             I
             suppose
             the
             Poles
             of
             their
             motion
             to
             be
             the
             Poles
             of
             the
             Aequinoctial
             ;
             which
             supposed
             ,
             it
             will
             follow
             ,
             (
             because
             the
             Sun
             ,
             the
             Earth
             and
             the
             Moon
             at
             every
             Full
             and
             Change
             are
             almost
             in
             one
             streight
             line
             )
             that
             this
             motion
             of
             the
             Earth
             will
             be
             made
             swifter
             than
             in
             the
             Quarters
             .
             For
             this
             motion
             of
             the
             Sun
             and
             Moon
             being
             communicated
             to
             the
             Earth
             ,
             that
             hath
             already
             the
             like
             motion
             ,
             maketh
             the
             same
             greater
             ;
             and
             much
             greater
             when
             they
             are
             all
             three
             in
             one
             streight
             line
             ,
             which
             is
             only
             at
             the
             Full
             and
             Change
             ,
             whose
             Tides
             are
             therefore
             called
             Spring
             Tides
             .
          
        
         
           
             A.
             
          
           
             But
             what
             then
             is
             the
             cause
             that
             the
             Spring-Tides
             themselves
             are
             twice
             a
             year
             ,
             namely
             when
             the
             Sun
             is
             in
             the
             Equinoctial
             ,
             greater
             than
             at
             any
             other
             times
             ?
          
        
         
           
             B.
             
          
           
             At
             other
             times
             of
             the
             year
             ,
             the
             Earth
             being
             out
             of
             the
             Aequinoctial
             ,
             the
             motion
             thereof
             ,
             by
             which
             the
             Tides
             are
             made
             ,
             will
             be
             less
             augmented
             ,
             by
             so
             much
             as
             a
             motion
             in
             the
             obliquity
             of
             23
             degrees
             
             or
             thereabout
             (
             which
             is
             the
             distance
             between
             the
             Aequinoctial
             and
             Ecliptick
             Circles
             )
             is
             weaker
             then
             the
             motion
             which
             is
             without
             obliquity
             .
          
        
         
           
             A.
             
          
           
             All
             this
             is
             reasonable
             enough
             ,
             if
             it
             be
             possible
             that
             such
             motions
             as
             you
             suppose
             in
             these
             bodies
             ,
             be
             really
             there
             .
             But
             that
             is
             a
             thing
             I
             have
             some
             reason
             to
             doubt
             of
             ;
             For
             ,
             the
             throwing
             off
             of
             Air
             ,
             consequent
             to
             these
             motions
             ,
             is
             the
             cause
             ,
             you
             say
             ,
             that
             other
             things
             come
             to
             the
             Earth
             ;
             And
             therefore
             the
             like
             motions
             in
             the
             Sun
             ,
             and
             Moon
             ,
             and
             Stars
             ,
             casting
             off
             the
             Air
             ,
             should
             also
             cause
             all
             other
             things
             to
             come
             to
             every
             one
             of
             them
             .
             From
             whence
             it
             will
             follow
             ,
             that
             the
             Sun
             ,
             Moon
             ,
             and
             Earth
             ,
             and
             all
             other
             bodies
             but
             Air
             ,
             should
             presently
             come
             together
             into
             one
             heap
             .
          
        
         
           
             B.
             
          
           
             That
             does
             not
             follow
             :
             For
             if
             two
             bodies
             cast
             off
             the
             Air
             ,
             the
             motion
             of
             that
             Air
             will
             be
             repress'd
             both
             ways
             ,
             and
             diverted
             into
             a
             course
             towards
             the
             Poles
             on
             both
             sides
             ;
             and
             then
             the
             two
             bodies
             cannot
             possibly
             come
             together
             .
          
        
         
           
             A.
             
          
           
             'T
             is
             true
             .
             And
             besides
             ,
             this
             driving
             off
             the
             Air
             on
             both
             sides
             ,
             North
             and
             South
             ,
             makes
             the
             like
             motion
             of
             Air
             there
             also
             .
             And
             this
             may
             answer
             to
             the
             Question
             ,
             How
             a
             stone
             could
             fall
             to
             the
             Earth
             under
             the
             Poles
             of
             the
             Ecliptick
             ,
             by
             the
             only
             casting
             off
             of
             Air
             ?
          
        
         
           
           
             B.
             
          
           
             It
             follows
             from
             hence
             ,
             that
             there
             is
             a
             certain
             and
             determinate
             distance
             of
             one
             of
             these
             bodies
             (
             the
             Stars
             )
             from
             another
             ,
             without
             any
             very
             sensible
             variation
             .
          
        
         
           
             A.
             
          
           
             All
             this
             is
             probable
             enough
             ,
             if
             it
             be
             true
             that
             there
             is
             no
             Vacuum
             ,
             no
             place
             empty
             in
             all
             the
             World.
             And
             supposing
             this
             motion
             of
             the
             Sun
             and
             Moon
             to
             be
             in
             the
             plain
             of
             the
             Aequinoctial
             ,
             methinks
             that
             this
             should
             be
             the
             cause
             of
             the
             Diurnal
             motion
             of
             the
             Earth
             ;
             And
             because
             this
             motion
             of
             the
             Earth
             is
             (
             you
             say
             )
             in
             the
             plain
             of
             the
             Aequinoctial
             ,
             the
             same
             should
             cause
             also
             a
             motion
             in
             the
             Moon
             on
             her
             own
             Center
             ,
             answerable
             to
             the
             Diurnal
             motion
             of
             the
             Earth
             .
          
        
         
           
             B.
             
          
           
             Why
             not
             ?
             what
             else
             can
             you
             think
             makes
             the
             Diurnal
             motion
             of
             the
             Earth
             ,
             but
             the
             Sun
             ?
             And
             for
             the
             Moon
             ,
             if
             it
             did
             not
             turn
             upon
             its
             own
             Center
             ,
             we
             should
             see
             sometimes
             one
             ,
             sometimes
             another
             face
             of
             the
             Moon
             ,
             which
             we
             do
             not
             .
          
        
      
       
         
         
           CHAP.
           III.
           Problems
           of
           Vacuum
           .
        
         
           
             WHat
             convincing
             Argument
             is
             there
             to
             prove
             ,
             that
             in
             all
             the
             world
             there
             is
             no
             empty
             place
             ?
          
        
         
           
             B.
             
          
           
             Many
             ;
             but
             I
             will
             name
             but
             one
             ;
             and
             that
             is
             ,
             the
             difficulty
             of
             separating
             two
             bodies
             hard
             and
             flat
             laid
             one
             upon
             another
             ;
             I
             say
             ,
             the
             difficulty
             ,
             not
             the
             impossibility
             .
             It
             is
             possible
             ,
             without
             introducing
             Vacuum
             ,
             to
             pull
             assunder
             any
             two
             bodies
             ,
             how
             hard
             and
             flat
             soever
             they
             be
             ,
             if
             the
             force
             used
             be
             greater
             than
             the
             resistance
             of
             the
             hardness
             .
             And
             in
             case
             there
             be
             any
             greater
             difficulty
             to
             part
             them
             ,
             (
             besides
             what
             proceeds
             from
             their
             hardness
             )
             then
             there
             is
             to
             pull
             them
             further
             assunder
             when
             they
             are
             parted
             ,
             that
             difficulty
             is
             Argument
             enough
             to
             prove
             there
             is
             no
             Vacuum
             .
          
        
         
           
             A.
             
          
           
             These
             Assertions
             need
             demonstration
             .
             And
             first
             ,
             how
             does
             the
             difficulty
             of
             separation
             argue
             the
             Plenitude
             of
             all
             the
             rest
             of
             the
             world
             ?
          
        
         
           
             B.
             
          
           
             If
             two
             flat
             polish'd
             Marbles
             lie
             one
             upon
             another
             ,
             you
             see
             they
             are
             hardly
             separated
             in
             all
             points
             at
             one
             and
             the
             same
             instant
             ;
             and
             yet
             the
             weight
             of
             either
             of
             
             them
             it
             is
             enough
             to
             make
             them
             slide
             off
             one
             from
             the
             other
             .
             Is
             not
             the
             cause
             of
             this
             ,
             that
             the
             Air
             succeeds
             the
             Marble
             that
             so
             slides
             ,
             and
             fills
             up
             the
             place
             it
             leaves
             .
          
        
         
           
             A.
             
          
           
             Yes
             certainly
             .
             What
             then
             ?
          
        
         
           
             B.
             
          
           
             But
             when
             you
             pull
             the
             whole
             Superficies
             assunder
             ,
             not
             without
             great
             difficulty
             ,
             what
             is
             the
             cause
             of
             that
             difficulty
             ?
          
        
         
           
             A.
             
          
           
             I
             think
             as
             most
             men
             do
             ,
             that
             the
             Air
             cannot
             fill
             up
             the
             space
             between
             in
             an
             instant
             ;
             For
             the
             parting
             is
             in
             an
             instant
             .
          
        
         
           
             B.
             
          
           
             Suppose
             there
             be
             Vacuum
             in
             that
             Air
             into
             which
             the
             Marble
             you
             pull
             off
             is
             to
             succeed
             ,
             shall
             there
             be
             no
             Vacuum
             in
             the
             Air
             that
             was
             round
             about
             the
             two
             Marbles
             when
             they
             touched
             ?
             Why
             cannot
             that
             Vacuum
             come
             into
             the
             place
             between
             ?
             Air
             cannot
             succeed
             in
             an
             instant
             ,
             because
             a
             body
             ;
             and
             consequently
             cannot
             be
             moved
             through
             the
             least
             space
             in
             an
             instant
             .
             But
             emptiness
             is
             not
             a
             body
             ,
             nor
             is
             moved
             ,
             but
             made
             by
             the
             act
             it self
             of
             separation
             .
             There
             is
             therefore
             (
             if
             you
             admit
             Vacuum
             )
             no
             necessity
             at
             all
             for
             the
             Air
             to
             fill
             the
             space
             left
             ,
             in
             an
             instant
             .
             And
             therefore
             ,
             with
             what
             ease
             the
             Marble
             coming
             off
             presseth
             out
             the
             Vacuum
             of
             the
             Air
             behind
             it
             ,
             with
             the
             same
             ease
             will
             the
             Marbles
             be
             pulled
             assunder
             .
             Seeing
             then
             ,
             if
             there
             were
             
             Vacuum
             ,
             there
             would
             be
             no
             difficulty
             of
             Separation
             ;
             it
             follows
             ,
             because
             there
             is
             difficulty
             of
             separation
             ,
             that
             there
             is
             no
             Vacuum
             .
          
        
         
           
             A.
             
          
           
             Well
             now
             ,
             supposing
             the
             world
             full
             ,
             how
             do
             you
             prove
             it
             possible
             to
             pull
             those
             Marbles
             assunder
             ?
          
        
         
           
             B.
             
          
           
             Take
             a
             piece
             of
             soft
             wax
             ;
             Do
             not
             you
             think
             the
             one
             half
             touches
             the
             other
             half
             as
             close
             as
             the
             smoothest
             Marbles
             ?
             yet
             you
             can
             pull
             them
             assunder
             .
             But
             how
             ?
             still
             as
             you
             pull
             ,
             the
             wax
             grows
             continually
             more
             and
             more
             slender
             ;
             there
             being
             a
             perpetual
             parting
             or
             discession
             of
             the
             outermost
             part
             of
             the
             wax
             one
             from
             another
             ;
             which
             the
             Air
             presently
             fills
             ,
             and
             so
             there
             is
             a
             continual
             lessening
             of
             the
             wax
             ,
             till
             it
             be
             no
             bigger
             than
             a
             hair
             ,
             and
             at
             last
             separation
             .
             If
             you
             can
             do
             the
             same
             to
             a
             Pillar
             of
             Marble
             ,
             till
             the
             outside
             give
             way
             ,
             the
             effect
             will
             be
             the
             same
             ,
             but
             much
             quicker
             ,
             after
             it
             once
             begins
             to
             break
             in
             the
             Superficies
             ;
             because
             the
             force
             that
             can
             master
             the
             first
             resistance
             of
             the
             hardness
             ,
             will
             quickly
             dispatch
             the
             rest
             .
          
        
         
           
             A.
             
          
           
             It
             seems
             so
             by
             the
             brittleness
             of
             some
             hard
             bodies
             .
             But
             I
             shall
             afterward
             put
             some
             Questions
             to
             you
             ,
             touching
             the
             nature
             of
             hardness
             .
             But
             now
             to
             return
             to
             our
             subject
             ,
          
        
         
           What
           reason
           can
           you
           render
           (
           without
           supposing
           Vacuum
           )
           of
           the
           effects
           produced
           in
           
           the
           Engine
           they
           use
           at
           
             Gresham
             Colledge
          
           ?
        
         
           
             B.
             
          
           
             That
             Engine
             produceth
             the
             same
             effects
             ,
             that
             a
             strong
             wind
             would
             produce
             in
             a
             narrow
             room
             .
          
        
         
           
             A.
             
          
           
             How
             comes
             the
             wind
             in
             ?
             You
             know
             the
             Engine
             is
             a
             hollow
             round
             pipe
             of
             brass
             ;
             into
             which
             is
             thrust
             a
             Cylinder
             of
             wood
             covered
             with
             Leather
             ,
             and
             fitted
             to
             the
             Cylinder
             so
             exactly
             as
             no
             Air
             can
             possibly
             pass
             between
             the
             leather
             and
             the
             brass
             ?
          
        
         
           
             B.
             
          
           
             I
             know
             it
             ;
             and
             that
             they
             may
             thrust
             it
             up
             ,
             there
             is
             a
             hole
             left
             in
             the
             Cylinder
             to
             let
             the
             Air
             out
             before
             it
             ;
             which
             they
             can
             stop
             when
             they
             please
             .
             There
             is
             also
             in
             the
             bottom
             of
             the
             Cylinder
             a
             passage
             into
             a
             hollow
             Globe
             of
             Glass
             ;
             which
             passage
             they
             can
             also
             open
             and
             shut
             at
             pleasure
             .
             And
             at
             the
             top
             of
             that
             Globe
             there
             is
             a
             wide
             mouth
             to
             put
             in
             what
             they
             please
             to
             try
             conclusions
             on
             ;
             and
             that
             also
             to
             be
             opened
             and
             shut
             as
             shall
             be
             needful
             .
             'T
             is
             of
             the
             nature
             of
             a
             Pop-gun
             which
             Children
             use
             ,
             but
             great
             ,
             costly
             ,
             and
             more
             ingenious
             .
             They
             thrust
             forward
             ,
             and
             pull
             back
             the
             wooden
             Cylinder
             (
             because
             it
             requires
             much
             strength
             )
             with
             an
             Iron
             screw
             .
             What
             is
             there
             in
             all
             this
             to
             prove
             the
             possibility
             of
             Vacuum
             .
          
        
         
           
             A.
             
          
           
             Whan
             this
             wooden
             Cylinder
             covered
             with
             leather
             ,
             fit
             and
             close
             is
             thrust
             home
             to
             the
             bottom
             ,
             and
             the
             holes
             in
             the
             hollow
             Cylinder
             
             of
             Brass
             close
             stopped
             ,
             how
             can
             it
             be
             drawn
             back
             ,
             as
             with
             the
             screw
             they
             draw
             it
             ,
             but
             that
             the
             space
             it
             leaves
             must
             needs
             be
             empty
             .
             For
             it
             is
             impossible
             that
             any
             Air
             can
             pass
             into
             the
             place
             to
             fill
             it
             ?
          
        
         
           
             B.
             
          
           
             Truly
             I
             think
             it
             close
             enough
             to
             keep
             out
             Straw
             and
             Feathers
             ,
             but
             not
             to
             keep
             out
             Air
             ,
             nor
             yet
             matter
             .
             For
             suppose
             they
             were
             not
             so
             exactly
             close
             but
             that
             there
             were
             round
             about
             a
             distance
             for
             a
             small
             hair
             to
             lye
             between
             ,
             Then
             will
             the
             pulling
             back
             of
             the
             Cylinder
             of
             wood
             force
             so
             much
             Air
             in
             ,
             as
             in
             retiring
             it
             forces
             back
             ,
             and
             that
             without
             any
             sensible
             difficulty
             .
             And
             the
             Air
             will
             so
             much
             more
             swiftly
             enter
             as
             the
             passage
             is
             left
             more
             narrow
             .
             Or
             if
             they
             touch
             ,
             and
             the
             contract
             be
             in
             some
             points
             ,
             and
             not
             in
             all
             ,
             the
             Air
             will
             enter
             as
             before
             in
             case
             the
             force
             be
             augmented
             accordingly
             .
             Lastly
             ,
             though
             they
             touch
             exactly
             ,
             if
             either
             the
             Leather
             yield
             ,
             or
             the
             Brass
             (
             which
             it
             may
             do
             to
             the
             force
             of
             a
             strong
             screw
             )
             the
             Air
             will
             again
             enter
             .
             Do
             you
             think
             it
             possible
             to
             make
             two
             superficies
             so
             exquisitly
             touch
             in
             all
             points
             as
             you
             suppose
             ,
             or
             Leather
             so
             hard
             as
             not
             to
             yield
             to
             the
             force
             of
             a
             screw
             ?
             The
             Body
             of
             Leather
             will
             give
             passage
             both
             to
             Air
             and
             Water
             ,
             as
             you
             will
             confess
             when
             you
             ride
             in
             Rainy
             and
             Windy
             weather
             .
             You
             
             may
             therefore
             be
             assured
             that
             in
             drawing
             out
             their
             wooden-leather
             Cylinder
             they
             force
             in
             as
             much
             Air
             as
             will
             fill
             the
             place
             it
             leaves
             ,
             and
             that
             with
             as
             much
             swiftness
             as
             is
             answerable
             to
             the
             strength
             that
             drives
             it
             in
             .
             The
             effect
             therefore
             of
             their
             pumping
             is
             nothing
             else
             but
             a
             vehement
             Wind
             ,
             a
             very
             vehement
             Wind
             coming
             in
             on
             all
             sides
             of
             the
             Cylinder
             at
             once
             into
             the
             hollow
             of
             the
             Brass
             Pipe
             ,
             and
             into
             the
             hollow
             of
             the
             Glass
             Globe
             joyned
             to
             it
             .
          
        
         
           
             A.
             
          
           
             I
             see
             the
             reason
             already
             of
             one
             of
             their
             wonders
             ,
             which
             is
             ,
             that
             the
             Cylinder
             they
             pump
             with
             ,
             if
             it
             be
             left
             to
             it self
             ,
             after
             it
             is
             pulled
             back
             will
             swiftly
             go
             up
             again
             .
             You
             will
             say
             the
             Air
             comes
             out
             again
             with
             the
             same
             violence
             by
             reflection
             ;
             and
             I
             believe
             it
             ?
          
        
         
           
             B.
             
          
           
             This
             is
             argument
             enough
             that
             the
             place
             was
             not
             empty
             .
             For
             what
             can
             fetch
             or
             drive
             up
             the
             Sucker
             ,
             as
             they
             call
             it
             ,
             if
             the
             place
             within
             were
             empty
             ;
             for
             that
             there
             is
             any
             weight
             in
             the
             Air
             to
             do
             it
             ,
             I
             have
             already
             demonstrated
             to
             be
             impossible
             .
          
           
             Besides
             ,
             you
             know
             ,
             when
             they
             have
             sucked
             out
             (
             as
             they
             think
             )
             all
             the
             Air
             from
             the
             Glass
             Globe
             ,
             they
             can
             nevertheless
             both
             see
             through
             it
             what
             is
             done
             ,
             and
             hear
             a
             sound
             from
             within
             when
             there
             is
             any
             made
             .
             Which
             (
             if
             there
             were
             no
             
             other
             ,
             but
             there
             are
             many
             other
             ,
             )
             is
             argument
             enough
             that
             the
             place
             is
             still
             full
             of
             Air.
             
          
        
         
           
             A.
             
          
           
             What
             say
             you
             to
             the
             swelling
             of
             a
             Bladder
             even
             to
             bursting
             ,
             if
             it
             be
             a
             little
             blown
             when
             it
             is
             put
             into
             the
             Receiver
             ,
             (
             for
             so
             they
             call
             the
             Globe
             of
             Glass
             ?
             )
          
        
         
           
             B.
             
          
           
             The
             stream
             of
             Air
             that
             from
             every
             side
             meeting
             together
             ,
             and
             turning
             in
             an
             infinite
             number
             of
             small
             points
             ,
             do
             pierce
             the
             Bladder
             in
             innumerable
             places
             with
             great
             violence
             at
             once
             ,
             like
             so
             many
             invisible
             small
             wimbles
             ;
             especially
             if
             the
             Bladder
             be
             a
             little
             blown
             before
             it
             be
             put
             in
             ,
             that
             it
             may
             make
             a
             little
             resistance
             .
             And
             when
             the
             Air
             has
             once
             pierced
             it
             ,
             it
             is
             easie
             to
             conceive
             ,
             that
             it
             must
             afterward
             by
             the
             same
             violent
             motion
             be
             extended
             till
             it
             break
             .
             If
             before
             it
             break
             you
             let
             in
             fresh
             Air
             upon
             it
             ,
             the
             violence
             of
             the
             motion
             will
             thereby
             be
             tempered
             ,
             and
             the
             Bladder
             be
             less
             extended
             .
             For
             that
             also
             they
             have
             observed
             .
             Can
             you
             imagine
             how
             a
             Bladder
             should
             be
             extended
             ,
             and
             broken
             ,
             by
             being
             too
             full
             of
             Emptiness
             .
          
