Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                <pb xlink:href="039/01/069.jpg" pagenum="41"/>
                <figure id="id.039.01.069.1.jpg" xlink:href="039/01/069/1.jpg" number="14"/>
                <p type="main">
                  <s>Nam perpendicula a centro
                    <emph type="italics"/>
                  S
                    <emph.end type="italics"/>
                    <lb/>
                  in tangentes
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                  PT, QT
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                  demiſſa (per
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                  Corol. </s>
                  <s>1. Prop.I.) ſunt reciproce
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                  ut velocitates corporis in punctis
                    <lb/>
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  V
                    <emph.end type="italics"/>
                  ; &c. </s>
                  <s>adeoque per conſtructio­
                    <lb/>
                  nem ut perpendicula
                    <emph type="italics"/>
                  AP, BQ
                    <emph.end type="italics"/>
                  di­
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                  recte, id eſt ut perpendicula a pun­
                    <lb/>
                  cto
                    <emph type="italics"/>
                  D
                    <emph.end type="italics"/>
                  in tangentes demiſſa. </s>
                  <s>Un­
                    <lb/>
                  de facile colligitur quod puncta
                    <lb/>
                    <emph type="italics"/>
                  S, D, T,
                    <emph.end type="italics"/>
                  ſunt in una recta. </s>
                  <s>Et ſimili
                    <lb/>
                  argumento puncta
                    <emph type="italics"/>
                  S, E, V
                    <emph.end type="italics"/>
                  ſunt eti­
                    <lb/>
                  am in una recta; & propterea centrum
                    <emph type="italics"/>
                  S
                    <emph.end type="italics"/>
                  in concurſu rectarum
                    <emph type="italics"/>
                  TD, VE
                    <emph.end type="italics"/>
                    <lb/>
                  verſatur.
                    <emph type="italics"/>
                  Q.E.D.
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                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                  PROPOSITIO VI. THEOREMA V.
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                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Si corpus in ſpatio non reſiſtente circa centrum immobile in Orbe quocun­
                    <lb/>
                  que revolvatur, & arcum quemvis jamjam naſcentem tempore quàm
                    <lb/>
                  minimo deſcribat, & ſagitta arcus duci intelligatur quæ chordam bi­
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                  ſecet, & producta tranſeat per centrum virium: erit vis centripeta
                    <lb/>
                  in medio arcus, ut ſagitta directe & tempus bis inverſe.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>Nam ſagitta dato tempore eſt ut vis (per Corol.4 Prop.I,) & augen­
                    <lb/>
                  do tempus in ratione quavis, ob auctum arcum in eadem ratione ſa­
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                  gitta augetur in ratione illa duplicata (per Corol. </s>
                  <s>2 & 3, Lem. </s>
                  <s>XI,) ad­
                    <lb/>
                  eoque eſt ut vis ſemel & tempus bis. </s>
                  <s>Subducatur duplicata ratio tempo­
                    <lb/>
                  ris utrinque, & fiet vis ut ſagitta directe & tempus bis inverſe.
                    <emph type="italics"/>
                  Q.E.D.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>Idem facile demonſtratur etiam per Corol. </s>
                  <s>4 Lem. </s>
                  <s>X. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  1. Si corpus
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  revolvendo
                    <lb/>
                    <figure id="id.039.01.069.2.jpg" xlink:href="039/01/069/2.jpg" number="15"/>
                    <lb/>
                  circa centrum
                    <emph type="italics"/>
                  S
                    <emph.end type="italics"/>
                  deſcribat lineam
                    <lb/>
                  curvam
                    <emph type="italics"/>
                  APQ,
                    <emph.end type="italics"/>
                  tangat verò recta
                    <lb/>
                    <emph type="italics"/>
                  ZPR
                    <emph.end type="italics"/>
                  curvam illam in puncto
                    <lb/>
                  quovis
                    <emph type="italics"/>
                  P,
                    <emph.end type="italics"/>
                  & ad tangentem ab alio
                    <lb/>
                  quovis Curvæ puncto
                    <emph type="italics"/>
                  Q
                    <emph.end type="italics"/>
                  agatur
                    <lb/>
                    <emph type="italics"/>
                  QR
                    <emph.end type="italics"/>
                  diſtantiæ
                    <emph type="italics"/>
                  SP
                    <emph.end type="italics"/>
                  parallela, ac
                    <lb/>
                  demittatur
                    <emph type="italics"/>
                  QT
                    <emph.end type="italics"/>
                  perpendicularis
                    <lb/>
                  ad diſtantiam illam
                    <emph type="italics"/>
                  SP:
                    <emph.end type="italics"/>
                  vis cen­
                    <lb/>
                  tripeta erit reciproce ut ſolidum
                    <lb/>
                  (
                    <emph type="italics"/>
                  SP quad.XQT quad./QR
                    <emph.end type="italics"/>
                  ) ſi modo ſolidi illius ea ſemper ſumatur quan­
                    <lb/>
                  titas, quæ ultimò fit ubi coeunt puncta
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                    <expan abbr="q.">que</expan>
                    <emph.end type="italics"/>
                  Nam
                    <emph type="italics"/>
                  QR
                    <emph.end type="italics"/>
                  æqualis </s>
                </p>
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