Newton, Isaac, Philosophia naturalis principia mathematica, 1713

Table of figures

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                  <s>
                    <margin.target id="note228"/>
                  DE MOTU
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                  CORPORUM</s>
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                  <s>
                    <emph type="center"/>
                  SECTIO IV.
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                    <arrow.to.target n="note229"/>
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                  <s>
                    <margin.target id="note229"/>
                  LIBER
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                  SECUNDUS.</s>
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                  <s>
                    <emph type="center"/>
                    <emph type="italics"/>
                  De Corporum Circulari Motu in Mediis reſiſtentibus.
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                    <emph.end type="center"/>
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                <p type="main">
                  <s>
                    <emph type="center"/>
                  LEMMA III.
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                  </s>
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                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Sit
                    <emph.end type="italics"/>
                  PQRr
                    <emph type="italics"/>
                  Spiralis quæ ſecet radios omnes
                    <emph.end type="italics"/>
                  SP, SQ, SR,
                    <emph type="italics"/>
                  &c. </s>
                  <s>
                    <lb/>
                  in æqualibus angulis. </s>
                  <s>Agatur recta
                    <emph.end type="italics"/>
                  PT
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                  quæ tangat eandem in
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                  puncto quovis
                    <emph.end type="italics"/>
                  P,
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                  ſecetque radium
                    <emph.end type="italics"/>
                  SQ
                    <emph type="italics"/>
                  in
                    <emph.end type="italics"/>
                  T;
                    <emph type="italics"/>
                  & ad Spiralem
                    <lb/>
                  erectis perpendiculis
                    <emph.end type="italics"/>
                  PO, QO
                    <emph type="italics"/>
                  concurrentibus in
                    <emph.end type="italics"/>
                  O,
                    <emph type="italics"/>
                  jungatur
                    <emph.end type="italics"/>
                    <lb/>
                  SO.
                    <emph type="italics"/>
                  Dico quod ſi puncta
                    <emph.end type="italics"/>
                  P
                    <emph type="italics"/>
                  &
                    <emph.end type="italics"/>
                  Q
                    <emph type="italics"/>
                  accedant ad invicem & co­
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                  eant, angulus
                    <emph.end type="italics"/>
                  PSO
                    <emph type="italics"/>
                  evadet rectus, & ultima ratio rectanguli
                    <emph.end type="italics"/>
                    <lb/>
                  TQX2PS
                    <emph type="italics"/>
                  ad
                    <emph.end type="italics"/>
                  PQ
                    <emph type="italics"/>
                  quad. </s>
                  <s>erit ratio æqualitatis.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>Etenim de angulis rectis
                    <emph type="italics"/>
                  OPQ, OQR
                    <emph.end type="italics"/>
                  ſubducantur anguli
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                  æquales
                    <emph type="italics"/>
                  SPQ, SQR,
                    <emph.end type="italics"/>
                  & manebunt anguli æquales
                    <emph type="italics"/>
                  OPS, OQS.
                    <emph.end type="italics"/>
                    <lb/>
                  Ergo Circulus qui tranſit
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                    <lb/>
                  per puncta
                    <emph type="italics"/>
                  O, S, P
                    <emph.end type="italics"/>
                  tranſ­
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                  ibit etiam per punctum
                    <emph type="italics"/>
                    <expan abbr="q.">que</expan>
                    <emph.end type="italics"/>
                    <lb/>
                  Coeant puncta
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  Q,
                    <emph.end type="italics"/>
                    <lb/>
                  & hic Circulus in loco co­
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                  itus
                    <emph type="italics"/>
                  PQ
                    <emph.end type="italics"/>
                  tanget Spiralem,
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                  adeoque perpendiculariter
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                  ſecabit rectam
                    <emph type="italics"/>
                  OP.
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                  Fiet
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                  igitur
                    <emph type="italics"/>
                  OP
                    <emph.end type="italics"/>
                  diameter Cir­
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                  culi hujus, & angulus
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                    <emph type="italics"/>
                  OSP
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                  in ſemicirculo re­
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                  ctus.
                    <emph type="italics"/>
                    <expan abbr="q.">que</expan>
                  E. D.
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                  </s>
                </p>
                <p type="main">
                  <s>Ad
                    <emph type="italics"/>
                  OP
                    <emph.end type="italics"/>
                  demittantur perpendicula
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                  QD, SE,
                    <emph.end type="italics"/>
                  & linearum ratio­
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                  nes ultimæ erunt hujuſmodi:
                    <emph type="italics"/>
                  TQ
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                  ad
                    <emph type="italics"/>
                  PD
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                  ut
                    <emph type="italics"/>
                  TS
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                  vel
                    <emph type="italics"/>
                  PS
                    <emph.end type="italics"/>
                  ad
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                  PE,
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                    <lb/>
                  ſeu 2
                    <emph type="italics"/>
                  PO
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                  ad 2
                    <emph type="italics"/>
                  PS.
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                  Item
                    <emph type="italics"/>
                  PD
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                  ad
                    <emph type="italics"/>
                  PQ
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                  ut
                    <emph type="italics"/>
                  PQ
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                  ad 2
                    <emph type="italics"/>
                  PO.
                    <emph.end type="italics"/>
                  Et ex
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                  æquo perturbate
                    <emph type="italics"/>
                  TQ
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                  ad
                    <emph type="italics"/>
                  PQ
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                  ut
                    <emph type="italics"/>
                  PQ
                    <emph.end type="italics"/>
                  ad 2
                    <emph type="italics"/>
                  PS.
                    <emph.end type="italics"/>
                  Unde fit
                    <emph type="italics"/>
                  PQq
                    <emph.end type="italics"/>
                    <lb/>
                  æquale
                    <emph type="italics"/>
                  TQX2PS.
                    <expan abbr="q.">que</expan>
                  E. D.
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