        
         
           
             A.
             
          
           
             How
             come
             living
             creatures
             to
             be
             killed
             in
             this
             Receiver
             ,
             in
             so
             little
             a
             time
             as
             3
             or
             4
             minutes
             of
             an
             hour
             ?
          
        
         
           
             B.
             
          
           
             If
             they
             suck
             into
             their
             lungs
             so
             violent
             a
             wind
             thus
             made
             ,
             you
             must
             needs
             
             think
             it
             will
             presently
             stop
             the
             passage
             of
             their
             bloud
             ;
             and
             that
             is
             death
             ;
             though
             they
             may
             recover
             if
             taken
             out
             before
             they
             be
             too
             cold
             .
             And
             so
             likewise
             will
             it
             put
             out
             fire
             ;
             but
             the
             Coals
             taken
             out
             whilst
             they
             are
             hot
             ,
             will
             revive
             again
             .
             'T
             is
             an
             ordinary
             thing
             in
             many
             Coal-pits
             ,
             (
             whereof
             I
             have
             seen
             the
             experience
             ,
             )
             that
             a
             wind
             proceeding
             from
             the
             sides
             of
             the
             Pit
             every
             way
             ,
             will
             extinguish
             any
             fire
             let
             down
             into
             it
             ,
             and
             kill
             the
             workmen
             ,
             unless
             they
             be
             quickly
             taken
             out
             .
          
        
         
           
             A.
             
          
           
             If
             you
             put
             a
             vessel
             of
             water
             into
             the
             Receiver
             ,
             and
             then
             suck
             out
             the
             Air
             ,
             the
             water
             will
             boil
             .
             What
             say
             you
             to
             that
             ?
          
        
         
           
             B.
             
          
           
             It
             is
             like
             enough
             it
             will
             dance
             in
             so
             great
             a
             bustling
             of
             the
             Air
             ;
             but
             I
             never
             heard
             it
             would
             be
             hot
             .
             Nor
             can
             I
             imagine
             how
             Vacuum
             should
             make
             any
             thing
             dance
             .
             I
             hope
             you
             are
             by
             this
             time
             satisfied
             ,
             that
             no
             experiment
             made
             with
             the
             Engine
             at
             
               Gresham
               Colledge
            
             ,
             is
             sufficient
             to
             prove
             that
             there
             is
             ,
             or
             that
             there
             may
             be
             Vacuum
             .
          
        
         
           
             A.
             
          
           
             The
             World
             you
             know
             is
             finite
             ,
             and
             consequently
             ,
             all
             that
             infinite
             space
             without
             it
             ,
             is
             empty
             .
             Why
             may
             not
             some
             of
             that
             Vacuum
             be
             brought
             in
             ,
             and
             mingled
             with
             the
             Air
             here
             ?
          
        
         
           
             B.
             
          
           
             I
             know
             nothing
             in
             matters
             without
             the
             World.
             
          
        
         
           
           
             A.
             
          
           
             What
             say
             you
             to
             Torricellioes
             Experiment
             in
             Quick-silver
             ,
             which
             is
             this
             .
             There
             is
             a
             Bason
             at
             A
             filled
             with
             Quick-silver
             ,
             suppose
             to
             B
             ,
             And
             CD
             a
             hollow
             glass
             pipe
             filled
             with
             the
             same
             .
             Which
             if
             you
             stop
             with
             your
             finger
             at
             B
             ,
             and
             so
             set
             it
             upright
             ,
             and
             then
             if
             you
             take
             away
             your
             finger
             ,
             the
             Quick-silver
             will
             fall
             from
             C
             downwards
             ,
             but
             not
             to
             the
             bottom
             .
             For
             it
             will
             stop
             by
             the
             way
             ,
             suppose
             at
             D.
             Is
             it
             not
             therefore
             necessary
             that
             that
             space
             between
             C
             and
             D
             be
             left
             empty
             ?
             Or
             will
             you
             say
             the
             Quick
             silver
             does
             not
             exactly
             touch
             the
             sides
             of
             the
             glass
             pipe
             ?
          
        
         
           
             B.
             
          
           
             I
             'le
             say
             neither
             .
             If
             a
             man
             thrust
             down
             into
             a
             vessel
             of
             Quick-silver
             a
             blown
             Bladder
             ,
             will
             not
             that
             Bladder
             come
             up
             to
             the
             top
             ?
          
        
         
           
             A.
             
          
           
             Yes
             certanly
             ,
             or
             a
             Bladder
             of
             Iron
             ,
             or
             of
             any
             thing
             else
             but
             Gold.
             
          
        
         
           
             B.
             
          
           
             You
             see
             then
             that
             Air
             can
             pierce
             Quick-silver
             .
          
        
         
           
             A.
             
          
           
             Yes
             ,
             with
             so
             much
             force
             as
             the
             weight
             of
             Quick-silver
             comes
             to
             .
          
        
         
           
             B.
             
          
           
             When
             the
             Quick-silver
             is
             fallen
             to
             D
             ,
             there
             is
             so
             much
             the
             more
             in
             the
             bason
             .
             And
             that
             takes
             up
             the
             place
             which
             so
             much
             Air
             took
             up
             before
             .
             Whither
             can
             this
             Air
             go
             if
             all
             the
             World
             without
             that
             glass
             pipe
             B
             C
             were
             full
             ?
             There
             must
             needs
             be
             the
             same
             or
             as
             much
             Air
             come
             
             to
             that
             space
             (
             which
             only
             is
             empty
             )
             between
             C
             and
             D.
             By
             what
             force
             ?
             By
             the
             weight
             of
             the
             Quick-silver
             between
             D
             and
             B.
             Which
             Quick-silver
             weigheth
             now
             upward
             ;
             or
             else
             it
             could
             never
             have
             raised
             that
             part
             higher
             ,
             which
             was
             at
             first
             in
             the
             Bason
             .
             So
             you
             see
             the
             weight
             of
             Quick-silver
             can
             press
             the
             Air
             through
             Quick-silver
             up
             into
             the
             pipe
             ,
             till
             it
             come
             to
             an
             equality
             of
             force
             as
             in
             D.
             Where
             the
             weight
             of
             the
             Quick-silver
             is
             equal
             to
             the
             force
             which
             is
             required
             in
             Air
             to
             go
             through
             it
             .
          
        
         
           
             A.
             
          
           
             If
             a
             man
             suck
             a
             Vial
             that
             has
             nothing
             in
             it
             but
             Air
             ,
             and
             presently
             dip
             the
             mouth
             of
             it
             into
             water
             ,
             the
             water
             will
             ascend
             into
             the
             Vial.
             Is
             not
             that
             an
             argument
             that
             part
             of
             the
             Air
             had
             been
             sucked
             out
             ,
             and
             part
             of
             the
             room
             within
             the
             Vial
             left
             empty
             ?
          
        
         
           
             B.
             
          
           
             No.
             If
             there
             were
             empty
             space
             in
             the
             World
             ,
             why
             should
             not
             there
             be
             also
             some
             empty
             space
             in
             the
             Vial
             before
             it
             was
             sucked
             ?
             And
             then
             why
             does
             not
             the
             water
             rise
             to
             fill
             that
             ,
             when
             a
             man
             sucks
             the
             Vial
             he
             draws
             nothing
             out
             neither
             into
             his
             Belly
             not
             into
             his
             Lungs
             ,
             nor
             into
             his
             Mouth
             ;
             only
             he
             sets
             the
             Air
             within
             the
             glass
             into
             a
             circular
             motion
             ,
             giving
             it
             at
             once
             an
             endeavour
             to
             go
             forth
             by
             the
             sucking
             ,
             and
             an
             endeavour
             to
             go
             back
             
             by
             not
             receiving
             it
             into
             his
             mouth
             .
             And
             so
             with
             a
             great
             deal
             of
             labour
             glues
             his
             lips
             to
             the
             neck
             of
             the
             Vial.
             Then
             taking
             it
             off
             ,
             and
             dipping
             the
             neck
             of
             the
             Vial
             into
             the
             water
             before
             the
             circulation
             cease
             ,
             the
             Air
             with
             the
             endeavour
             it
             hath
             now
             gotten
             ,
             pierces
             the
             water
             and
             goes
             out
             .
             And
             so
             much
             Air
             as
             goes
             out
             ,
             so
             much
             matter
             comes
             up
             into
             the
             room
             of
             it
             .
          
        
      
       
         
           CHAP.
           IIII.
           Problems
           of
           Heat
           and
           Light.
           
        
         
           
             A.
             
          
           
             WHat
             is
             the
             cause
             of
             Heat
             ?
          
        
         
           
             B.
             
          
           
             How
             know
             you
             ,
             that
             any
             thing
             is
             Hot
             but
             your self
             ?
          
        
         
           
             A.
             
          
           
             Because
             I
             perceive
             by
             sense
             it
             Heats
             me
             .
          
        
         
           
             B.
             
          
           
             It
             is
             no
             good
             argument
             ,
             The
             thing
             Heats
             me
             ;
             therefore
             it
             is
             Hot.
             But
             what
             alteration
             do
             you
             find
             in
             your
             body
             at
             any
             time
             by
             being
             Hot
             ?
          
        
         
           
             A.
             
          
           
             I
             find
             my
             skin
             more
             extended
             in
             Summer
             than
             in
             Winter
             ;
             and
             am
             sometimes
             fainter
             and
             weaker
             then
             ordinary
             ,
             as
             if
             my
             Spirits
             were
             exhaled
             ;
             and
             I
             sweat
             .
          
        
         
           
             B.
             
          
           
             Then
             that
             is
             it
             you
             would
             know
             the
             cause
             of
             .
             I
             have
             told
             you
             before
             that
             
             by
             the
             motion
             I
             suppose
             both
             in
             the
             Sun
             ,
             and
             in
             the
             Earth
             ,
             the
             Air
             is
             dissipated
             ,
             and
             consequently
             that
             there
             would
             be
             an
             infinite
             number
             of
             small
             empty
             places
             but
             that
             the
             World
             being
             full
             ,
             there
             comes
             from
             the
             next
             parts
             other
             Air
             into
             the
             spaces
             ,
             they
             would
             else
             make
             empty
             .
             When
             therefore
             this
             motion
             of
             the
             Sun
             is
             excercised
             upon
             the
             Superficies
             of
             the
             Earth
             ,
             if
             there
             do
             not
             come
             out
             of
             the
             Earth
             it self
             some
             corporal
             substance
             to
             supply
             that
             tearing
             of
             the
             Air
             ,
             we
             must
             return
             again
             to
             the
             admission
             of
             Vacuum
             .
             If
             there
             do
             ,
             then
             you
             see
             how
             by
             this
             motion
             fluid
             bodies
             are
             made
             to
             exhale
             out
             of
             the
             Earth
             .
             The
             like
             happens
             to
             a
             mans
             body
             or
             hand
             ,
             which
             when
             he
             perceives
             ,
             he
             says
             he
             is
             Hot.
             And
             so
             of
             the
             Earth
             when
             it
             sendeth
             forth
             Water
             and
             Earth
             together
             in
             Plants
             ,
             we
             say
             it
             does
             it
             by
             Heat
             from
             the
             Sun.
             
          
        
         
           
             A.
             
          
           
             'T
             is
             very
             probable
             ,
             and
             no
             less
             probable
             ,
             that
             the
             same
             action
             of
             the
             Sun
             ,
             is
             that
             which
             from
             the
             Sea
             and
             moist
             places
             of
             the
             Earth
             ,
             but
             especially
             from
             the
             Sea
             fetcheth
             up
             the
             water
             into
             the
             Clouds
             .
             But
             there
             be
             many
             ways
             of
             Heating
             besides
             the
             action
             of
             the
             Sun
             or
             of
             Fire
             .
             Two
             pieces
             of
             Wood
             will
             take
             Fire
             if
             in
             Torning
             they
             be
             prest
             together
             .
          
        
         
           
             B.
             
          
           
             Here
             again
             you
             have
             a
             manifest
             laceration
             
             of
             the
             Air
             by
             the
             reciprocal
             and
             contrary
             motions
             of
             the
             two
             pieces
             of
             wood
             ,
             which
             necessarily
             causeth
             a
             coming
             forth
             of
             whatsoever
             is
             Aereal
             or
             fluid
             within
             them
             ,
             and
             (
             the
             motion
             pursued
             )
             a
             dissipation
             also
             of
             the
             other
             more
             solid
             parts
             into
             Ashes
             .
          
        
         
           
             A.
             
          
           
             How
             comes
             it
             to
             pass
             that
             a
             man
             is
             warmed
             even
             to
             sweating
             almost
             with
             every
             extraordinary
             labour
             of
             his
             body
             ?
          
        
         
           
             B.
             
          
           
             It
             is
             easie
             to
             understand
             ,
             how
             by
             that
             labour
             all
             that
             is
             liquid
             in
             his
             body
             is
             tossed
             up
             and
             down
             ,
             and
             thereby
             part
             of
             it
             also
             cast
             forth
             .
          
        
         
           
             A.
             
          
           
             There
             be
             some
             things
             that
             make
             a
             man
             Hot
             without
             sweat
             or
             other
             evaporation
             ,
             as
             Caustiques
             ,
             Nettles
             and
             other
             things
             .
          
        
         
           
             B.
             
          
           
             No
             doubt
             .
             But
             they
             touch
             the
             part
             they
             so
             Heat
             ,
             and
             cannot
             work
             that
             effect
             at
             any
             distance
             .
          
        
         
           
             A.
             
          
           
             How
             does
             Heat
             cause
             light
             ,
             and
             that
             partially
             in
             some
             bodies
             more
             ,
             in
             some
             less
             ,
             though
             the
             Heat
             be
             equal
             ?
          
        
         
           
             B.
             
          
           
             Heat
             does
             not
             cause
             Light
             at
             all
             .
             But
             in
             many
             Bodies
             ,
             the
             same
             cause
             ,
             that
             is
             to
             say
             ,
             the
             same
             motion
             causeth
             both
             together
             ;
             so
             that
             they
             are
             not
             to
             one
             another
             as
             cause
             and
             effect
             ,
             but
             are
             concomitant
             Effects
             ,
             sometimes
             of
             one
             and
             the
             same
             motion
             .
          
        
         
           
             A.
             
          
           
             How
             ?
          
        
         
           
           
             B.
             
          
           
             You
             know
             the
             rubbing
             or
             heard
             pressing
             of
             the
             Eye
             ,
             or
             a
             stroke
             upon
             it
             makes
             an
             apparition
             of
             Light
             without
             and
             before
             it
             ,
             which
             way
             soever
             you
             look
             .
             This
             can
             proceed
             from
             nothing
             else
             but
             from
             the
             restitution
             of
             the
             Organ
             pressed
             or
             stricken
             ,
             unto
             its
             former
             ordinary
             situation
             of
             parts
             .
             Does
             not
             the
             Sun
             by
             his
             thrusting
             back
             the
             Air
             upon
             you
             eyes
             press
             them
             ?
             Or
             does
             not
             those
             bodies
             whereon
             the
             Sun
             shines
             (
             though
             by
             reflection
             )
             do
             the
             same
             ,
             though
             not
             so
             strongly
             ?
             And
             do
             not
             the
             Organs
             of
             Sight
             ,
             the
             Eye
             ,
             the
             Heart
             ,
             and
             Brains
             resist
             that
             pressure
             by
             an
             endeavour
             of
             restitution
             outwards
             ?
             Why
             then
             should
             there
             not
             be
             without
             and
             before
             the
             Eye
             ,
             an
             apparition
             of
             Light
             in
             this
             case
             as
             well
             as
             in
             the
             other
             ?
          
        
         
           
             A.
             
          
           
             I
             grant
             there
             must
             .
             But
             what
             is
             that
             which
             appears
             after
             the
             pressing
             of
             the
             eye
             ?
             For
             there
             is
             nothing
             without
             ,
             that
             was
             not
             there
             before
             ;
             or
             if
             there
             were
             ,
             methinks
             another
             should
             see
             it
             better
             ,
             or
             as
             well
             as
             he
             ;
             or
             if
             in
             the
             dark
             ,
             methinks
             it
             should
             enlighten
             the
             place
             .
          
        
         
           
             B.
             
          
           
             It
             is
             a
             fancy
             ,
             such
             as
             is
             the
             appearance
             of
             your
             face
             in
             a
             Looking-glass
             ;
             such
             as
             is
             a
             Dream
             ;
             such
             as
             is
             a
             Ghost
             ;
             such
             as
             is
             a
             spot
             before
             the
             Eye
             that
             hath
             stared
             upon
             the
             Son
             or
             Fire
             .
             For
             all
             these
             
             are
             of
             the
             Regiment
             of
             Fancy
             ,
             without
             any
             body
             concealed
             under
             them
             ,
             or
             behind
             them
             ,
             by
             which
             they
             are
             produced
             .
          
        
         
           
             A.
             
          
           
             And
             when
             you
             look
             towards
             the
             Sun
             or
             Moon
             ,
             why
             is
             not
             that
             also
             which
             appears
             before
             your
             Eyes
             at
             that
             time
             a
             fancy
             ?
          
        
         
           
             B.
             
          
           
             So
             it
             is
             .
             Though
             the
             Sun
             it self
             be
             a
             real
             Body
             ,
             yet
             that
             bright
             Circle
             of
             about
             a
             foot
             Diameter
             cannot
             be
             the
             Sun
             ,
             unless
             there
             be
             two
             Suns
             ,
             a
             greater
             and
             a
             lesser
             .
             And
             because
             you
             may
             see
             that
             which
             you
             call
             the
             Sun
             ,
             both
             above
             you
             in
             the
             Skie
             ,
             and
             before
             you
             in
             the
             Water
             ,
             and
             two
             Suns
             (
             by
             distorting
             your
             Eye
             )
             in
             two
             places
             of
             the
             Skie
             ,
             one
             of
             them
             must
             needs
             be
             Fancy
             .
             And
             if
             one
             ,
             both
             .
             All
             sense
             is
             Fancy
             though
             the
             cause
             be
             always
             in
             a
             real
             Body
             .
          
        
         
           
             A.
             
          
           
             I
             see
             by
             this
             that
             those
             things
             which
             the
             Learned
             call
             the
             Accidents
             of
             Bodies
             ,
             are
             indeed
             nothing
             else
             but
             diversity
             of
             Fancy
             ;
             and
             are
             inherent
             in
             the
             Sentient
             ,
             and
             not
             in
             the
             Objects
             ,
             except
             Motion
             and
             Quantity
             .
             And
             I
             perceive
             by
             your
             Doctrine
             you
             have
             been
             tampering
             with
             Leviathan
             .
             But
             how
             comes
             Wood
             with
             a
             certain
             degree
             of
             Heat
             to
             shine
             ,
             and
             Iron
             also
             with
             a
             greater
             degree
             ;
             but
             no
             Heat
             at
             all
             to
             be
             able
             to
             make
             water
             shine
             ?
          
        
         
           
             B.
             
          
           
             That
             which
             shineth
             hath
             the
             same
             
             Motion
             in
             its
             parts
             that
             I
             have
             all
             this
             while
             supposed
             in
             the
             Sun
             and
             Earth
             .
             In
             which
             Motion
             there
             must
             needs
             be
             a
             competent
             degree
             of
             swiftness
             ,
             to
             move
             the
             sense
             ,
             that
             is
             ,
             to
             make
             it
             visible
             .
             All
             Bodies
             that
             are
             not
             fluid
             will
             shine
             with
             Heat
             ,
             if
             the
             Heat
             be
             very
             great
             .
             Iron
             will
             shine
             and
             Gold
             will
             shine
             ;
             but
             water
             will
             not
             ,
             because
             the
             parts
             are
             carried
             away
             before
             they
             attain
             to
             that
             degree
             of
             swiftness
             ;
             which
             is
             requisite
             .
          
        
         
           
             A.
             
          
           
             There
             are
             many
             fluid
             Bodies
             ,
             whose
             parts
             evaporate
             ,
             and
             yet
             they
             make
             a
             flame
             ,
             as
             Oyl
             ,
             and
             Wine
             ,
             and
             other
             strong
             drinks
             :
          
        
         
           
             B.
             
          
           
             As
             for
             Oyl
             I
             never
             saw
             any
             inflamed
             by
             it self
             ;
             how
             much
             soever
             Heated
             ,
             therefore
             I
             do
             not
             think
             they
             are
             the
             parts
             of
             the
             Oyl
             ,
             but
             of
             the
             combustible
             body
             oyled
             that
             shine
             ,
             but
             the
             parts
             of
             Wine
             and
             strong
             Drinks
             have
             partly
             a
             strong
             Motion
             of
             themselves
             ,
             and
             may
             be
             made
             to
             shine
             ,
             but
             not
             with
             boiling
             ,
             but
             by
             adding
             to
             them
             as
             they
             rise
             the
             flame
             of
             some
             other
             body
             .
          
        
         
           
             A.
             
          
           
             How
             can
             it
             be
             known
             that
             the
             particles
             of
             Wine
             have
             such
             a
             Motion
             as
             you
             suppose
             ?
          
        
         
           
             B.
             
          
           
             Have
             you
             ever
             been
             so
             much
             distempered
             with
             drinking
             Wine
             ,
             as
             to
             think
             the
             Windows
             and
             Table
             move
             ?
          
        
         
           
             A.
             
          
           
             I
             confess
             (
             though
             you
             be
             not
             my
             Confessor
             ,
             )
             
             I
             have
             ,
             but
             very
             seldom
             ,
             and
             I
             remember
             the
             window
             seemed
             to
             go
             and
             come
             in
             a
             kind
             of
             circling
             Motion
             ,
             such
             as
             you
             have
             described
             .
             But
             what
             of
             that
             ?
          
        
         
           
             B.
             
          
           
             Nothing
             ,
             but
             that
             it
             was
             the
             Wine
             that
             caused
             it
             ;
             which
             having
             a
             good
             degree
             of
             that
             Motion
             before
             ,
             did
             when
             it
             was
             Heated
             in
             the
             Veins
             ,
             give
             that
             concussion
             (
             which
             you
             thought
             was
             in
             the
             window
             ,
             )
             to
             the
             Veins
             themselves
             ,
             and
             (
             by
             the
             continuation
             of
             the
             parts
             of
             mans
             Body
             )
             to
             the
             Brain
             ;
             and
             that
             was
             it
             which
             made
             the
             window
             seem
             to
             move
             .
          
        
         
           
             A.
             
          
           
             What
             is
             Flame
             ?
             For
             I
             have
             often
             thought
             the
             Flame
             that
             comes
             out
             of
             a
             small
             heap
             of
             Straw
             ,
             to
             be
             more
             (
             before
             it
             hath
             done
             Flaming
             ,
             )
             then
             a
             hundred
             times
             the
             Straw
             it self
             .
          
        
         
           
             B.
             
          
           
             It
             was
             but
             your
             Fancy
             .
             If
             you
             take
             a
             stick
             in
             your
             hand
             by
             one
             end
             ,
             the
             other
             end
             burning
             ,
             and
             move
             it
             swiftly
             ,
             the
             burning
             end
             ,
             if
             the
             Motion
             be
             circular
             ,
             shall
             seem
             a
             circle
             ;
             if
             streight
             ,
             a
             streight
             line
             of
             Fire
             ,
             longer
             or
             shorter
             ,
             according
             to
             the
             swiftness
             of
             the
             Motion
             ,
             or
             to
             the
             space
             it
             moves
             in
             .
             You
             know
             the
             cause
             of
             that
             .
          
        
         
           
             A.
             
          
           
             I
             think
             it
             is
             ,
             because
             the
             impression
             of
             that
             visible
             Object
             ,
             which
             was
             made
             at
             the
             first
             instant
             of
             the
             Motion
             did
             last
             till
             it
             was
             ended
             .
             For
             then
             it
             will
             follow
             that
             it
             
             must
             be
             visible
             all
             the
             way
             ,
             the
             impressions
             in
             all
             points
             of
             the
             time
             being
             equal
             .
          
        
         
           
             B.
             
          
           
             The
             cause
             can
             be
             no
             other
             .
             The
             smallest
             spark
             of
             Fire
             flying
             up
             seems
             a
             line
             drawn
             upward
             ;
             and
             again
             by
             that
             swift
             circular
             Motion
             which
             we
             have
             supposed
             for
             the
             cause
             of
             Light
             ,
             seems
             also
             broader
             then
             it
             is
             .
             And
             consequently
             the
             Flame
             of
             every
             thing
             must
             needs
             seem
             much
             greater
             then
             it
             is
             .
          
        
         
           
             A.
             
          
           
             What
             are
             those
             sparks
             that
             flie
             out
             of
             the
             Fire
             ?
          
        
         
           
             B.
             
          
           
             They
             are
             small
             pieces
             of
             the
             wood
             or
             Coals
             ,
             or
             other
             Fuel
             loosened
             and
             carried
             away
             with
             the
             Air
             that
             cometh
             up
             with
             them
             .
             And
             being
             extiguished
             before
             their
             parts
             be
             quite
             dissipated
             into
             others
             ,
             are
             so
             much
             Soot
             ,
             and
             black
             ,
             and
             may
             be
             fired
             again
             .
          
        
         
           
             A.
             
          
           
             A
             Spark
             of
             Fire
             may
             be
             stricken
             out
             of
             a
             cold
             stone
             .
             It
             is
             not
             therefore
             Heat
             that
             makes
             this
             shining
             .
          
        
         
           
             B.
             
          
           
             No
             'T
             is
             the
             Motion
             that
             makes
             both
             the
             Heat
             and
             shining
             ;
             and
             the
             stroke
             makes
             the
             Motion
             .
             For
             every
             of
             those
             Sparks
             ,
             is
             a
             little
             parcel
             of
             the
             stone
             ,
             which
             swiftly
             moved
             ,
             imprinteth
             the
             same
             Motion
             into
             the
             matter
             prepared
             ,
             or
             〈◊〉
             receive
             it
             .
          
        
         
           
             A.
             
          
           
             How
             comes
             the
             Light
             of
             the
             Sun
             to
             burn
             almost
             any
             combustible
             matter
             by
             rerefraction
             
             through
             a
             convex
             glass
             ,
             and
             by
             reflection
             from
             a
             concave
             ?
          
        
         
           
             B.
             
          
           
             The
             Air
             moved
             by
             the
             Sun
             presseth
             the
             convex
             glass
             in
             such
             manner
             as
             the
             action
             continued
             through
             it
             ,
             proceedeth
             not
             in
             the
             same
             streight
             line
             by
             which
             it
             proceeded
             from
             the
             Sun
             ,
             but
             tendeth
             more
             toward
             the
             center
             of
             the
             body
             it
             enters
             .
             Also
             when
             the
             action
             is
             continued
             through
             the
             convex
             body
             it
             bendeth
             again
             the
             same
             way
             .
             By
             which
             means
             the
             whole
             action
             of
             the
             Sun-beams
             are
             enclosed
             within
             a
             very
             small
             compass
             ;
             in
             which
             place
             therefore
             there
             must
             be
             a
             very
             vehement
             Motion
             ;
             and
             consequently
             if
             there
             be
             in
             that
             place
             combustible
             matter
             ,
             such
             as
             is
             not
             very
             hard
             kindle
             ,
             the
             parts
             of
             it
             will
             be
             dissipated
             ,
             and
             receive
             that
             Motion
             which
             worketh
             on
             the
             Eye
             as
             other
             Fire
             does
             .
          
           
             The
             same
             reason
             is
             to
             be
             given
             for
             burning
             by
             Reflection
             .
             For
             there
             also
             the
             Beams
             are
             collected
             into
             almost
             a
             point
             .
          
        
         
           
             A.
             
          
           
             Why
             may
             not
             the
             Sun-beams
             be
             such
             a
             Body
             as
             we
             call
             Fire
             ,
             and
             pass
             through
             the
             pores
             of
             the
             glass
             so
             disposed
             as
             to
             cary
             them
             to
             a
             point
             ,
             or
             very
             near
             ?
          
        
         
           
             B.
             
          
           
             Can
             there
             be
             a
             glass
             that
             is
             all
             pores
             ;
             If
             there
             cannot
             ,
             then
             cannot
             this
             effect
             be
             produced
             by
             the
             passing
             of
             Fire
             through
             the
             pores
             .
             You
             have
             seen
             men
             
             llght
             their
             Tobacco
             at
             the
             Sun
             with
             a
             burning
             glass
             ,
             or
             with
             a
             ball
             of
             Cristal
             ,
             held
             which
             way
             they
             will
             indifferently
             .
             Which
             must
             be
             impossible
             ,
             unless
             the
             ball
             were
             all
             pores
             .
             Again
             ,
             neither
             you
             nor
             I
             can
             conceive
             any
             other
             Fire
             then
             we
             have
             seen
             ,
             nor
             then
             such
             as
             water
             will
             put
             out
             .
             But
             not
             only
             a
             solid
             Globe
             of
             Glass
             or
             Cristal
             will
             serve
             for
             a
             burning
             Glass
             ,
             but
             also
             a
             hollow
             one
             filled
             with
             water
             .
             How
             then
             does
             the
             Fire
             from
             the
             Sun
             pass
             through
             the
             glass
             of
             water
             without
             being
             put
             out
             before
             it
             come
             to
             the
             matter
             they
             would
             have
             it
             burn
             ?
          
        
         
           
             A.
             
          
           
             I
             know
             not
             .
             There
             comes
             nothing
             from
             the
             Sun.
             If
             there
             did
             ,
             there
             is
             come
             so
             much
             from
             it
             already
             ,
             that
             at
             this
             day
             we
             had
             had
             no
             Sun
             ,
          
        
      
       
         
         
           CHAP.
           V.
           Problems
           of
           Hard
           and
           Soft
           .
        
         
           
             A.
             
          
           
             WHat
             call
             you
             Hard
             ,
             and
             what
             Soft
             .
          
        
         
           
             B.
             
          
           
             That
             body
             whereof
             no
             one
             part
             is
             easily
             put
             out
             of
             its
             place
             ,
             without
             removing
             the
             whole
             ,
             is
             that
             which
             I
             and
             all
             men
             call
             Hard
             ;
             and
             the
             contrary
             Soft
             .
             So
             that
             they
             ,
             are
             but
             degrees
             one
             of
             another
             .
          
        
         
           
             A.
             
          
           
             What
             is
             the
             cause
             that
             makes
             one
             body
             Harder
             then
             another
             ,
             or
             (
             seeing
             you
             say
             they
             are
             but
             degrees
             of
             one
             another
             )
             what
             makes
             one
             body
             Softer
             then
             another
             ,
             and
             the
             same
             body
             sometimes
             Harder
             ,
             sometimes
             Softer
             ?
          
        
         
           
             B.
             
          
           
             The
             same
             Motion
             which
             we
             have
             supposed
             from
             the
             beginning
             for
             the
             cause
             of
             so
             many
             other
             effects
             .
             Which
             Motion
             not
             being
             upon
             the
             center
             of
             the
             part
             moved
             ,
             but
             the
             part
             it self
             going
             in
             another
             circle
             to
             and
             again
             ,
             it
             is
             not
             necessary
             that
             the
             Motion
             be
             perfectly
             circular
             .
             For
             it
             is
             not
             circulation
             ,
             but
             the
             reciprocation
             ,
             I
             mean
             the
             to
             and
             again
             that
             does
             cast
             off
             ,
             and
             lacerrate
             the
             Air
             ,
             and
             consequently
             produce
             the
             fore-mentioned
             effects
             .
          
        
         
         
           For
           the
           cause
           therefore
           of
           Hardness
           ,
           I
           suppose
           the
           reciprocation
           of
           Motion
           in
           those
           things
           which
           are
           Hard
           ,
           to
           be
           very
           swift
           ,
           and
           in
           very
           small
           circles
           .
        
         
           
             A.
             
          
           
             This
             is
             somewhat
             hard
             to
             believe
             .
             I
             would
             you
             could
             supply
             it
             with
             some
             visible
             experience
             .
          
        
         
           
             B.
             
          
           
             When
             you
             see
             (
             for
             example
             )
             a
             Cross-bow
             bent
             ,
             do
             you
             think
             the
             parts
             of
             it
             stir
             ?
          
        
         
           
             A.
             
          
           
             No.
             I
             am
             sure
             they
             do
             not
             .
          
        
         
           
             B.
             
          
           
             How
             are
             you
             sure
             ?
             You
             have
             no
             argument
             for
             it
             ,
             but
             that
             you
             do
             not
             see
             the
             Motion
             .
             When
             I
             see
             you
             sitting
             still
             ,
             must
             I
             believe
             there
             is
             no
             Motion
             in
             your
             parts
             within
             ,
             when
             there
             are
             so
             many
             arguments
             to
             convince
             me
             there
             is
             .
          
        
         
           
             A.
             
          
           
             What
             argument
             have
             you
             to
             convince
             me
             that
             there
             is
             Motion
             in
             a
             Cross-bow
             when
             it
             stands
             bent
             ?
          
        
         
           
             B.
             
          
           
             If
             you
             cut
             the
             string
             ,
             or
             any
             way
             set
             the
             Bow
             at
             liberty
             it
             will
             have
             then
             a
             very
             visible
             Motion
             .
             What
             can
             be
             the
             cause
             of
             that
             ?
          
        
         
           
             A.
             
          
           
             Why
             the
             setting
             of
             the
             Bow
             at
             liberty
             .
          
        
         
           
             B.
             
          
           
             If
             the
             Bow
             had
             been
             crooked
             before
             it
             was
             bent
             ,
             and
             a
             string
             tied
             to
             both
             ends
             ,
             and
             then
             cut
             asunder
             ,
             the
             Bow
             would
             not
             have
             stir'd
             .
             Where
             lies
             the
             difference
             ?
          
        
         
           
             A.
             
          
           
             The
             Bow
             bent
             has
             a
             Spring
             ;
             unbent
             it
             has
             none
             ,
             how
             crooked
             soever
             .
          
        
         
           
           
             B.
             
          
           
             What
             mean
             you
             by
             Spring
             ?
          
        
         
           
             A.
             
          
           
             An
             endeavour
             of
             restitution
             to
             it's
             former
             posture
             .
          
        
         
           
             B.
             
          
           
             I
             understand
             Spring
             as
             well
             as
             I
             do
             endeavour
             .
          
        
         
           
             A.
             
          
           
             I
             mean
             a
             Prnciple
             or
             beginning
             of
             Motion
             in
             a
             contrary
             way
             to
             that
             of
             the
             force
             which
             bent
             it
             .
          
        
         
           
             B.
             
          
           
             But
             the
             beginning
             of
             Motion
             is
             also
             Motion
             ,
             how
             insensible
             soever
             it
             be
             .
             And
             you
             know
             that
             nothing
             can
             give
             a
             beginning
             of
             Motion
             to
             it self
             .
             What
             is
             it
             therefore
             that
             gives
             the
             Bow
             (
             which
             you
             say
             you
             are
             sure
             was
             at
             rest
             when
             it
             stood
             bent
             )
             its
             first
             endeavour
             to
             return
             to
             its
             former
             posture
             ?
          
        
         
           
             A.
             
          
           
             It
             was
             he
             that
             bent
             it
             .
          
        
         
           
             B.
             
          
           
             That
             cannot
             be
             .
             For
             he
             gave
             it
             an
             endeavour
             to
             come
             forward
             ,
             and
             the
             Bow
             endeavours
             to
             go
             backward
             .
          
        
         
           
             A.
             
          
           
             Well
             ,
             grant
             that
             endeavour
             be
             Motiou
             ,
             and
             Motion
             in
             the
             Bow
             unbent
             ,
             how
             do
             you
             derive
             from
             thence
             ,
             that
             being
             set
             at
             liberty
             it
             must
             return
             to
             its
             former
             posture
             ?
          
        
         
           
             B.
             
          
           
             Thus
             There
             being
             within
             the
             Bow
             a
             swift
             (
             though
             invisible
             )
             Motion
             of
             all
             the
             parts
             ,
             and
             consequently
             of
             the
             whole
             ;
             the
             bending
             causeth
             that
             Motion
             ,
             which
             was
             along
             the
             Bow
             (
             that
             was
             beaten
             out
             when
             it
             was
             hot
             into
             that
             length
             )
             to
             operate
             
             a
             cross
             the
             length
             in
             every
             part
             of
             it
             ,
             and
             the
             more
             by
             how
             much
             it
             is
             more
             bent
             ;
             and
             consequently
             endeavours
             to
             unbend
             it
             all
             the
             while
             it
             stands
             bent
             .
             And
             therefore
             when
             the
             force
             which
             kept
             it
             bent
             is
             removed
             ,
             it
             must
             of
             necessity
             return
             to
             the
             posture
             it
             had
             before
             .
          
        
         
           
             A.
             
          
           
             But
             has
             that
             endeavour
             no
             effect
             at
             all
             before
             the
             impediment
             be
             removed
             ?
             For
             if
             endeavour
             be
             Motion
             ,
             and
             every
             Motion
             have
             some
             effect
             more
             or
             less
             ,
             methinks
             this
             endavour
             should
             in
             time
             produce
             something
             .
          
        
         
           
             B.
             
          
           
             So
             it
             does
             .
             For
             in
             time
             (
             in
             a
             long
             time
             )
             the
             course
             of
             this
             internal
             Motion
             will
             lie
             along
             the
             Bow
             ,
             not
             according
             to
             the
             former
             ,
             but
             to
             the
             new
             acquired
             posture
             .
             And
             then
             it
             will
             be
             as
             uneasie
             to
             return
             it
             to
             its
             former
             posture
             ,
             as
             it
             was
             before
             to
             bend
             it
             .
          
        
         
           
             A.
             
          
           
             That
             's
             true
             .
             For
             Bows
             long
             bent
             lose
             their
             appetite
             to
             restitution
             ,
             long
             custom
             becoming
             nature
             .
             But
             from
             this
             internal
             reciprocation
             of
             the
             parts
             ,
             how
             do
             you
             infer
             the
             Hardness
             of
             the
             whole
             Body
             .
          
        
         
           
             B.
             
          
           
             If
             you
             apply
             force
             to
             any
             single
             part
             of
             such
             a
             body
             ,
             you
             must
             needs
             disorder
             the
             Motion
             of
             the
             next
             parts
             to
             it
             before
             it
             yield
             ,
             and
             there
             disordered
             ,
             the
             Motion
             of
             the
             next
             again
             must
             also
             be
             disordered
             ;
             and
             consequently
             no
             one
             part
             can
             yield
             
             without
             force
             sufficient
             to
             disorder
             all
             .
             But
             then
             the
             whole
             body
             must
             also
             yield
             .
             Now
             when
             a
             body
             is
             of
             such
             a
             nature
             as
             no
             single
             part
             can
             be
             removed
             without
             removing
             the
             whole
             ,
             men
             say
             that
             body
             is
             Hard.
             
          
        
         
           
             A.
             
          
           
             Why
             does
             the
             Fire
             melt
             divers
             Hard
             bodies
             ,
             and
             yet
             not
             all
             ?
          
        
         
           
             B.
             
          
           
             The
             hardest
             bodies
             are
             those
             wherein
             the
             Motion
             of
             the
             parts
             are
             the
             most
             swift
             ,
             and
             yet
             in
             the
             least
             circles
             .
          
           
             Wherefore
             if
             the
             Fire
             ,
             the
             Motion
             of
             whose
             parts
             are
             swift
             ,
             and
             in
             greater
             circiles
             ,
             he
             made
             so
             swit
             ,
             as
             to
             be
             strong
             enough
             to
             master
             the
             Motion
             of
             the
             parts
             of
             the
             Hard
             body
             ,
             it
             will
             make
             those
             parts
             to
             move
             in
             a
             greater
             compass
             ,
             and
             thereby
             weaken
             their
             resistance
             ,
             that
             is
             to
             say
             ,
             Soften
             them
             ,
             which
             is
             a
             degree
             of
             liquefaction
             .
             And
             when
             the
             Moton
             is
             so
             weakened
             ,
             as
             that
             the
             parts
             lose
             their
             coherence
             by
             the
             force
             of
             their
             own
             weight
             ,
             then
             we
             count
             the
             body
             melted
             .
          
        
         
           
             A.
             
          
           
             Why
             are
             the
             Hardest
             things
             the
             most
             brittle
             ,
             insomuch
             that
             what
             force
             soever
             is
             enough
             to
             bend
             them
             ,
             is
             enough
             also
             to
             break
             them
             ?
          
        
         
           
             B.
             
          
           
             In
             bending
             a
             Hard
             body
             ,
             as
             (
             for
             example
             )
             a
             Rod
             of
             Iron
             ,
             you
             do
             not
             inlarge
             the
             space
             of
             the
             internal
             Motion
             of
             the
             parts
             of
             Iron
             ,
             as
             the
             Fire
             does
             ;
             
             but
             you
             master
             and
             interrupt
             the
             Motion
             ,
             and
             that
             chiefly
             in
             one
             place
             .
             In
             which
             place
             the
             Motion
             that
             makes
             the
             Iron
             Hard
             being
             once
             overcome
             ,
             the
             prosecution
             of
             that
             bending
             must
             needs
             suddenly
             master
             the
             Motions
             of
             the
             parts
             next
             unto
             it
             ,
             being
             almost
             mastered
             before
             .
          
        
         
           
             A.
             
          
           
             I
             have
             seen
             a
             small
             piece
             of
             glass
             ,
             the
             figure
             whereof
             is
             this
             
               A
               A
               B
               C.
            
             Which
             piece
             of
             glass
             if
             you
             bend
             toward
             to
             top
             ,
             as
             in
             C
             ,
             the
             whole
             body
             will
             shatter
             asunder
             into
             a
             Million
             of
             pieces
             ,
             and
             be
             like
             to
             so
             much
             dust
             .
             I
             would
             fain
             see
             you
             give
             a
             probable
             reason
             of
             that
             .
          
        
         
           
             B.
             
          
           
             I
             have
             seen
             the
             Experiment
             .
             The
             making
             of
             the
             glass
             ,
             is
             thus
             ,
             They
             dip
             an
             Iron
             Rod
             into
             the
             molten
             glass
             that
             stands
             in
             a
             Vessel
             within
             the
             Furnace
             .
             Upon
             which
             Iron
             Rod
             taken
             out
             ,
             there
             will
             hang
             a
             drop
             of
             molten
             but
             tough
             Mettal
             of
             the
             figure
             you
             have
             described
             ,
             which
             they
             let
             fall
             into
             the
             water
             .
             So
             that
             the
             main
             drop
             comes
             first
             to
             the
             water
             ,
             and
             after
             it
             the
             tail
             ,
             which
             though
             streight
             whilst
             it
             hung
             on
             the
             end
             of
             the
             Rod
             ,
             yet
             by
             falling
             into
             the
             water
             becomes
             crooked
             .
             Now
             you
             know
             the
             making
             of
             it
             ,
             you
             may
             consider
             what
             must
             be
             the
             consequence
             of
             it
             .
             Because
             the
             main
             drop
             A
             comes
             first
             to
             the
             water
             ,
             it
             is
             therefore
             first
             quenched
             ,
             and
             consequently
             that
             the
             Motion
             
             of
             the
             parts
             of
             that
             drop
             ,
             which
             by
             the
             Fire
             were
             made
             to
             be
             moved
             in
             a
             larger
             compass
             ,
             is
             by
             the
             water
             made
             to
             shrink
             into
             lesser
             circles
             towards
             the
             other
             end
             B
             ,
             but
             with
             the
             same
             or
             not
             much
             less
             swiftness
             .
          
        
         
           
             A.
             
          
           
             Why
             so
             ?
          
        
         
           
             B.
             
          
           
             If
             you
             take
             any
             long
             piece
             of
             Iron
             ,
             Glass
             ,
             or
             other
             uniform
             and
             continued
             body
             ;
             and
             having
             Heated
             one
             end
             thereof
             ,
             you
             hold
             the
             other
             end
             in
             your
             hand
             ,
             and
             so
             quench
             it
             suddenly
             ,
             though
             before
             ,
             you
             held
             it
             easily
             enough
             ,
             yet
             now
             it
             will
             burn
             your
             fingers
             .
          
        
         
           
             A.
             
          
           
             It
             will
             so
             .
          
        
         
           
             B.
             
          
           
             You
             see
             then
             how
             the
             Motion
             of
             the
             parts
             from
             A
             toward
             C
             is
             made
             more
             violent
             and
             in
             less
             compass
             by
             quenching
             the
             other
             parts
             first
             .
             Besides
             ,
             the
             whole
             Motion
             that
             was
             in
             all
             the
             parts
             of
             the
             main
             drop
             A
             ,
             is
             now
             united
             in
             the
             small
             end
             B
             C.
             And
             this
             I
             take
             to
             be
             the
             cause
             why
             that
             small
             part
             B
             C
             is
             so
             exceeding
             stiff
             .
             Seeing
             also
             this
             Motion
             in
             every
             small
             part
             of
             the
             glass
             ,
             is
             not
             only
             circular
             ,
             but
             proceeds
             also
             all
             along
             the
             glass
             from
             A
             to
             B
             ,
             the
             whole
             Motion
             compounded
             will
             be
             such
             as
             the
             Motion
             of
             Spinning
             any
             Soft
             matter
             unto
             Thread
             ,
             and
             will
             dispose
             the
             whole
             body
             of
             the
             glass
             in
             Threads
             ,
             which
             in
             other
             Hard
             bodies
             are
             called
             the
             grain
             .
          
        
         
         
           Therefore
           if
           you
           bend
           this
           body
           (
           for
           example
           )
           in
           C
           (
           which
           to
           do
           will
           require
           more
           force
           then
           a
           man
           would
           think
           that
           has
           not
           tryed
           )
           those
           threads
           of
           Glass
           must
           needs
           be
           all
           bent
           at
           the
           same
           time
           ,
           and
           stand
           so
           ,
           till
           by
           the
           breaking
           of
           the
           Glass
           at
           C
           ,
           they
           be
           all
           at
           once
           set
           at
           liberty
           .
           And
           then
           all
           at
           once
           being
           suddenly
           unbent
           ,
           like
           so
           many
           brittle
           ,
           and
           over-bent
           Bows
           ,
           their
           Strings
           breaking
           ,
           be
           shivered
           in
           pieces
           .
        
         
           
             A.
             
          
           
             'T
             is
             like
             enough
             to
             be
             so
             .
             And
             if
             nature
             have
             betrayed
             her self
             in
             any
             thing
             ,
             I
             think
             it
             is
             in
             this
             ,
             and
             in
             that
             other
             experience
             of
             the
             Cross-bow
             ;
             which
             strongly
             and
             evidently
             demonstrates
             the
             internal
             reciprocation
             of
             the
             Motion
             ,
             which
             you
             suppose
             to
             be
             in
             the
             internal
             parts
             of
             every
             Hard
             body
             .
             And
             I
             have
             observed
             somewhat
             in
             Looking-glasses
             which
             much
             confirms
             that
             there
             is
             some
             such
             Motion
             in
             the
             internal
             parts
             of
             Glass
             ,
             as
             you
             have
             supposed
             for
             the
             cause
             of
             Hardness
             .
             For
             let
             the
             Glass
             be
             
               A
               B
            
             ,
             and
             let
             the
             Object
             at
             C
             be
             a
             Candle
             ,
             and
             the
             Eye
             at
             D.
             Now
             by
             divers
             Reflections
             and
             Refractions
             in
             the
             two
             superficies
             of
             the
             Glass
             ,
             if
             the
             Lines
             of
             Vision
             be
             very
             oblique
             ,
             you
             shall
             see
             many
             images
             of
             the
             Candle
             ,
             as
             
               E
               ,
               F
               ,
               G
            
             ,
             in
             such
             order
             and
             position
             as
             is
             here
             described
             .
             But
             if
             you
             remove
             your
             Eye
             to
             C
             ,
             and
             the
             Candle
             to
             D
             ,
             
             they
             will
             appear
             in
             a
             situation
             manifestly
             different
             from
             this
             .
             Which
             you
             will
             yet
             more
             plainly
             perceive
             if
             the
             Looking-Glass
             be
             coloured
             ,
             as
             I
             have
             obseved
             in
             Red
             and
             Blew
             Glasses
             ;
             and
             could
             never
             conceive
             any
             probable
             cause
             of
             it
             ,
             till
             now
             you
             tell
             me
             of
             this
             secret
             Motion
             of
             the
             parts
             across
             the
             grain
             of
             the
             Glass
             ,
             acquired
             by
             cooling
             it
             this
             or
             that
             way
             .
          
        
         
           
             B.
             
          
           
             There
             be
             very
             many
             kinds
             of
             Hard
             bodies
             ,
             Metals
             ,
             Stones
             ,
             and
             other
             kinds
             in
             the
             bowels
             of
             the
             Earth
             ,
             that
             have
             been
             there
             ever
             sence
             the
             beginning
             of
             the
             World
             ;
             and
             I
             believe
             also
             many
             different
             sorts
             of
             Juices
             that
             may
             be
             made
             Hard.
             But
             for
             one
             general
             cause
             of
             Hardness
             it
             can
             be
             no
             other
             then
             such
             an
             internal
             Motion
             of
             parts
             as
             I
             have
             already
             described
             ,
             whatsoever
             may
             be
             the
             cause
             of
             the
             several
             concomitant
             qualities
             of
             their
             Hardness
             in
             particular
             .
          
        
         
           
             A.
             
          
           
             We
             see
             water
             Hardened
             every
             Frosty
             day
             .
             It
             's
             likely
             therefore
             you
             may
             give
             a
             pribable
             cause
             of
             Ice
             .
             What
             is
             the
             cause
             of
             Freezing
             of
             the
             Ocean
             towards
             the
             Poles
             of
             the
             Earth
             ?
          
        
         
           
             B.
             
          
           
             You
             know
             the
             Sun
             being
             always
             between
             the
             Tropicks
             ,
             and
             (
             as
             we
             have
             supposed
             )
             always
             casting
             off
             the
             Air
             ;
             and
             the
             Earth
             likewise
             casting
             it
             off
             from
             it's
             self
             ,
             there
             must
             needs
             on
             both
             
             sides
             be
             a
             great
             Stream
             of
             Air
             towards
             the
             Poles
             ,
             shaving
             the
             superficies
             of
             the
             Earth
             and
             Sea
             ,
             in
             the
             Northern
             and
             Southern
             Climates
             .
             This
             shaving
             of
             the
             Earth
             and
             Sea
             by
             the
             Stream
             of
             Air
             must
             needs
             contract
             and
             make
             to
             shrink
             those
             little
             Circles
             of
             the
             internal
             parts
             of
             Earth
             and
             Water
             ,
             and
             consequently
             Harden
             them
             ,
             first
             at
             the
             superficies
             ,
             into
             a
             thin
             skin
             ,
             which
             is
             the
             first
             Ice
             ;
             and
             afterwards
             the
             same
             Motion
             continuing
             ,
             and
             the
             first
             Ice
             co-operating
             ,
             the
             Ice
             becomes
             thicker
             .
             And
             this
             I
             conceive
             to
             be
             the
             cause
             of
             the
             Freezing
             of
             the
             Ocean
             .
          
        
         
           
             A.
             
          
           
             If
             that
             be
             the
             cause
             ,
             I
             need
             not
             ask
             how
             a
             Bottle
             of
             water
             is
             made
             to
             Freeze
             in
             warm
             weather
             with
             Snow
             ,
             or
             Ice
             mingled
             with
             Salt.
             For
             when
             the
             Bottle
             is
             in
             the
             midst
             of
             it
             ,
             the
             Wind
             that
             goeth
             out
             both
             of
             the
             Salt
             and
             of
             the
             Ice
             as
             they
             dissolve
             ,
             must
             needs
             shave
             the
             superficies
             of
             the
             Bottle
             ,
             and
             the
             Bottle
             work
             accordingly
             on
             the
             water
             without
             it
             ,
             and
             so
             give
             it
             first
             a
             thin
             skin
             ,
             and
             at
             last
             thicken
             it
             into
             a
             solid
             piece
             of
             Ice
             .
             But
             how
             comes
             it
             to
             pass
             that
             water
             does
             not
             use
             to
             Freeze
             in
             a
             deep
             Pit
             ?
          
        
         
           
             B.
             
          
           
             A
             deep
             Pit
             is
             a
             very
             thick
             Bottle
             ,
             and
             such
             as
             the
             Air
             cannot
             come
             at
             but
             only
             at
             the
             top
             ,
             or
             where
             the
             Earth
             is
             very
             loose
             and
             spungy
             .
          
        
         
           
           
             A.
             
          
           
             Why
             will
             not
             Wine
             Freeze
             as
             well
             as
             Water
             ?
          
        
         
           
             B.
             
          
           
             So
             it
             will
             when
             the
             Frost
             is
             great
             enough
             .
             But
             the
             internal
             Motion
             of
             the
             parts
             of
             Wine
             and
             other
             Heating
             Liquors
             is
             in
             greater
             Circles
             and
             stronger
             then
             the
             Motion
             of
             the
             parts
             of
             water
             ;
             and
             therefore
             less
             easily
             to
             be
             Frozen
             ,
             especally
             quite
             through
             ,
             because
             those
             parts
             that
             have
             the
             strongest
             Motion
             retire
             to
             the
             center
             of
             the
             Vessel
             .
          
        
      
       
         
           CHAP.
           VI.
           Problems
           of
           Rain
           ,
           Wind
           ,
           and
           other
           WEATHER
           .
        
         
           
             A.
             
          
           
             WHat
             is
             the
             original
             cause
             of
             Rain
             ?
             and
             how
             is
             it
             generated
             ?
          
        
         
           
             B.
             
          
           
             The
             motion
             of
             the
             Air
             (
             such
             as
             I
             have
             described
             to
             you
             already
             )
             tending
             to
             the
             dis-union
             of
             the
             parts
             of
             the
             Air
             ,
             must
             needs
             cause
             a
             continual
             endeavour
             (
             there
             being
             no
             possibility
             of
             Vacuum
             )
             of
             whatsoever
             fluid
             parts
             there
             are
             upon
             the
             face
             of
             the
             Earth
             and
             Sea
             ,
             to
             supply
             the
             place
             which
             would
             else
             be
             empty
             .
          
           
             This
             makes
             the
             water
             ,
             and
             also
             very
             small
             and
             loose
             parts
             of
             the
             Earth
             and
             Sea
             
             to
             rise
             ,
             and
             mingle
             themselves
             with
             the
             Air
             ,
             and
             to
             become
             mist
             and
             Clouds
             .
             Of
             which
             the
             greatest
             quantity
             arise
             there
             ,
             where
             there
             is
             most
             water
             ,
             namely
             ,
             from
             the
             large
             parts
             of
             the
             Ocean
             ;
             which
             are
             the
             South
             Sea
             ,
             the
             Indian
             Sea
             ,
             and
             the
             Sea
             that
             divideth
             Europe
             and
             Africa
             from
             America
             ;
             over
             which
             the
             Sun
             ,
             for
             the
             greatest
             part
             of
             the
             year
             is
             perpendicular
             ,
             and
             consequently
             raiseth
             a
             greater
             quantity
             of
             water
             .
             Which
             afterwards
             gathered
             into
             Clouds
             ,
             falls
             down
             in
             Rain
             .
          
        
         
           
             A.
             
          
           
             If
             the
             Sun
             can
             thus
             draw
             up
             the
             water
             ;
             though
             but
             in
             small
             drops
             ,
             why
             can
             it
             not
             as
             easily
             hold
             it
             up
             ?
          
        
         
           
             B.
             
          
           
             It
             is
             likely
             it
             would
             also
             hold
             them
             up
             ,
             if
             they
             did
             not
             grow
             greater
             by
             meeting
             together
             ,
             nor
             were
             carried
             away
             by
             the
             Air
             towards
             the
             Poles
             .
          
        
         
           
             A.
             
          
           
             What
             makes
             them
             gather
             together
             ?
          
        
         
           
             B.
             
          
           
             It
             is
             not
             improbable
             that
             they
             are
             carried
             against
             Hills
             ,
             and
             there
             stopt
             till
             more
             overtake
             them
             .
             And
             when
             they
             are
             carried
             towards
             the
             North
             or
             South
             where
             the
             force
             of
             the
             Sun
             is
             more
             oblique
             and
             thereby
             weaker
             ,
             they
             descend
             gently
             by
             their
             own
             weight
             .
             And
             because
             they
             tend
             all
             to
             the
             center
             of
             the
             Earth
             ,
             they
             must
             needs
             be
             united
             in
             their
             way
             for
             want
             of
             room
             ,
             and
             so
             grow
             bigger
             .
             And
             then
             it
             Rains.
             
          
        
         
           
           
             A.
             
          
           
             What
             is
             the
             reason
             it
             Rains
             so
             seldom
             ,
             but
             Snows
             so
             often
             upon
             very
             high
             Mountains
             ?
          
        
         
           
             B.
             
          
           
             Because
             perhaps
             when
             the
             water
             is
             drawn
             up
             higher
             then
             the
             highest
             Mountains
             ,
             where
             the
             course
             of
             the
             Air
             between
             the
             Aequator
             and
             the
             Poles
             is
             free
             from
             stopping
             ,
             the
             Stream
             of
             the
             Air
             Freezeth
             it
             into
             Snow
             .
             And
             't
             is
             in
             those
             places
             only
             where
             the
             Hills
             shelter
             it
             from
             that
             Stream
             ,
             that
             it
             falls
             in
             Rain
             .
          
        
         
           
             A.
             
          
           
             Why
             is
             there
             so
             little
             Rain
             in
             Egypt
             ,
             and
             yet
             so
             much
             in
             other
             parts
             nearer
             the
             Aequinoctial
             ,
             as
             to
             make
             the
             Nile
             overflow
             the
             Countrey
             ?
          
        
         
           
             B.
             
          
           
             The
             cause
             of
             the
             falling
             of
             Rain
             ,
             I
             told
             you
             was
             the
             the
             stopping
             ,
             and
             consequently
             the
             collection
             of
             Clouds
             about
             great
             Mountains
             ,
             especially
             when
             the
             Sun
             is
             near
             the
             Aequinoctial
             ,
             and
             thereby
             draws
             up
             the
             water
             more
             potently
             ,
             and
             from
             greater
             Seas
             .
             If
             you
             consider
             therefore
             that
             the
             Mountains
             in
             which
             are
             the
             springs
             of
             Nile
             ,
             lye
             near
             the
             Aequinoctial
             and
             are
             exceeding
             great
             ,
             and
             near
             the
             Indian
             Sea
             ,
             you
             will
             not
             think
             it
             strange
             there
             should
             be
             great
             store
             of
             Snow
             .
             This
             as
             it
             melts
             makes
             the
             Rain
             of
             Nile
             to
             rise
             ,
             which
             in
             April
             and
             May
             going
             on
             toward
             Egypt
             arrived
             there
             about
             the
             time
             of
             the
             Solstice
             ,
             and
             overflow
             the
             Countrey
             .
          
        
         
           
           
             A.
             
          
           
             Why
             should
             not
             the
             Nile
             then
             overflow
             that
             Countrey
             twice
             a
             year
             ?
             For
             it
             comes
             twice
             a
             year
             to
             the
             Aequinoctial
             .
          
        
         
           
             B.
             
          
           
             From
             the
             
               Autumnal
               Aequinox
            
             ,
             the
             Sun
             goeth
             on
             toward
             the
             Southern
             Tropique
             .
             And
             therefore
             cannot
             dissolve
             ,
             the
             Snow
             on
             that
             side
             of
             the
             Hills
             that
             look
             towards
             Egypt
             .
          
        
         
           
             A.
             
          
           
             But
             then
             there
             ought
             to
             be
             such
             another
             Innundation
             Southward
             .
          
        
         
           
             B.
             
          
           
             No
             doubt
             but
             there
             is
             a
             greater
             descent
             of
             water
             there
             in
             their
             Summer
             then
             at
             other
             times
             ;
             as
             there
             must
             be
             wheresoever
             there
             is
             much
             Snow
             melted
             .
             But
             what
             should
             that
             innundate
             ,
             unless
             it
             should
             overflow
             the
             Sea
             that
             comes
             close
             to
             the
             foot
             of
             those
             Mountains
             ?
             And
             for
             the
             cause
             why
             it
             seldom
             Rains
             in
             Egypt
             ,
             it
             may
             be
             this
             ,
             That
             there
             are
             no
             very
             high
             Hills
             near
             it
             to
             collect
             the
             Clouds
             .
             The
             Mountains
             whence
             Nile
             riseth
             being
             near
             2000
             Miles
             off
             .
             The
             nearest
             on
             one
             side
             are
             the
             Mountains
             of
             Nubia
             ,
             and
             on
             the
             other
             side
             Sina
             ,
             and
             the
             Mountains
             of
             Arrabia
             .
          
        
         
           
             A.
             
          
           
             Whence
             think
             you
             proceed
             the
             Winds
             ?
          
        
         
           
             B.
             
          
           
             From
             the
             Motion
             (
             I
             think
             )
             especially
             of
             the
             Clouds
             ,
             partly
             also
             from
             whatsoever
             is
             moved
             in
             the
             Air.
             
          
        
         
           
             A.
             
          
           
             It
             is
             manifest
             ,
             that
             the
             Clouds
             are
             
             moved
             by
             the
             Winds
             ;
             so
             that
             there
             were
             Winds
             before
             any
             clouds
             could
             be
             moved
             .
             Therefore
             I
             think
             you
             make
             the
             Effect
             before
             the
             Cause
             .
          
        
         
           
             B.
             
          
           
             If
             nothing
             could
             move
             a
             Cloud
             but
             Wind
             ,
             your
             objection
             were
             good
             .
             But
             you
             allow
             a
             Cloud
             to
             descend
             by
             it's
             own
             weight
             .
             But
             when
             it
             so
             descends
             ,
             it
             must
             needs
             move
             the
             Air
             before
             it
             ,
             even
             to
             the
             Earth
             ,
             and
             the
             Earth
             again
             repel
             it
             ,
             and
             so
             make
             lateral
             Winds
             every
             way
             .
             Which
             will
             carry
             forwards
             other
             Clouds
             if
             there
             be
             any
             in
             their
             way
             ,
             but
             not
             the
             Cloud
             that
             made
             them
             The
             Vapour
             of
             the
             water
             rising
             into
             Clouds
             ,
             must
             needs
             also
             as
             they
             rise
             ,
             raise
             a
             Wind
             ?
          
        
         
           
             A.
             
          
           
             I
             grant
             it
             .
             But
             how
             can
             the
             slow
             motion
             of
             a
             Cloud
             make
             so
             swift
             a
             Wind
             as
             it
             does
             ?
          
        
         
           
             B.
             
          
           
             It
             is
             not
             one
             or
             two
             little
             Clouds
             ,
             but
             many
             and
             great
             ones
             that
             do
             it
             .
             Besides
             ,
             when
             the
             Air
             is
             driven
             into
             places
             already
             covered
             ;
             it
             cannot
             but
             be
             much
             the
             swifter
             for
             the
             narrowness
             of
             the
             passage
          
        
         
           
             A.
             
          
           
             Why
             does
             the
             South
             Wind
             more
             often
             then
             any
             other
             bring
             Rain
             with
             it
             ?
          
        
         
           
             B.
             
          
           
             Where
             the
             Sun
             hath
             most
             power
             ,
             and
             where
             the
             Seas
             are
             greatest
             ,
             that
             is
             in
             the
             South
             ,
             there
             is
             most
             water
             in
             the
             Air
             ;
             which
             a
             South
             wind
             can
             only
             bring
             
             to
             us
             .
             But
             I
             have
             seen
             great
             showers
             of
             Rain
             sometimes
             also
             when
             the
             wind
             hath
             been
             North
             ,
             but
             it
             was
             in
             Summer
             ,
             and
             came
             first
             ,
             I
             think
             ,
             from
             the
             South
             or
             West
             ,
             and
             was
             but
             brought
             back
             from
             the
             North.
             
          
        
         
           
             A.
             
          
           
             I
             have
             seen
             at
             Sea
             very
             great
             Waves
             when
             there
             was
             no
             Wind
             at
             all
             .
             What
             was
             it
             then
             that
             troubled
             the
             Water
             ?
          
        
         
           
             B.
             
          
           
             But
             had
             you
             not
             Wind
             enough
             presently
             after
             ?
          
        
         
           
             A.
             
          
           
             We
             had
             a
             Storm
             within
             a
             little
             more
             then
             a
             quarter
             of
             an
             hour
             after
             .
          
        
         
           
             B.
             
          
           
             That
             Storm
             was
             then
             coming
             and
             had
             moved
             the
             Water
             before
             it
             .
             But
             the
             Wind
             you
             could
             not
             perceive
             ,
             for
             it
             came
             downwards
             with
             the
             descending
             of
             the
             Clouds
             ,
             and
             pressing
             the
             Water
             bounded
             above
             your
             Sail
             till
             it
             came
             very
             near
             .
             And
             that
             was
             it
             that
             made
             you
             think
             there
             was
             no
             Wind
             at
             all
             .
          
        
         
           
             A.
             
          
           
             How
             comes
             it
             to
             pass
             that
             a
             Ship
             should
             go
             against
             the
             Wind
             which
             moves
             it
             ,
             even
             almost
             point
             blank
             ,
             as
             if
             it
             were
             not
             driven
             but
             drawn
             ?
          
        
         
           
             B.
             
          
           
             You
             are
             to
             know
             first
             ,
             that
             what
             Body
             soever
             is
             carryed
             against
             another
             Body
             ,
             whether
             perpendicularly
             ,
             or
             obliquely
             ,
             it
             drives
             it
             in
             a
             perpendicular
             to
             the
             superficies
             it
             lighteth
             on
             .
             As
             for
             Example
             ,
             a
             Bullet
             shot
             against
             a
             flat
             wall
             ,
             
             maketh
             the
             Stone
             (
             or
             other
             matter
             it
             hits
             )
             to
             retire
             in
             a
             perpendicular
             to
             that
             flat
             ;
             or
             ,
             if
             the
             Wall
             be
             round
             ,
             towards
             the
             center
             ,
             that
             is
             to
             say
             ,
             perpendicularly
             .
             For
             if
             the
             way
             of
             the
             motion
             be
             oblique
             to
             the
             Wall
             ,
             the
             motion
             is
             compounded
             of
             two
             motions
             ,
             one
             parrallel
             to
             the
             Wall
             ,
             and
             the
             other
             perpendicular
             .
             By
             the
             former
             whereof
             the
             Bullet
             is
             carried
             along
             the
             Wall
             side
             ,
             by
             the
             other
             it
             approacheth
             to
             it
             .
             Now
             the
             former
             of
             these
             motions
             can
             have
             no
             effect
             upon
             it
             ;
             all
             the
             battery
             is
             from
             the
             motion
             perpendicular
             ,
             in
             which
             it
             approacheth
             .
             And
             therefore
             the
             part
             it
             hits
             must
             also
             retire
             perpendicularly
             .
             If
             it
             were
             not
             so
             ,
             a
             Bullet
             with
             the
             same
             swiftness
             would
             execute
             as
             much
             obliquely
             shot
             ,
             as
             perpendicularly
             ;
             which
             you
             know
             it
             does
             not
             .
          
        
         
           
             A.
             
          
           
             How
             do
             you
             apply
             this
             to
             a
             Ship
             ?
          
        
         
           
             B.
             
          
           
             Let
             
               A.
               B.
            
             be
             the
             Ship
             ,
             the
             head
             of
             it
             A.
             If
             the
             Wind
             blow
             just
             from
             A.
             towards
             B.
             't
             is
             true
             ,
             the
             Ship
             cannot
             go
             forward
             howsoever
             the
             sail
             be
             set
             .
             Let
             
               C.
               D.
            
             be
             perpendicular
             to
             the
             Ship
             ,
             and
             let
             the
             Sail
             
               E.
               C.
            
             be
             never
             so
             little
             oblique
             to
             it
             ,
             and
             
               F.
               C.
            
             perpendicular
             to
             
               E.
               C.
            
             and
             then
             you
             see
             the
             Ship
             will
             gain
             the
             space
             
               D.
               F.
            
             to
             the
             headward
             .
          
        
         
           
             A.
             
          
           
             It
             will
             so
             ,
             but
             when
             it
             is
             very
             near
             
             to
             the
             Wind
             it
             will
             go
             forward
             very
             slowly
             ,
             and
             make
             more
             way
             with
             her
             side
             to
             the
             Leeward
             .
          
        
         
           
             A.
             
          
           
             It
             will
             indeed
             go
             slower
             in
             the
             proportion
             of
             the
             Line
             
               A.
               E.
            
             to
             the
             Line
             
               C.
               E.
            
             But
             the
             Ship
             will
             not
             go
             so
             fast
             as
             you
             think
             sideward
             :
             One
             is
             the
             force
             of
             that
             Wind
             which
             lights
             on
             the
             side
             of
             the
             Ship
             it self
             ;
             the
             other
             is
             ,
             the
             bellying
             of
             the
             Sail
             ;
             for
             the
             former
             ,
             it
             is
             not
             much
             because
             the
             Ship
             does
             not
             easily
             put
             from
             her
             the
             Water
             with
             her
             side
             ;
             and
             bellying
             of
             the
             Sail
             ,
             gives
             some
             little
             hold
             for
             the
             Wind
             to
             drive
             the
             Ship
             a
             stern
             .
          
        
         
           
             A.
             
          
           
             For
             the
             motion
             sideward
             I
             agree
             with
             you
             ;
             but
             I
             had
             thought
             the
             bellying
             of
             the
             Sail
             ,
             had
             made
             the
             Ship
             go
             faster
             .
          
        
         
           
             B.
             
          
           
             But
             it
             does
             not
             ;
             only
             in
             a
             fore-wind
             it
             hinders
             least
             .
          
        
         
           
             A.
             
          
           
             By
             this
             reason
             a
             broad
             thin
             Board
             should
             make
             the
             best
             Sail.
             
          
        
         
           
             B.
             
          
           
             You
             may
             easily
             foresee
             the
             great
             incommodities
             of
             such
             a
             Sail.
             But
             I
             have
             seen
             tryed
             in
             little
             what
             such
             a
             Wind
             can
             do
             in
             such
             a
             case
             .
             For
             I
             have
             seen
             a
             Board
             set
             upon
             four
             truckles
             ,
             with
             a
             staff
             set
             up
             in
             the
             midst
             of
             it
             for
             a
             Mast
             ,
             and
             another
             very
             thin
             and
             broad
             Board
             fastned
             to
             that
             staff
             in
             the
             stead
             of
             a
             Sail
             ;
             and
             so
             set
             as
             to
             receive
             the
             Wind
             very
             obliquely
             ,
             I
             mean
             so
             as
             to
             be
             within
             a
             point
             of
             the
             
             Compass
             directly
             opposite
             to
             it
             ;
             and
             so
             placed
             upon
             a
             reasonable
             smooth
             pavement
             where
             the
             Wind
             blew
             somewhat
             strongly
             .
             The
             event
             was
             first
             ,
             that
             it
             stood
             doubting
             whether
             it
             should
             stir
             at
             all
             or
             no
             ,
             but
             that
             was
             not
             long
             ;
             and
             then
             it
             ran
             a
             head
             extream
             swiftly
             ,
             till
             it
             was
             overthrown
             by
             a
             Rub.
             
          
        
         
           
             A.
             
          
           
             Before
             you
             leave
             the
             Ship
             tell
             me
             how
             it
             comes
             about
             that
             so
             small
             a
             thing
             as
             a
             Rudder
             ,
             can
             so
             easily
             turn
             the
             greatest
             Ship
             ?
          
        
         
           
             B.
             
          
           
             'T
             is
             not
             the
             Rudder
             only
             ,
             there
             must
             also
             be
             a
             stream
             to
             do
             it
             ;
             you
             shall
             never
             turn
             a
             Ship
             with
             a
             Rudder
             in
             a
             standing
             pooll
             ,
             nor
             in
             a
             natural
             current
             .
          
           
             You
             must
             make
             a
             stream
             from
             head
             to
             stern
             ,
             either
             with
             Oares
             or
             with
             Sails
             :
             when
             you
             have
             made
             such
             a
             stream
             ,
             the
             turning
             of
             the
             Rudder
             obliquely
             holds
             the
             Water
             from
             passing
             freely
             ;
             and
             the
             Ship
             or
             Boat
             cannot
             go
             on
             directly
             ,
             but
             as
             the
             Rudder
             inclines
             to
             the
             stern
             ,
             so
             will
             the
             Ship
             turn
             .
             But
             this
             is
             too
             well
             known
             to
             insist
             upon
             :
             you
             have
             observed
             ,
             that
             the
             Rudders
             of
             the
             greatest
             Ships
             are
             not
             very
             broad
             ,
             but
             go
             deep
             into
             the
             Water
             ,
             whereas
             Western
             Barges
             ,
             though
             but
             small
             Vessels
             ,
             have
             their
             Rudders
             much
             broader
             ,
             which
             argues
             that
             the
             holding
             of
             Water
             from
             passing
             is
             the
             
             office
             of
             a
             Rudder
             :
             and
             therefore
             to
             a
             Ship
             that
             draws
             much
             Water
             the
             Rudder
             is
             made
             deep
             accordingly
             ,
             and
             in
             Barges
             that
             draw
             little
             Water
             ,
             the
             Rudders
             as
             less
             deep
             ,
             must
             so
             much
             the
             more
             be
             extended
             in
             breadth
             .
          
        
         
           
             A.
             
          
           
             What
             makes
             Snow
             ?
          
        
         
           
             B.
             
          
           
             The
             same
             cause
             which
             (
             speaking
             of
             Hardness
             )
             I
             supposed
             for
             the
             cause
             of
             Ice
             .
             For
             the
             Stream
             of
             Air
             proceeding
             from
             .
             That
             both
             the
             Earth
             and
             the
             Sun
             cast
             off
             the
             Air
             ,
             and
             consequently
             maketh
             a
             stream
             of
             Air
             from
             the
             Aequinoctial
             towards
             the
             Poles
             ,
             passing
             amongst
             the
             Clouds
             ,
             shaving
             those
             small
             drops
             of
             Water
             whereof
             the
             Clouds
             consist
             ,
             and
             congeals
             them
             as
             they
             do
             the
             Water
             of
             the
             Sea
             ,
             or
             of
             a
             River
             .
             And
             these
             small
             frozen
             drops
             are
             that
             which
             we
             call
             Snow
             .
          
        
         
           
             A.
             
          
           
             But
             then
             how
             are
             great
             drops
             frozen
             into
             Hailstones
             ,
             and
             that
             especially
             (
             as
             we
             see
             they
             are
             )
             in
             Summer
             ?
          
        
         
           
             B.
             
          
           
             It
             is
             especially
             in
             Summer
             ;
             and
             hot
             weather
             ,
             that
             the
             drops
             of
             Water
             which
             make
             the
             Clouds
             ,
             are
             great
             enough
             ;
             but
             it
             is
             then
             also
             that
             Clouds
             are
             sooner
             and
             more
             plentifully
             carryed
             up
             .
             And
             therefore
             the
             current
             of
             the
             Air
             strengthned
             between
             the
             Earth
             and
             the
             Clouds
             ,
             becomes
             more
             swift
             ;
             and
             thereby
             freezeth
             
             the
             drops
             of
             Water
             ,
             not
             in
             the
             Cloud
             it self
             ,
             but
             as
             they
             are
             falling
             .
             Nor
             does
             it
             freeze
             them
             throughly
             ,
             the
             time
             of
             their
             falling
             not
             permitting
             it
             ,
             but
             gives
             them
             only
             a
             thin
             coat
             of
             Ice
             ;
             as
             is
             manifest
             by
             their
             suddain
             dissolving
             .
          
        
         
           
             A.
             
          
           
             Why
             are
             not
             somteimes
             also
             whole
             Clouds
             when
             pregnant
             and
             ready
             to
             drop
             ,
             frozen
             into
             one
             piece
             of
             Ice
             ?
          
        
         
           
             B.
             
          
           
             I
             belive
             they
             are
             so
             whensoever
             it
             Thunders
             .
          
        
         
           
             A.
             
          
           
             But
             upon
             what
             ground
             do
             you
             believe
             it
             ?
          
        
         
           
             B.
             
          
           
             From
             the
             manner
             or
             kind
             of
             noise
             they
             make
             ,
             namely
             a
             crack
             ;
             which
             I
             see
             not
             how
             it
             can
             possibly
             be
             made
             by
             Water
             or
             any
             other
             soft
             Bodies
             whatsoever
             .
          
        
         
           
             A.
             
          
           
             Yes
             ,
             the
             Powder
             they
             call
             
               Aurum
               Fulminans
            
             ,
             when
             throughly
             warm
             ,
             gives
             just
             such
             another
             crack
             as
             Thunder
             .
          
        
         
           
             B.
             
          
           
             But
             why
             may
             not
             every
             small
             grain
             of
             that
             
               Aurum
               Fulminans
            
             by
             it self
             be
             heard
             ,
             though
             a
             heap
             of
             them
             together
             be
             soft
             ,
             as
             is
             any
             heap
             of
             Sand.
             Salts
             of
             all
             sorts
             are
             of
             the
             nature
             of
             Ice
             .
             But
             Gold
             is
             dissolved
             into
             
               Aurum
               Fulminans
            
             by
             Nitre
             and
             other
             Salts
             .
             And
             the
             least
             grain
             of
             it
             gives
             a
             little
             crack
             in
             the
             fire
             by
             it self
             .
             And
             therefore
             when
             they
             are
             so
             warmed
             by
             degrees
             ,
             the
             crack
             cannot
             chuse
             but
             be
             very
             great
             .
          
        
         
           
           
             A.
             
          
           
             But
             before
             it
             be
             
               Aurum
               Fulminans
            
             they
             use
             to
             wash
             away
             the
             Salt
             (
             which
             they
             call
             dulcifying
             it
             ,
             )
             and
             then
             they
             dry
             it
             gently
             by
             degrees
             .
          
        
         
           
             B.
             
          
           
             That
             is
             ,
             they
             exhale
             the
             pure
             Water
             that
             is
             left
             in
             the
             Powder
             ,
             and
             leave
             the
             Salt
             behind
             to
             Harden
             with
             drying
             .
             Other
             Powder
             made
             of
             Salts
             without
             any
             Gold
             in
             them
             will
             give
             a
             crack
             as
             great
             as
             
               Aurum
               Fulminans
            
             .
             A
             very
             great
             Chymist
             of
             our
             times
             hath
             written
             ,
             that
             Salt
             of
             
               Tarter
               ,
               Salt-peter
            
             ,
             and
             a
             little
             Brimstone
             ground
             together
             into
             a
             Powder
             ,
             and
             dryed
             ,
             a
             few
             grains
             of
             that
             Powder
             will
             be
             made
             by
             the
             fire
             to
             give
             as
             great
             a
             Clap
             as
             a
             Musquet
             .
          
        
         
           
             A.
             
          
           
             Me
             thinks
             it
             were
             worth
             your
             tryal
             to
             see
             what
             effect
             a
             Quart
             or
             a
             Pint
             of
             
               Aurum
               Fulminans
            
             would
             produce
             ,
             being
             put
             into
             a
             great
             Gun
             made
             strong
             enough
             on
             purpose
             ,
             and
             the
             Breech
             of
             the
             Gun
             set
             in
             hot
             Cinders
             ,
             so
             as
             to
             heat
             by
             degrees
             ,
             till
             the
             Powder
             fly
             .
          
        
         
           
             B.
             
          
           
             I
             pray
             you
             try
             it
             your self
             ;
             I
             cannot
             spare
             so
             much
             Money
             .
          
        
         
           
             A.
             
          
           
             What
             is
             it
             that
             breaketh
             the
             Clouds
             when
             they
             are
             frozen
             ?
          
        
         
           
             B.
             
          
           
             In
             very
             hot
             weather
             the
             Sun
             raiseth
             from
             the
             Sea
             and
             all
             moist
             places
             abundance
             of
             Water
             ,
             and
             to
             a
             great
             height
             .
             And
             whilst
             this
             Water
             hangs
             over
             us
             in
             
             Clouds
             ,
             or
             is
             again
             descending
             ,
             it
             raiseth
             other
             Clouds
             ,
             and
             it
             hapens
             very
             often
             that
             they
             press
             the
             Air
             between
             them
             ,
             and
             squeeze
             it
             through
             the
             Clouds
             themselves
             very
             violently
             ;
             which
             as
             it
             passes
             shaves
             and
             hardens
             them
             in
             the
             manner
             declared
             .
          
        
         
           
             A.
             
          
           
             That
             has
             already
             been
             granted
             ,
             my
             question
             is
             what
             breaks
             them
             ?
          
        
         
           
             B.
             
          
           
             I
             must
             here
             take
             in
             one
             supposition
             more
             .
          
        
         
           
             A.
             
          
           
             Then
             your
             Basen
             (
             it
             seems
             )
             holds
             not
             all
             you
             have
             need
             of
             .
          
        
         
           
             B.
             
          
           
             It
             may
             for
             all
             this
             ,
             for
             the
             supposition
             I
             add
             is
             no
             more
             but
             this
             ;
             that
             what
             internal
             motion
             I
             ascribe
             to
             the
             Earth
             ,
             and
             other
             the
             Concrete
             parts
             of
             the
             World
             ,
             is
             to
             be
             supposed
             also
             in
             every
             of
             their
             parts
             how
             small
             soever
             ;
             for
             what
             reason
             is
             there
             to
             think
             ,
             in
             case
             the
             whole
             Earth
             have
             in
             truth
             the
             motion
             I
             have
             ascribed
             to
             it
             ,
             that
             one
             part
             of
             it
             taken
             away
             ,
             the
             remaining
             part
             should
             love
             that
             motion
             .
             If
             you
             break
             a
             Load-stone
             both
             parts
             will
             retain
             their
             vertue
             ,
             though
             weakened
             according
             to
             the
             diminution
             of
             their
             quantity
             ;
             I
             suppose
             therefore
             in
             every
             small
             part
             of
             the
             Earth
             ,
             the
             same
             kind
             of
             motion
             ,
             which
             I
             have
             supposed
             in
             the
             whole
             :
             and
             so
             I
             recede
             not
             yet
             from
             my
             Basen
             .
          
        
         
           
           
             A.
             
          
           
             Let
             it
             be
             supposed
             ,
             and
             withall
             ,
             that
             abundance
             of
             Earth
             (
             which
             I
             see
             you
             aim
             at
             ,
             )
             be
             drawn
             up
             together
             with
             the
             Water
             .
             What
             then
             ?
          
        
         
           
             B.
             
          
           
             Then
             if
             many
             pregnant
             Clouds
             ,
             some
             ascending
             and
             some
             descending
             meet
             together
             ,
             and
             make
             concavities
             between
             ,
             and
             by
             the
             pressing
             out
             of
             the
             Air
             ,
             as
             I
             have
             said
             before
             ,
             become
             Ice
             ;
             those
             Atomes
             (
             as
             I
             may
             call
             them
             )
             of
             Earth
             will
             be
             by
             the
             straining
             of
             the
             Air
             through
             the
             water
             of
             the
             Clouds
             ,
             be
             left
             behind
             ,
             and
             remain
             in
             the
             Cavities
             of
             the
             Clouds
             ,
             and
             be
             more
             in
             number
             then
             for
             the
             proportion
             of
             the
             Air
             therein
             .
             Therefore
             for
             want
             of
             liberty
             they
             must
             needs
             justle
             one
             another
             ,
             and
             become
             (
             as
             they
             are
             more
             and
             more
             streightened
             of
             room
             )
             more
             and
             more
             swift
             ,
             and
             consequently
             at
             last
             break
             the
             Ice
             suddenly
             and
             violently
             ,
             now
             in
             one
             place
             ,
             and
             by
             and
             by
             in
             another
             ;
             and
             make
             thereby
             so
             many
             claps
             of
             Thunder
             ,
             and
             so
             many
             Flashes
             of
             Lightning
             .
             For
             the
             Air
             Recoiling
             upon
             our
             Eyes
             ,
             is
             that
             which
             maketh
             those
             Flashes
             to
             our
             Fancy
             .
          
        
         
           
             A.
             
          
           
             But
             I
             have
             seen
             Lightning
             in
             a
             very
             clear
             Evening
             ,
             when
             there
             has
             been
             neither
             Thunder
             nor
             Clouds
             .
          
        
         
           
             B.
             
          
           
             Yes
             in
             a
             clear
             evening
             ;
             because
             the
             Clouds
             and
             the
             Rain
             were
             below
             the
             
             Horison
             ,
             perhaps
             40
             or
             50
             Miles
             off
             ;
             so
             that
             you
             could
             not
             see
             the
             Clouds
             nor
             hear
             the
             Thunder
             .
          
        
         
           
             A.
             
          
           
             If
             the
             Clouds
             be
             indeed
             Frozen
             into
             Ice
             ,
             I
             shall
             not
             wonder
             if
             they
             be
             sometimes
             also
             so
             scituated
             ,
             as
             (
             like
             Looking-Glasses
             )
             to
             make
             us
             see
             sometimes
             three
             or
             more
             Suns
             by
             Refraction
             and
             Reflection
             .
          
        
      
       
         
           CHAP.
           VII
           .
           Problems
           of
           Motion
           Perpendicular
           ,
           Oblique
           ;
           of
           Pression
           and
           Percussion
           ;
           Reflection
           and
           Refraction
           ;
           Attraction
           and
           Repulsion
           .
        
         
           
             IF
             a
             Bullet
             from
             a
             certain
             point
             given
             ,
             be
             shot
             against
             a
             wall
             Perpendicularly
             and
             again
             from
             the
             same
             Point
             Oblique
             ,
             What
             will
             be
             the
             proportion
             of
             the
             Forces
             wherewith
             they
             urge
             the
             wall
             ?
          
           
             For
             Example
             ,
             let
             the
             wall
             be
             
               A
               B
            
             ,
             a
             point
             given
             E
             ,
             a
             Gun
             
               C
               E
            
             that
             carries
             the
             Bullet
             Perpendicularly
             to
             F
             ,
             and
             another
             Gun
             
               D
               E
            
             that
             carries
             the
             like
             Bullet
             with
             the
             same
             swiftness
             Oblique
             to
             G
             ;
             In
             what
             proportion
             will
             their
             Forces
             be
             upon
             the
             Wall
             ?
          
        
         
           
             B.
             
          
           
             The
             force
             of
             the
             stroke
             Perpendicular
             from
             E
             to
             F
             will
             be
             greater
             then
             
             the
             Oblique
             force
             from
             E
             to
             G
             ,
             in
             the
             proportion
             of
             the
             line
             E
             G
             to
             the
             line
             E
             F.
             
          
        
         
           
             A.
             
          
           
             How
             can
             the
             difference
             be
             so
             much
             ?
             Can
             the
             Bullet
             lose
             so
             much
             of
             its
             force
             in
             the
             way
             from
             E
             to
             G
             ?
          
        
         
           
             B.
             
          
           
             No
             we
             will
             suppose
             it
             loseth
             nothing
             of
             its
             swiftness
             .
             But
             the
             cause
             is
             ,
             That
             their
             swiftness
             being
             equal
             ,
             the
             one
             is
             longer
             in
             coming
             to
             the
             wall
             then
             the
             other
             ,
             in
             Proportion
             of
             Time
             ,
             as
             E
             G
             to
             E
             F.
             For
             though
             their
             swiftness
             be
             the
             same
             ▪
             considered
             in
             themselves
             ,
             yet
             the
             swiftness
             of
             their
             approach
             to
             the
             wall
             is
             greater
             in
             E
             F
             then
             in
             E
             G
             ,
             in
             proportion
             of
             the
             lines
             themselves
             .
          
        
         
           
             A.
             
          
           
             When
             a
             Bullet
             enters
             not
             ,
             but
             rebounds
             from
             the
             wall
             ,
             does
             it
             make
             the
             same
             Angle
             going
             off
             ,
             which
             it
             did
             falling
             on
             ,
             as
             the
             Sun-beams
             do
             ?
          
        
         
           
             B.
             
          
           
             If
             you
             measure
             the
             Angles
             close
             by
             the
             wall
             there
             difference
             will
             not
             be
             ensible
             ;
             otherwise
             it
             will
             be
             great
             enough
             ,
             For
             the
             Motion
             of
             the
             Bullet
             grows
             continually
             weaker
             .
             But
             it
             is
             not
             so
             with
             the
             Sun-beams
             which
             press
             continually
             and
             equally
             .
          
        
         
           
             A.
             
          
           
             What
             is
             the
             cause
             of
             Reflection
             ?
             When
             a
             body
             can
             go
             no
             further
             on
             ,
             it
             has
             lost
             its
             Motion
             .
             Whence
             then
             comes
             the
             Motion
             by
             which
             it
             reboundeth
             ?
          
        
         
           
           
             B.
             
          
           
             This
             Motion
             of
             rebounding
             or
             reflecting
             proceedeth
             from
             the
             resistance
             .
             There
             is
             a
             difference
             to
             be
             considered
             between
             the
             Reflection
             of
             Light
             ,
             and
             of
             a
             Bullet
             ,
             answerable
             to
             their
             different
             Motions
             ,
             pressing
             and
             striking
             .
             For
             the
             action
             which
             makes
             Reflection
             of
             Light
             ,
             is
             the
             Pressure
             of
             the
             Air
             upon
             the
             Reflecting
             Body
             ,
             caused
             by
             the
             Sun
             ,
             or
             other
             shining
             body
             ,
             and
             is
             but
             a
             contrary
             endeavour
             ;
             as
             if
             two
             men
             should
             press
             with
             their
             breasts
             upon
             the
             two
             ends
             of
             a
             Staff
             ,
             though
             they
             did
             not
             remove
             one
             another
             ,
             yet
             they
             would
             find
             in
             themselves
             a
             great
             disposition
             to
             press
             backward
             upon
             whatsoever
             is
             behind
             them
             ,
             though
             not
             a
             total
             going
             out
             of
             their
             places
             .
             Such
             is
             the
             way
             of
             Reflecting
             Light.
             Now
             ,
             when
             the
             falling
             on
             of
             the
             Sun-beams
             is
             Oblique
             ,
             the
             action
             of
             them
             is
             nevertheless
             Perpendicular
             to
             the
             Superficies
             it
             falls
             on
             .
             And
             therefore
             the
             Reflecting
             Body
             ,
             by
             resisting
             ,
             turneth
             back
             that
             Motion
             Perpendicularly
             ,
             as
             from
             F
             to
             E
             ,
             but
             taketh
             nothing
             from
             the
             force
             that
             goes
             on
             parallel
             in
             the
             line
             of
             E
             H
             ;
             because
             the
             Motion
             never
             presses
             .
             And
             thus
             of
             the
             two
             Motions
             from
             F
             to
             E
             ,
             and
             from
             E
             to
             H
             is
             a
             compounded
             Motion
             in
             the
             line
             F
             H
             ,
             which
             maketh
             an
             Angle
             in
             B
             G
             ,
             equal
             to
             the
             Angle
             F
             G
             E.
             
          
        
         
         
           But
           in
           Percussion
           (
           which
           is
           the
           Motion
           of
           the
           Bullet
           against
           a
           wall
           ,
           )
           the
           Bullet
           no
           sooner
           goeth
           off
           then
           it
           loseth
           of
           its
           swiftness
           ,
           and
           inclineth
           to
           the
           Earth
           by
           its
           weight
           .
           So
           that
           the
           Angles
           made
           in
           falling
           on
           and
           going
           off
           ,
           cannot
           be
           equal
           ,
           unless
           they
           be
           measured
           close
           to
           the
           point
           where
           the
           stroke
           is
           made
           .
        
         
           
             A.
             
          
           
             If
             a
             man
             set
             a
             Board
             upright
             upon
             its
             edge
             ,
             though
             it
             may
             very
             easily
             be
             cast
             down
             with
             a
             little
             Pressure
             of
             ones
             finger
             ,
             yet
             a
             Bullet
             from
             a
             Musquet
             shall
             not
             throw
             it
             down
             but
             go
             through
             it
             .
             What
             is
             the
             cause
             of
             that
             ?
          
        
         
           
             B.
             
          
           
             In
             pressing
             with
             your
             finger
             you
             spend
             time
             to
             throw
             it
             down
             .
             For
             the
             Motion
             you
             give
             to
             the
             part
             you
             touch
             is
             communicated
             to
             every
             other
             part
             before
             it
             fall
             .
             For
             the
             whole
             cannot
             fall
             till
             every
             part
             be
             moved
             .
             But
             the
             stroke
             of
             a
             Bullet
             is
             so
             swift
             ,
             as
             it
             breaks
             through
             before
             the
             Motion
             of
             the
             part
             it
             hits
             can
             be
             communicated
             to
             all
             the
             other
             parts
             that
             must
             fall
             with
             it
             .
          
        
         
           
             A.
             
          
           
             The
             stroke
             of
             a
             Hammer
             will
             drive
             a
             Nail
             a
             great
             way
             into
             a
             piece
             of
             Wood
             on
             a
             sudden
             .
             What
             weight
             laid
             upon
             the
             head
             of
             a
             Nail
             ,
             and
             in
             how
             much
             time
             will
             do
             the
             same
             ?
             It
             is
             a
             question
             I
             have
             heard
             propounded
             amonst
             Naturalists
             ,
          
        
         
           
             B.
             
          
           
             The
             different
             manner
             of
             the
             operation
             
             of
             weight
             from
             the
             operation
             of
             a
             stroke
             ,
             makes
             it
             uncalculable
             .
             The
             suddenness
             of
             the
             stroke
             upon
             one
             point
             of
             the
             wood
             takes
             away
             the
             time
             of
             resistance
             from
             the
             rest
             .
             Therefore
             the
             Nail
             enters
             so
             far
             as
             it
             does
             .
             But
             the
             weight
             not
             only
             gives
             them
             time
             ,
             but
             also
             augments
             the
             resistance
             ;
             but
             how
             much
             ,
             and
             in
             how
             much
             time
             ,
             is
             (
             I
             think
             )
             impossible
             to
             determine
             .
          
        
         
           
             A.
             
          
           
             What
             is
             tbe
             difference
             between
             Reflection
             and
             Recoiling
             ?
          
        
         
           
             B.
             
          
           
             Any
             Reflection
             may
             (
             and
             not
             unproperly
             )
             be
             called
             recoiling
             ;
             but
             not
             contrariwise
             every
             Recoiling
             Reflection
             .
             Reflection
             is
             always
             made
             by
             the
             Re-action
             of
             a
             Body
             prest
             or
             stricken
             ;
             but
             Recoiling
             not
             always
             .
             The
             Recoiling
             of
             a
             Gun
             is
             not
             caused
             by
             its
             own
             pressing
             upon
             the
             Gun-powder
             ,
             but
             by
             the
             force
             of
             the
             Powder
             it self
             ,
             inflamed
             and
             moved
             every
             way
             alike
             :
          
        
         
           
             A.
             
          
           
             I
             had
             thought
             it
             had
             been
             by
             the
             sudden
             re-entring
             of
             the
             Air
             after
             the
             flame
             and
             Bullet
             were
             gone
             out
             .
             For
             it
             is
             impossible
             that
             so
             much
             room
             as
             is
             left
             empty
             by
             the
             discharging
             of
             the
             Gun
             ,
             should
             be
             so
             suddenly
             filled
             with
             the
             Air
             that
             entereth
             at
             the
             Touch-hole
             .
          
        
         
           
             B.
             
          
           
             The
             flame
             is
             nothing
             but
             the
             Powder
             it self
             ,
             which
             scattered
             into
             its
             smallest
             
             parts
             seems
             ,
             of
             greater
             bulk
             by
             much
             ,
             then
             in
             truth
             it
             is
             ,
             because
             they
             shine
             .
             And
             as
             the
             parts
             scatter
             more
             and
             more
             ,
             so
             still
             more
             Air
             gets
             between
             them
             ,
             entring
             not
             only
             at
             the
             Touch-hole
             ,
             but
             also
             at
             the
             mouh
             of
             the
             Gun.
             which
             two
             ways
             being
             opposite
             ,
             it
             will
             be
             much
             too
             weak
             to
             make
             the
             Gun
             Recoil
             .
          
        
         
           
             A.
             
          
           
             I
             have
             heard
             that
             a
             great
             Gun
             charged
             too
             much
             or
             too
             little
             ,
             will
             Shoot
             (
             not
             above
             ,
             nor
             below
             but
             )
             besides
             the
             mark
             ;
             and
             charged
             with
             one
             certain
             charge
             between
             both
             will
             hit
             it
             .
          
        
         
           
             B.
             
          
           
             How
             that
             should
             be
             I
             cannot
             imagine
             .
             For
             when
             all
             things
             in
             the
             cause
             are
             equal
             ,
             the
             effects
             cannot
             be
             unnequal
             .
             As
             soon
             as
             Fire
             is
             given
             ,
             and
             before
             the
             Bullet
             be
             out
             ,
             the
             Gun
             begins
             to
             Recoil
             .
             If
             then
             there
             be
             any
             unevenness
             or
             rub
             in
             the
             ground
             more
             on
             one
             side
             then
             on
             the
             other
             ,
             it
             shall
             shoot
             besides
             the
             mark
             ,
             whether
             too
             much
             ,
             or
             too
             little
             ,
             or
             justly
             charged
             ;
             because
             if
             the
             line
             wherein
             the
             Gun
             Recoileth
             decline
             ,
             the
             way
             of
             the
             Bullet
             will
             also
             decline
             to
             the
             contrary
             side
             of
             the
             mark
             .
             Therefore
             I
             can
             imagine
             no
             cause
             of
             this
             event
             ,
             but
             either
             in
             the
             ground
             it
             Recoils
             on
             ,
             or
             in
             the
             unequal
             weight
             of
             the
             parts
             of
             the
             Breech
             .
          
        
         
           
             A.
             
          
           
             How
             comes
             Refractin
             ?
          
        
         
           
             B.
             
          
           
             When
             the
             action
             is
             in
             a
             line
             Perpendicular
             
             to
             the
             superficies
             of
             the
             Body
             wrought
             upon
             ,
             there
             will
             be
             no
             Refraction
             at
             all
             .
             The
             action
             will
             proceed
             still
             in
             the
             same
             straight
             Line
             ,
             whether
             it
             be
             Pression
             as
             in
             Light
             ,
             or
             in
             Percussion
             as
             in
             the
             shooting
             of
             a
             Bullet
             .
             But
             when
             the
             Pression
             is
             Oblique
             ,
             then
             will
             the
             Refraction
             be
             that
             way
             which
             the
             Nature
             of
             the
             Bodies
             through
             which
             the
             Action
             proceeds
             shall
             determin
             .
          
        
         
           
             H.
             
          
           
             How
             is
             light
             Refracted
             ?
          
        
         
           
             B.
             
          
           
             If
             is
             pass
             through
             a
             Body
             of
             less
             ,
             into
             a
             Body
             of
             greater
             resistance
             ,
             and
             to
             the
             Point
             of
             the
             Superficies
             it
             falleth
             on
             ,
             you
             draw
             a
             Line
             Perpendicular
             to
             the
             same
             superficies
             ,
             the
             Action
             will
             proceed
             not
             in
             the
             same
             Line
             by
             which
             it
             fell
             on
             ,
             but
             in
             another
             Line
             bending
             toward
             that
             Perpendiculare
             .
          
        
         
           
             A.
             
          
           
             What
             is
             the
             reason
             of
             that
             ?
          
        
         
           
             B.
             
          
           
             I
             told
             you
             before
             ,
             that
             the
             falling
             on
             worketh
             only
             in
             the
             Perpendicular
             ;
             But
             as
             soon
             as
             the
             Action
             proceedeth
             further
             inward
             then
             a
             meer
             touch
             ,
             it
             worketh
             partly
             in
             the
             Perpendicular
             ,
             and
             partly
             forward
             ,
             and
             would
             proceed
             in
             the
             same
             line
             in
             which
             it
             fell
             on
             ,
             but
             for
             for
             the
             greater
             resistance
             which
             now
             weakneth
             the
             Motion
             forward
             ,
             and
             makes
             it
             to
             incline
             towards
             the
             Perpendicular
             .
          
        
         
           
           
             A.
             
          
           
             In
             transparent
             Bodies
             it
             may
             be
             so
             ;
             but
             there
             be
             Bodies
             through
             which
             the
             Light
             cannot
             pass
             at
             all
             .
          
        
         
           
             B.
             
          
           
             But
             the
             Action
             by
             which
             Light
             is
             made
             ,
             passeth
             through
             all
             Bodies
             .
             For
             this
             Action
             is
             Pression
             ;
             and
             whatsoever
             is
             prest
             ,
             presseth
             that
             which
             is
             next
             behind
             ,
             and
             so
             continually
             .
             But
             the
             cause
             why
             there
             is
             no
             Light
             seen
             through
             it
             ,
             is
             the
             uneveness
             of
             the
             parts
             within
             ,
             whereby
             the
             Action
             is
             by
             an
             infinite
             number
             of
             Reflections
             so
             diverted
             and
             weakned
             ,
             that
             before
             it
             hath
             proceeded
             through
             ,
             it
             hath
             not
             strength
             left
             towork
             upon
             the
             Eye
             strongly
             enough
             to
             produce
             sight
             .
          
        
         
           
             A.
             
          
           
             If
             the
             Body
             being
             transparent
             the
             Action
             proceed
             quite
             through
             ,
             into
             a
             Body
             again
             of
             less
             resistance
             ,
             as
             out
             of
             Glass
             into
             the
             Air
             ,
             which
             way
             shall
             it
             then
             proceed
             in
             the
             Air
             ?
          
        
         
           
             B.
             
          
           
             From
             the
             Point
             where
             it
             goeth
             forth
             ,
             draw
             a
             Perpendicular
             to
             the
             superficies
             of
             the
             Glass
             ,
             the
             Action
             now
             freed
             from
             the
             resistance
             it
             suffered
             ,
             will
             go
             from
             that
             Perpendicular
             ,
             as
             much
             as
             it
             did
             before
             come
             towards
             it
             .
          
        
         
           
             A.
             
          
           
             When
             a
             Bullet
             from
             out
             of
             the
             Air
             entreth
             into
             a
             Wall
             of
             Earth
             ,
             will
             that
             also
             be
             Refracted
             towards
             the
             Perpendicular
             ?
          
        
         
           
           
             B.
             
          
           
             If
             the
             Earth
             be
             all
             of
             one
             kind
             ,
             it
             will.
             For
             the
             parallel
             Motion
             ,
             will
             there
             also
             at
             the
             first
             entrance
             be
             resisted
             ,
             which
             it
             was
             not
             before
             it
             entred
             .
          
        
         
           
             A.
             
          
           
             How
             then
             comes
             a
             Bullet
             ,
             when
             shot
             very
             Obliquely
             into
             any
             broad
             Water
             ,
             and
             having
             entred
             ,
             yet
             to
             rise
             ,
             again
             into
             the
             Air
             ?
          
        
         
           
             B.
             
          
           
             When
             a
             Bullet
             is
             shot
             very
             Obliquely
             ,
             though
             the
             Motion
             be
             never
             so
             swift
             ,
             yet
             approach
             downwards
             to
             the
             Water
             is
             very
             slow
             ,
             and
             when
             it
             cometh
             to
             it
             ,
             it
             casteth
             up
             much
             Water
             before
             it
             ,
             which
             with
             its
             weight
             presseth
             downwards
             again
             ,
             and
             maketh
             the
             Water
             to
             rise
             under
             the
             Bullet
             with
             force
             enough
             to
             master
             the
             weak
             Motion
             of
             the
             Bullet
             downwards
             ,
             and
             to
             make
             it
             rise
             in
             such
             manner
             as
             Bodies
             use
             to
             rise
             by
             Reflection
             .
          
        
         
           
             A.
             
          
           
             By
             what
             Motion
             (
             seeing
             you
             ascribe
             all
             Effects
             to
             Motion
             )
             can
             a
             Load-stone
             draw
             Iron
             to
             it
             ?
          
        
         
           
             B.
             
          
           
             By
             the
             same
             Motion
             hitherto
             supposed
             .
             But
             though
             all
             the
             smallest
             parts
             of
             the
             Earth
             have
             this
             Motion
             ,
             yet
             it
             is
             not
             supposed
             that
             their
             Motions
             are
             in
             equal
             Circles
             ;
             nor
             that
             they
             keep
             just
             time
             with
             one
             another
             ;
             nor
             that
             they
             have
             all
             the
             same
             Poles
             .
             If
             they
             had
             ,
             all
             Bodies
             would
             draw
             one
             another
             
             alike
             .
             For
             such
             an
             agreement
             of
             Motion
             ,
             of
             Way
             ,
             of
             Swiftness
             ,
             of
             Poles
             ,
             cannot
             be
             maintained
             without
             the
             conjunction
             of
             the
             Bodies
             themselves
             in
             the
             Center
             of
             their
             common
             Motion
             ,
             but
             by
             violence
             .
          
        
         
           If
           therefore
           the
           Iron
           have
           but
           so
           much
           of
           the
           Nature
           of
           the
           Load-stone
           as
           redily
           to
           receive
           from
           it
           the
           like
           Motion
           ,
           as
           one
           String
           of
           a
           Lute
           doth
           from
           another
           String
           strained
           to
           the
           same
           Note
           (
           as
           it
           is
           like
           enough
           it
           hath
           ,
           the
           Load-stone
           being
           but
           one
           kind
           of
           Iron
           Ore
           )
           it
           must
           needs
           after
           that
           Motion
           received
           from
           it
           ,
           (
           unless
           the
           greatness
           of
           the
           weight
           hinder
           )
           come
           nearer
           to
           it
           ,
           because
           at
           distance
           their
           Motions
           will
           differ
           in
           time
           ,
           and
           oppose
           each
           other
           whereby
           they
           will
           be
           forced
           to
           a
           common
           Center
           .
           If
           the
           Iron
           be
           lifted
           up
           from
           the
           Earth
           ,
           the
           Motion
           of
           the
           Load-stone
           must
           be
           stronger
           ,
           or
           the
           Body
           of
           it
           nearer
           ,
           to
           overcome
           the
           Weight
           ;
           and
           then
           the
           Iron
           will
           leap
           up
           to
           the
           Load-stone
           as
           as
           Swiftly
           as
           from
           the
           same
           distance
           ,
           it
           would
           fall
           down
           to
           the
           Earth
           ;
           but
           if
           both
           the
           Stone
           and
           the
           Iron
           be
           set
           floating
           upon
           the
           Water
           ,
           the
           attraction
           will
           begin
           to
           be
           manifest
           at
           a
           greater
           distance
           ,
           because
           the
           hindrance
           of
           the
           weight
           is
           in
           part
           removed
           .
        
         
           
           
             A.
             
          
           
             But
             why
             does
             the
             Load-stone
             if
             it
             float
             on
             a
             Calm
             Water
             ,
             never
             fail
             to
             place
             it self
             at
             last
             in
             the
             Meridian
             just
             North
             and
             South
             .
          
        
         
           
             B.
             
          
           
             Not
             so
             ,
             just
             in
             the
             Meridian
             ,
             but
             almost
             in
             all
             places
             with
             some
             variations
             .
             But
             the
             cause
             I
             think
             is
             ,
             that
             the
             Axis
             of
             this
             Magnetical
             Motion
             is
             parallel
             to
             the
             Axis
             of
             the
             Ecliptique
             ,
             which
             is
             the
             Axis
             of
             the
             like
             Motion
             in
             the
             Earth
             ,
             and
             consequently
             that
             it
             cannot
             freely
             exercise
             its
             Natural
             Motion
             in
             any
             other
             Scituation
             .
          
        
         
           
             A.
             
          
           
             Whence
             may
             this
             consent
             of
             Motion
             in
             the
             Load-stone
             and
             the
             Earth
             proceed
             ?
             Do
             you
             think
             (
             as
             some
             have
             written
             )
             that
             the
             Earth
             is
             a
             great
             Load-stone
             ?
          
        
         
           
             B.
             
          
           
             Dr.
             Gilbert
             that
             was
             the
             first
             that
             wrote
             any
             thing
             of
             this
             Subject
             rationally
             ,
             inclines
             to
             that
             opinion
             .
             Decartes
             thought
             the
             Earth
             (
             excepting
             this
             upper
             crust
             of
             a
             few
             Miles
             depth
             )
             to
             be
             of
             the
             same
             Nature
             with
             all
             other
             Stars
             ,
             and
             bright
             .
             For
             my
             part
             I
             am
             content
             to
             be
             ignorant
             ;
             but
             I
             believe
             the
             
               Load
               stone
            
             hath
             given
             its
             virtue
             by
             a
             long
             habitude
             in
             the
             Mine
             ,
             the
             Vein
             of
             it
             lying
             in
             the
             plain
             of
             some
             of
             the
             Meridians
             ,
             or
             rather
             of
             some
             of
             the
             great
             Circles
             that
             pass
             through
             the
             Poles
             of
             the
             Ecliptique
             ,
             which
             are
             the
             same
             with
             the
             Poles
             of
             
             the
             like
             Motion
             supposed
             in
             the
             Earth
             .
          
        
         
           
             A.
             
          
           
             If
             that
             be
             true
             ▪
             I
             need
             not
             ask
             why
             the
             filings
             of
             Iron
             laid
             on
             a
             Load-stone
             equally
             distant
             from
             its
             Poles
             will
             lie
             parallel
             to
             the
             Axis
             ,
             but
             one
             each
             side
             incline
             to
             the
             Pole
             that
             is
             next
             it
             .
             Nor
             why
             by
             drawing
             a
             Load-ston
             all
             a
             long
             a
             Needle
             of
             Iron
             ,
             the
             Needle
             will
             receive
             the
             same
             Poles
             Nor
             why
             when
             the
             Load-stone
             and
             Iron
             (
             or
             two
             Load-stones
             )
             are
             put
             together
             floating
             upon
             Water
             ,
             will
             fall
             one
             of
             them
             a
             Stern
             of
             the
             other
             ,
             that
             their
             like
             parts
             may
             look
             the
             same
             way
             ,
             and
             their
             unlike
             touch
             ,
             in
             which
             Action
             they
             are
             commonly
             said
             to
             Repel
             one
             another
             .
             For
             all
             this
             may
             be
             deriv'd
             from
             the
             union
             of
             their
             Motions
             .
             One
             thing
             more
             I
             desire
             to
             know
             ,
             and
             that
             is
             ;
             What
             are
             those
             things
             they
             call
             Spirits
             ?
             I
             mean
             
               Ghosts
               ,
               Fairies
               ,
               Hobgoblins
            
             ,
             and
             the
             like
             Apparitions
             .
          
        
         
           
             B.
             
          
           
             They
             are
             no
             part
             of
             the
             Subject
             of
             Natural
             Philosophy
             .
          
        
         
           
             A.
             
          
           
             That
             which
             in
             all
             Ages
             ,
             and
             all
             places
             is
             commonly
             seen
             (
             as
             those
             have
             been
             ,
             unless
             a
             great
             part
             of
             Mankind
             by
             Lyers
             )
             cannot
             ,
             I
             think
             ,
             be
             supernatural
             .
          
        
         
           
             B.
             
          
           
             All
             this
             that
             I
             have
             hitherto
             said
             ,
             though
             upon
             better
             ground
             than
             can
             be
             had
             for
             a
             discourse
             of
             Ghosts
             ,
             you
             ought
             to
             take
             but
             for
             a
             Dream
             .
          
        
         
           
           
             A.
             
          
           
             I
             do
             so
             .
             But
             there
             be
             some
             Dreams
             more
             like
             sense
             then
             others
             .
             And
             that
             which
             is
             like
             sense
             pleases
             me
             as
             well
             (
             in
             natural
             Philosophy
             )
             as
             if
             it
             were
             the
             very
             truth
             .
          
        
         
           
             B.
             
          
           
             I
             was
             Dreaming
             also
             once
             of
             these
             things
             ;
             but
             was
             weakened
             by
             their
             noise
             .
             And
             they
             never
             came
             into
             any
             Dream
             of
             mine
             since
             ,
             unless
             Apparitionrs
             in
             Dreams
             and
             Ghoasts
             be
             all
             one
             .
          
        
      
       
         
           CHAP.
           VIII
           .
           The
           Delphique
           Problem
           or
           Duplication
           of
           the
           Cube
           .
        
         
           
             A.
             
          
           
             HAve
             you
             seen
             a
             Printed
             Paper
             sent
             from
             Paris
             ,
             containing
             the
             Duplication
             of
             the
             Cube
             ,
             written
             in
             French
             ?
          
        
         
           
             B.
             
          
           
             Yes
             .
             It
             was
             I
             that
             Writ
             it
             ,
             and
             sent
             it
             thither
             to
             be
             Printed
             ,
             on
             purpose
             to
             see
             what
             objections
             would
             be
             made
             to
             it
             by
             our
             Professors
             of
             Algebra
             here
             .
          
        
         
           
             A.
             
          
           
             Then
             you
             have
             also
             seen
             the
             confutations
             of
             it
             by
             Algebra
             .
          
        
         
           
             B.
             
          
           
             I
             have
             seen
             some
             of
             them
             ;
             and
             have
             one
             by
             me
             .
             For
             there
             was
             but
             one
             that
             was
             rightly
             Calculated
             ,
             and
             that
             is
             it
             which
             I
             have
             kept
             .
          
        
         
           
           
             A.
             
          
           
             Your
             Demonstration
             then
             is
             confuted
             though
             but
             by
             one
             .
          
        
         
           
             B.
             
          
           
             That
             does
             not
             follow
             .
             For
             though
             an
             Arithmetical
             Calculation
             be
             true
             in
             Numbers
             ,
             yet
             the
             same
             may
             be
             ,
             or
             rather
             must
             be
             false
             ,
             if
             the
             Units
             be
             not
             constantly
             the
             same
             .
          
        
         
           
             A.
             
          
           
             Is
             their
             Calculation
             so
             inconstant
             ,
             or
             rather
             so
             foolish
             as
             you
             make
             it
             ?
          
        
         
           
             B.
             
          
           
             Yes
             .
             For
             the
             same
             number
             is
             sometimes
             so
             many
             Lines
             ,
             sometimes
             so
             many
             Plains
             ,
             and
             sometimes
             so
             many
             Solids
             ;
             as
             you
             shall
             plainly
             see
             ,
             if
             you
             will
             take
             the
             pains
             to
             examine
             first
             a
             Demonstration
             I
             have
             to
             prove
             the
             said
             Duplication
             ,
             and
             after
             that
             ,
             the
             Algebrique
             Calculation
             which
             is
             pretended
             to
             confute
             it
             .
             And
             not
             only
             that
             this
             one
             is
             false
             ,
             but
             also
             any
             other
             Arithmetical
             account
             used
             in
             Geometry
             ,
             unless
             the
             numbers
             be
             always
             so
             many
             Lines
             ,
             or
             always
             so
             many
             superficies
             ,
             or
             always
             many
             solids
             .
          
        
         
           
             A.
             
          
           
             Let
             me
             see
             the
             Geometrical
             Demonstration
             .
          
        
         
           
             B.
             
          
           
             There
             it
             is
             :
             Read
             it
             .
          
        
         
           
             To
             find
             a
             Cube
             double
             to
             a
             Cube
             given
             .
          
        
         
           LEt
           the
           side
           of
           the
           Cube
           given
           be
           V
           D.
           Produce
           V
           D
           to
           A
           ,
           till
           A
           D
           be
           double
           to
           D
           V.
           Then
           make
           
           the
           square
           of
           A
           D
           ,
           namely
           A
           B
           C
           D.
           Divide
           A
           B
           and
           C
           D
           in
           the
           middle
           at
           E
           and
           F.
           Draw
           E
           F.
           Draw
           also
           A
           C
           cutting
           E
           F
           in
           I.
           Then
           in
           the
           sides
           B
           C
           and
           A
           D
           take
           B
           R
           and
           A
           S
           each
           of
           them
           equal
           to
           A
           I
           or
           I
           C.
           
        
         
           Lastly
           ,
           divide
           S
           D
           in
           the
           middle
           at
           T
           ,
           and
           upon
           the
           Center
           T
           ,
           with
           the
           distance
           T
           V
           ,
           describe
           a
           semi-circle
           cutting
           A
           D
           in
           Y
           ,
           and
           D
           C
           in
           X.
           
        
         
           I
           say
           the
           Cube
           of
           D
           X
           is
           double
           to
           the
           Cube
           of
           D
           V.
           For
           the
           three
           lines
           D
           Y
           ,
           D
           X
           ,
           D
           V
           are
           in
           continual
           proportion
           .
           And
           Cntinuing
           the
           semi-circle
           V
           X
           Y
           till
           it
           cut
           the
           line
           R
           S
           drawn
           and
           produced
           in
           Z
           ,
           the
           line
           S
           Z
           ,
           will
           be
           equal
           to
           D
           X.
           And
           drawing
           X
           Z
           it
           will
           pass
           through
           T.
           And
           the
           four
           lines
           T
           V
           ,
           T
           X
           ,
           T
           Y
           and
           T
           Z
           will
           be
           equal
           .
           And
           therefore
           joyning
           Y
           X
           and
           Y
           Z
           ,
           the
           Figure
           V
           X
           Y
           Z
           will
           be
           a
           Rectangle
           .
        
         
           Produce
           C
           D
           to
           P
           so
           as
           D
           P
           be
           equal
           to
           A
           D.
           Now
           if
           Y
           Z
           produced
           fall
           on
           P
           ,
           there
           will
           be
           three
           Rectangle
           equiangled
           Triangles
           ,
           D
           P
           Y
           ,
           D
           Y
           X
           ,
           and
           D
           X
           V
           ;
           and
           consequently
           four
           continual
           proportionals
           ,
           D
           P
           ,
           D
           Y
           ,
           D
           X
           ▪
           and
           D
           V
           ,
           whereof
           D
           X
           is
           the
           least
           of
           the
           means
           .
           And
           therefore
           the
           Cube
           of
           D
           X
           will
           be
           double
           to
           the
           Cube
           of
           D
           V.
           
        
         
           
           
             A.
             
          
           
             That
             's
             true
             ;
             and
             the
             Cube
             of
             
               D
               Y
            
             will
             be
             double
             to
             the
             Cube
             of
             
               D
               X
            
             ;
             and
             the
             Cube
             of
             
               D
               P
            
             double
             to
             the
             Cube
             of
             
               D
               Y.
            
             But
             that
             
               Y
               Z
            
             produced
             ,
             falls
             upon
             P
             ,
             is
             the
             thing
             they
             deny
             ,
             and
             which
             you
             ought
             to
             demonstrate
             .
          
        
         
           
             B.
             
          
           
             If
             Y
             Z
             produced
             fall
             not
             on
             P
             ,
             then
             draw
             P
             Y
             ,
             and
             from
             V
             let
             fall
             a
             perpendicular
             upon
             P
             Y
             ,
             suppose
             at
             u.
             Divide
             P
             V
             in
             the
             midst
             at
             a
             ,
             and
             joyn
             
               a
               u
            
             ;
             which
             done
             
               a
               u
            
             will
             be
             equal
             to
             a
             V
             or
             a
             P.
             For
             because
             V
             u
             P
             is
             a
             right
             Angle
             ,
             the
             point
             u
             will
             be
             in
             the
             semi-circle
             whereof
             P
             V
             is
             the
             Diameter
             .
          
           
             Therefore
             drawing
             V
             R
             ,
             the
             Angle
             u
             V
             R
             will
             be
             a
             right
             Angle
             .
          
        
         
           
             A.
             
          
           
             Why
             so
             ?
          
        
         
           
             B.
             
          
           
             Because
             T
             V
             and
             T
             Y
             are
             equal
             ;
             and
             T
             D
             ,
             T
             Sequal
             ;
             S
             V
             will
             also
             be
             equal
             to
             D
             V.
             And
             because
             D
             P
             and
             R
             S
             are
             equal
             and
             parallel
             ,
             R
             Y
             will
             be
             equal
             and
             parallel
             to
             P
             V.
             And
             therefore
             V
             R
             and
             P
             Y
             that
             joyn
             them
             will
             be
             equal
             and
             parallel
             .
             And
             the
             Angles
             P
             u
             V
             ,
             R
             V
             u
             will
             be
             alternate
             ,
             and
             consequently
             equal
             .
             But
             P
             u
             V
             is
             a
             right
             Angle
             ;
             therefore
             also
             R
             V
             u
             will
             be
             a
             right
             Angle
             .
          
        
         
           
             A.
             
          
           
             Hitherto
             all
             is
             evident
             .
             Proceed
             .
          
        
         
           
             B.
             
          
           
             From
             the
             point
             Y
             raise
             a
             perpendicular
             
             cutting
             V
             R
             wheresoever
             in
             t
             ,
             and
             then
             (
             because
             P
             Y
             and
             V
             R
             are
             parallel
             )
             the
             Angle
             Y
             t
             V
             will
             be
             a
             right
             Angle
             .
             And
             the
             figure
             u
             Y
             t
             V
             a
             Rectangle
             ,
             and
             
               u
               t
            
             equal
             to
             Y
             V.
             But
             Y
             V
             is
             equal
             to
             Z
             X
             ;
             and
             therefore
             Z
             X
             is
             equal
             to
             
               u
               t.
            
             And
             
               u
               t
            
             must
             pass
             through
             the
             point
             T
             (
             For
             the
             Diameters
             of
             any
             Rectangle
             ,
             divide
             each
             other
             in
             the
             middle
             )
             therefore
             Z
             and
             u
             are
             the
             same
             point
             ,
             and
             X
             and
             t
             the
             same
             point
             .
             Therefore
             Y
             Z
             produced
             falls
             upon
             P.
             and
             D
             X
             is
             the
             lesser
             of
             the
             two
             means
             between
             A
             D
             and
             D
             V.
             And
             the
             Cube
             of
             D
             X
             double
             to
             the
             Cube
             of
             D
             V
             which
             was
             to
             be
             demostraten
             .
          
        
         
           
             A
             
          
           
             I
             cannot
             imagine
             what
             fault
             there
             can
             be
             in
             this
             Demonstration
             ,
             and
             yet
             there
             is
             one
             thing
             which
             seems
             a
             little
             strange
             to
             me
             .
             And
             't
             is
             this
             .
             You
             take
             
               B
               R
            
             ,
             which
             is
             half
             the
             Diagonal
             ,
             and
             which
             is
             the
             sine
             of
             45
             degrees
             ,
             and
             which
             is
             also
             the
             mean
             proportional
             between
             the
             two
             Extreams
             .
             And
             yet
             you
             bring
             none
             of
             these
             proprieties
             into
             your
             Demonstration
             .
             So
             that
             though
             you
             argue
             from
             the
             Construction
             ,
             yet
             you
             do
             not
             argue
             from
             the
             Cause
             .
             And
             this
             perhaps
             your
             adversaries
             will
             object
             (
             at
             least
             )
             against
             the
             Art
             of
             you
             Demonstratieon
             ,
             or
             
             enqure
             by
             what
             luck
             you
             pitched
             upon
             half
             the
             Diagonal
             for
             your
             Foundation
             .
          
        
         
           
             B.
             
          
           
             I
             see
             you
             let
             nothing
             pass
             .
             But
             for
             answer
             you
             must
             know
             ,
             That
             if
             a
             man
             argue
             from
             the
             negative
             of
             the
             truth
             ,
             though
             he
             know
             not
             that
             it
             is
             the
             truth
             which
             is
             denyed
             ,
             yet
             he
             will
             fall
             at
             last
             ,
             after
             many
             consequences
             ,
             into
             one
             absurdity
             or
             another
             .
             For
             though
             false
             do
             often
             produce
             Truth
             ,
             yet
             it
             produces
             also
             absurdity
             ,
             as
             it
             hath
             done
             here
             .
             But
             Truth
             produceth
             nothing
             but
             Truth
             .
             Therefore
             in
             Demonstrations
             that
             tend
             to
             absurdity
             ,
             it
             is
             no
             good
             Logick
             to
             require
             all
             along
             the
             operation
             of
             the
             cause
             .
          
        
         
           
             A.
             
          
           
             Have
             you
             drawn
             from
             hence
             no
             Corollaries
             ?
          
        
         
           
             B.
             
          
           
             No.
             I
             leave
             that
             for
             others
             that
             will
             ;
             unless
             you
             take
             this
             for
             a
             Corollary
             ,
             That
             ,
             what
             Arithmetical
             Calculation
             soever
             contradicts
             it
             ,
             is
             false
             .
          
        
         
           
             A.
             
          
           
             Let
             me
             see
             now
             the
             Algebrical
             Demonstration
             against
             it
             .
          
        
         
           
             B.
             
          
           
             Here
             it
             is
             .
          
           
             Let
             A
             B
             or
             A
             D
             be
             equal
             to
             2
          
           
             Then
             D
             F
             or
             D
             V
             is
             equal
             to
             1
          
           
             And
             B
             R
             or
             A
             S
             is
             equal
             to
             the
             square
             root
             of
             2
          
           
             And
             A
             V
             equal
             to
             3
             
               want
               the
               square
               root
               of
            
             2.
             
          
           
             The
             Cube
             of
             A
             B
             is
             equal
             to
             8
          
           
           
             The
             Cube
             of
             D
             Y
             is
             equal
             to
             45
             
               want
               the
               Square
               Root
               of
            
             1682
             that
             is
             almost
             equal
             to
             4
          
           
             For
             45
             want
             the
             Square
             Root
             of
             6681
             is
             equal
             to
             4
          
           
             Therefore
             D
             Y
             is
             a
             little
             less
             then
             the
             greater
             of
             the
             two
             Means
             between
             AD
             and
             DV
             .
          
        
         
           
             A.
             
          
           
             There
             is
             I
             see
             some
             little
             difference
             between
             this
             Arithmetical
             aud
             your
             Geometrical
             Demonstration
             .
             And
             though
             it
             be
             insensible
             ,
             yet
             if
             his
             Calculation
             be
             true
             ,
             yours
             must
             needs
             be
             false
             ,
             which
             I
             am
             sure
             cannot
             be
             .
          
        
         
           
             B.
             
          
           
             His
             Calculation
             is
             so
             true
             ,
             that
             there
             is
             never
             a
             Proposition
             in
             it
             false
             ,
             till
             he
             come
             to
             the
             conclusion
             ,
             that
             the
             Cube
             of
             D
             Y.
             is
             equal
             to
             45
             ,
             want
             the
             square
             Root
             of
             1682.
             
             But
             that
             ,
             and
             the
             rest
             ,
             is
             false
             .
          
        
         
           
             A.
             
          
           
             I
             shall
             easily
             see
             that
             
               A
               D.
            
             is
             certainly
             2
             ,
             whereof
             
               D
               V.
            
             is
             1
             ,
             and
             
               A
               V.
            
             is
             certainly
             3
             ,
             whereof
             
               D
               V.
            
             is
             1.
             
          
        
         
           
             B.
             
          
           
             Right
             .
          
        
         
           
             A.
             
          
           
             And
             
               B
               R.
            
             is
             without
             doubt
             the
             square
             Root
             of
             2.
             
          
        
         
           
             B.
             
          
           
             Why
             ,
             what
             is
             2
             ?
          
        
         
           
             A.
             
          
           
             2
             ,
             is
             the
             Line
             
               A
               D.
            
             as
             being
             double
             to
             
               D
               V.
            
             which
             is
             1.
             
          
        
         
           
             B.
             
          
           
             And
             so
             ,
             the
             Line
             B
             R.
             is
             the
             square
             Root
             of
             the
             Line
             A
             D.
             
          
        
         
           
           
             A.
             
          
           
             Out
             upon
             it
             it
             ,
             it
             's
             absurd
             .
             Why
             do
             you
             grant
             it
             to
             be
             true
             in
             Arithmetick
             ?
          
        
         
           
             B.
             
          
           
             In
             Arithmetick
             the
             numbers
             consist
             of
             so
             many
             Units
             ;
             and
             are
             never
             considered
             there
             as
             nothings
             .
             And
             therefore
             every
             one
             Line
             has
             some
             Latitude
             ,
             and
             if
             you
             allow
             to
             BI
             .
             the
             Semi-diagonal
             the
             same
             Latitude
             you
             do
             to
             AB
             .
             or
             to
             BR
             .
             you
             will
             quickly
             see
             the
             Square
             of
             half
             the
             Diagonal
             to
             be
             equal
             to
             twice
             the
             Square
             of
             half
             AB
             .
          
        
         
           
             A.
             
          
           
             Well
             ,
             but
             then
             your
             Demonstration
             is
             not
             confuted
             ;
             for
             the
             Point
             Y
             ,
             will
             have
             Latitude
             enough
             to
             take
             in
             that
             little
             difference
             which
             is
             between
             the
             Root
             of
             1681
             and
             the
             Root
             of
             1682.
             
             This
             putting
             off
             an
             Vuit
             sometimes
             for
             one
             Line
             ,
             sometimes
             for
             one
             Square
             ,
             must
             needs
             marr
             the
             reckoning
             .
             Again
             he
             says
             the
             Cube
             of
             AB
             .
             is
             equal
             to
             8.
             but
             seeing
             AB
             .
             is
             2
             ,
             the
             Cube
             of
             AB
             .
             must
             be
             just
             equal
             to
             four
             of
             its
             own
             sides
             ;
             so
             that
             the
             Vnit
             which
             was
             before
             sometimes
             a
             Line
             ,
             sometimes
             a
             Square
             ,
             is
             now
             a
             Cube
             .
          
        
         
           
             B.
             
          
           
             It
             can
             be
             no
             otherwise
             when
             you
             so
             apply
             Arithmetick
             to
             Geometry
             ,
             as
             to
             mumber
             the
             Lines
             of
             a
             Plain
             ,
             or
             the
             Plains
             of
             a
             Cube
             .
          
        
         
           
             A.
             
          
           
             In
             the
             next
             place
             ,
             I
             find
             that
             the
             Cube
             of
             DY
             .
             is
             equal
             to
             45
             ,
             want
             the
             
             Square
             Root
             of
             1622.
             
             What
             is
             that
             45
             ?
             Lines
             ,
             or
             Squares
             ,
             or
             Cubes
             ?
          
        
         
           
             B.
             
          
           
             Cubes
             ,
             Cubes
             of
             DV
             .
          
        
         
           
             A.
             
          
           
             Then
             if
             you
             add
             to
             45
             Cubes
             of
             DV
             .
             the
             Square
             Root
             of
             1682
             ,
             the
             sum
             will
             be
             45
             Cubes
             of
             DV
             .
             And
             if
             you
             add
             to
             the
             Cube
             of
             DY
             .
             the
             same
             Root
             of
             1682
             ,
             the
             sum
             will
             be
             the
             Cube
             of
             DY
             .
             plus
             the
             Square
             Root
             of
             1682.
             
             And
             these
             two
             sums
             must
             be
             equal
             .
          
        
         
           
             B.
             
          
           
             They
             must
             so
             .
          
        
         
           
             A.
             
          
           
             But
             the
             Square
             Root
             of
             1682
             ,
             being
             a
             Line
             ,
             adds
             nothing
             to
             a
             Cube
             ;
             therefore
             the
             Cube
             alone
             of
             DY
             .
             which
             he
             says
             is
             equal
             almost
             to
             4.
             
             Cubes
             of
             DV
             .
             is
             equal
             to
             45
             Cubes
             of
             the
             same
             DV
             .
          
        
         
           
             B.
             
          
           
             All
             these
             impossibilities
             do
             necessarily
             follow
             the
             confounding
             of
             Arithmetick
             and
             Geometry
             .
          
        
         
           
             A.
             
          
           
             I
             pray
             you
             let
             me
             see
             the
             Operation
             by
             which
             the
             Cube
             of
             DY
             .
             (
             that
             is
             the
             Cube
             of
             3
             ,
             want
             the
             Root
             of
             2
             ,
             )
             is
             found
             equal
             to
             45
             ,
             want
             the
             Square
             Root
             of
             1682.
             
          
        
         
         
           A
           detection
           of
           the
           absurd
           use
           of
           Arithmetick
           as
           it
           is
           now
           applyed
           to
           Geometry
           .
        
         
           
             B.
             
          
           
             Here
             it
             is
             .
          
           
             3
             —
             r.
             2.
             
          
           
             3
             —
             r.
             2.
             
          
           
             —
             r.
             18
             ✚
             2
             :
          
           
             9
             —
             r.
             18
          
           
             9
             —
             r.
             72
             ✚
             2.
             
          
           
             3
             —
             r.
             2.
             
          
           
             —
             r.
             162
             ✚
             12
             —
             r.
             8.
             
          
           
             27
             —
             r.
             648
             ✚
             6
          
           
             27
             —
             r.
             658
             —
             r.
             162
             ✚
             18
             —
             r.
             8.
             
          
        
         
           
             A.
             
          
           
             Why
             for
             two
             Roots
             of
             18
             do
             you
             put
             the
             Root
             of
             72.
             
          
        
         
           
             B.
             
          
           
             Because
             2
             Roots
             of
             18
             is
             equal
             to
             one
             Root
             of
             4
             times
             18
             ,
             which
             is
             72.
             
          
        
         
           
             A.
             
          
           
             Next
             we
             have
             ,
             That
             the
             Root
             of
             2
             Multiplyed
             into
             2
             ,
             makes
             the
             Root
             of
             8.
             
             How
             is
             that
             true
             ?
          
        
         
           
             B.
             
          
           
             Does
             it
             not
             make
             2
             Roots
             of
             2
             ?
             And
             is
             not
             BR
             .
             the
             Root
             of
             2
             ,
             and
             2
             BR
             equal
             to
             the
             Diagonal
             ?
             And
             is
             not
             
             the
             diagonal
             the
             root
             of
             a
             square
             equal
             to
             8
             squares
             of
             DV
             ?
          
        
         
           
             A.
             
          
           
             'T
             is
             true
             .
             But
             here
             the
             root
             of
             8
             is
             put
             for
             the
             Cube
             of
             the
             root
             of
             2.
             
             Can
             a
             line
             be
             equal
             to
             a
             Cube
             ?
          
        
         
           
             B.
             
          
           
             No.
             But
             here
             we
             are
             in
             Arithmetick
             again
             ,
             and
             8
             is
             a
             Cubique
             number
             .
          
        
         
           
             A.
             
          
           
             How
             does
             the
             root
             of
             2
             multiplyed
             into
             the
             root
             of
             72
             make
             12
             ?
          
        
         
           
             B.
             
          
           
             Because
             it
             makes
             the
             root
             of
             2
             times
             72
             ,
             that
             is
             to
             say
             the
             root
             of
             144
             which
             is
             12.
             
          
        
         
           
             A.
             
          
           
             How
             does
             9
             roots
             of
             2
             make
             the
             root
             of
             162
             ?
          
        
         
           
             B.
             
          
           
             Because
             it
             makes
             the
             root
             of
             2
             squares
             of
             9
             ,
             that
             is
             the
             root
             of
             162.
             
          
        
         
           
             A.
             
          
           
             How
             does
             3
             roots
             of
             72
             make
             the
             root
             of
             648
             ?
          
        
         
           
             B.
             
          
           
             Because
             it
             makes
             the
             root
             of
             9
             times
             72
             ,
             that
             is
             of
             648.
             
          
        
         
           
             A.
             
          
           
             For
             the
             total
             Sum
             I
             see
             27
             and
             18
             which
             make
             45.
             
             Therefore
             the
             root
             of
             648
             together
             with
             the
             root
             of
             162●
             and
             of
             8
             ,
             which
             are
             to
             be
             deducted
             from
             45
             ,
             ought
             to
             be
             equal
             to
             the
             root
             of
             1682.
             
          
        
         
           
             B.
             
          
           
             So
             they
             are
             .
             For
             648
             multiplyed
             by
             162
             makes
             104976
             of
             which
             the
             double
             root
             is
             —
             648
             and
             648
             and
             162
             added
             together
             make
             —
             810.
             
          
           
           
             Therefore
             the
             root
             of
             948
             ,
             added
             to
             the
             root
             of
             162
             makes
             the
             root
             of
             —
             1459
          
           
             Again
             1458
             into
             8
             is
             11664.
             
             The
             double
             root
             whereof
             is
             —
             216.
             
          
           
             The
             Sum
             of
             1458
             and
             8
             added
             together
             is
             —
             1466.
             
          
           
             The
             Sum
             of
             1466
             and
             216
             is
             1682
             ,
             and
             the
             root
             ,
             the
             root
             of
             —
             1682.
             
          
        
         
           
             A.
             
          
           
             I
             see
             the
             Calculation
             in
             numbers
             is
             right
             ,
             though
             false
             in
             lines
             .
             The
             reason
             whereof
             can
             be
             no
             other
             then
             some
             difference
             between
             multiplying
             numbers
             into
             lines
             or
             plains
             ,
             and
             multiplying
             lines
             into
             the
             same
             lines
             or
             plains
             .
          
        
         
           
             B.
             
          
           
             The
             difference
             is
             manifest
             .
             For
             when
             you
             multiply
             a
             number
             into
             lines
             ,
             the
             product
             is
             lines
             ;
             as
             the
             number
             2
             multiplyed
             into
             3
             lines
             is
             no
             more
             then
             3
             lines
             2
             times
             told
             .
             But
             if
             you
             multiply
             lines
             into
             lines
             you
             make
             plains
             ,
             and
             if
             you
             multiply
             lines
             into
             plains
             you
             make
             solid
             bodies
             .
             In
             Geometry
             there
             are
             but
             three
             dimensions
             ,
             Length
             ,
             Superficies
             ,
             and
             Body
             .
             In
             Arithmetick
             there
             is
             but
             one
             ,
             and
             that
             is
             Number
             or
             Length
             which
             you
             will.
             And
             though
             there
             be
             some
             Numbers
             called
             Plain
             ,
             others
             Solid
             ,
             others
             Plano-solid
             ,
             others
             Square
             ,
             others
             Cubique
             ,
             others
             Square-square
             ,
             others
             Quadrato-cubique
             ,
             others
             Cubi-cubique
             &c.
             yet
             are
             all
             these
             but
             one
             dimension
             ,
             namely
             Number
             ,
             
             or
             a
             file
             of
             things
             Numbered
             .
          
        
         
           
             A.
             
          
           
             But
             seeing
             this
             way
             of
             Calculation
             by
             Numbers
             is
             so
             apparently
             false
             ,
             what
             is
             the
             reason
             this
             Calculation
             came
             so
             near
             the
             truth
             .
          
        
         
           
             B.
             
          
           
             It
             is
             because
             in
             Arithmetick
             Units
             are
             not
             Nothings
             ,
             and
             therefore
             have
             breadth
             .
             And
             therefore
             many
             Lines
             set
             together
             make
             a
             superficies
             though
             their
             breadth
             be
             insensible
             .
             And
             the
             greater
             the
             number
             is
             into
             which
             you
             divide
             your
             Line
             ,
             the
             less
             sensible
             will
             be
             your
             errour
             .
          
        
         
           
             A.
             
          
           
             Archimedes
             ,
             to
             find
             a
             streight
             Line
             equal
             to
             the
             circumferrence
             of
             a
             Circle
             ,
             used
             this
             may
             of
             extracting
             Roots
             .
             And
             't
             is
             the
             way
             also
             by
             which
             the
             Table
             of
             
               Sines
               ,
               Secants
            
             aud
             Tangents
             have
             been
             calculated
             ,
             Are
             they
             all
             Cut
             ?
          
        
         
           
             B.
             
          
           
             As
             for
             Archimedes
             ,
             there
             is
             no
             man
             that
             does
             more
             admire
             him
             then
             I
             do
             .
             But
             there
             is
             no
             man
             that
             cannot
             Err.
             His
             reasoning
             is
             good
             .
             But
             he
             ads
             all
             other
             Geometricans
             before
             and
             after
             him
             ,
             have
             had
             two
             Principles
             that
             cross
             one
             another
             when
             they
             are
             applyed
             to
             one
             and
             the
             same
             Science
             .
             One
             is
             ,
             that
             a
             Point
             is
             no
             part
             of
             a
             Line
             which
             is
             true
             in
             Geometry
             ,
             where
             a
             part
             of
             a
             Line
             when
             it
             is
             called
             a
             Point
             ,
             is
             not
             reckoned
             ;
             another
             is
             ,
             that
             a
             Unit
             is
             part
             of
             a
             
             Number
             which
             is
             also
             true
             ;
             but
             when
             they
             reckon
             by
             Arethmetick
             in
             Geometry
             ,
             there
             a
             Unit
             is
             somtimes
             part
             of
             a
             Line
             ,
             sometimes
             a
             part
             of
             a
             Square
             ,
             and
             sometimes
             part
             of
             a
             Cube
             .
          
           
             As
             for
             the
             Table
             of
             
               Sines
               ,
               Secants
            
             and
             Tangents
             ,
             I
             am
             not
             the
             first
             that
             find
             fault
             with
             them
             .
             Yet
             I
             deny
             not
             but
             they
             are
             true
             enough
             for
             the
             reckoning
             of
             Acres
             in
             a
             Map
             of
             Land.
             
          
        
         
           
             A.
             
          
           
             What
             a
             deal
             of
             Labour
             has
             been
             lost
             by
             them
             that
             being
             Professors
             of
             Geometry
             have
             read
             nothing
             else
             to
             their
             Auditors
             but
             such
             stuff
             as
             this
             you
             have
             here
             seen
             .
             And
             some
             of
             them
             have
             written
             great
             Books
             of
             it
             in
             strange
             characters
             ,
             such
             as
             in
             troublesome
             times
             ,
             a
             man
             would
             suspect
             to
             be
             a
             Cypher
             .
          
        
         
           
             B.
             
          
           
             I
             think
             you
             have
             seen
             enough
             to
             satisfie
             you
             ,
             that
             what
             I
             have
             written
             heretofore
             concerning
             the
             Quadrature
             of
             the
             Circle
             ,
             and
             of
             other
             Figures
             made
             in
             imitation
             of
             the
             Parabola
             ,
             has
             not
             been
             yet
             confuted
             .
          
        
         
           
             A.
             
          
           
             I
             see
             you
             have
             wrested
             out
             of
             the
             hands
             of
             our
             Antagonists
             this
             weapon
             of
             Algebra
             ,
             so
             as
             they
             can
             never
             make
             use
             of
             it
             again
             .
             Which
             I
             consider
             as
             a
             thing
             of
             much
             more
             consequence
             to
             the
             science
             of
             Geometry
             ,
             then
             either
             of
             the
             Duplication
             of
             the
             Cube
             ,
             or
             the
             finding
             of
             two
             mean
             Proportionals
             ,
             or
             the
             Quadrature
             of
             a
             Circle
             ,
             or
             all
             these
             Problems
             put
             together
             .
          
        
         
           FINIS
           .
        
      
    
     
       
         
         
           Books
           Written
           by
           this
           Author
           ,
           and
           Printed
           for
           William
           Crooke
           .
        
         
           
             1
             
               DE
               Mirabilibus
               Pecci
            
             ,
             in
             Quarto
             Latin
             ,
             in
             Octavo
             in
             English
             and
             Lantin
             .
          
           
             2
             Three
             Papers
             to
             the
             
               Royal
               Society
            
             against
             Dr.
             Wallis
             .
          
           
             3
             Lumathematica
             .
          
           
             4
             Prima
             partis
             Doctrinae
             Wallisianae
             de
             
               Motu
               Censura
               Brevis
            
             .
          
           
             5
             
               Resetum
               Geometricum
            
             ,
             sive
             propositiones
             aliquot
             frustra
             antehac
             tentatae
             .
          
           
             6
             Principia
             &
             Poblemata
             aliquot
             Geometrica
             ,
             ante
             desperata
             ,
             nunc
             breviter
             explicata
             &
             demonstrata
             .
          
           
             7
             
               Quadratura
               Circuli
               Cubatio
               Sphaere
            
             duplicatio
             Cubi
             Breviter
             demonstrata
             .
          
           
             8
             Consideration
             on
             his
             
               Loyalty
               ,
               Reputation
               ,
               Religion
            
             and
             Manners
             ;
             by
             himself
             .
          
           
             9
             
               De
               Principio
            
             &
             
               Ratione
               Geometri
            
             .
          
           
             20
             The
             Travels
             of
             
               Vlises
               Translated
            
             from
             Homer
             .
          
           
             11
             Epistol
             .
             ad
             Dr.
             Wood.
             
          
           
             12
             The
             Translation
             of
             all
             
               Homers
               Works
            
             into
             English.
             
          
           
             13
             The
             Epitome
             of
             the
             
               Civil
               Wars
            
             of
             Enland
             from
             1640
             to
             1660.
             
          
           
             14
             
               Aristotles
               Rhetorick
               Translated
            
             into
             English
             by
             him
             ,
             with
             his
             own
             Rhetorick
             to
             it
             .
          
           
             
             15
             
               A
               Dialogue
               betwixt
               a
               Student
            
             in
             the
             Common-Laws
             of
             England
             ,
             and
             a
             Philosopher
             in
             which
             is
             set
             forth
             the
             Errors
             in
             some
             Practise
             .
          
           
             16
             
               A
               Narration
            
             of
             Heresie
             and
             the
             Punnishment
             thereof
             .
          
           
             17
             
               Ten
               Dialogues
            
             of
             
               Natural
               Philosophy
            
             .
          
           
             18
             
               A
               Poem
            
             in
             Latin
             of
             his
             Life
             .
          
           
             19
             —
             idem
             the
             same
             in
             English.
             
          
           
             20
             
               His
               Life
            
             written
             in
             Latin
             ,
             part
             by
             himself
             and
             the
             rest
             by
             Dr.
             
               R.
               B.
            
             wherein
             is
             contained
             the
             most
             material
             parts
             of
             his
             Life
             .
          
           
             21
             
               Seven
               Philosophical
               Problems
            
             ,
             and
             two
             Propositions
             of
             Geometry
             .
             With
             an
             Apology
             for
             Himself
             ,
             and
             his
             Writings
             .
             Dedicated
             to
             the
             King
             ,
             in
             the
             year
             1662.