Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                <pb xlink:href="039/01/081.jpg" pagenum="53"/>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
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                  1. Ex tribus noviſſimis Propoſitionibus conſequens eſt, quod </s>
                </p>
                <p type="main">
                  <s>
                    <arrow.to.target n="note29"/>
                  ſi corpus quodvis
                    <emph type="italics"/>
                  P,
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                  ſecundum lineam quamvis rectam
                    <emph type="italics"/>
                  PR,
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                  qua­
                    <lb/>
                  cunque cum velocitate exeat de loco
                    <emph type="italics"/>
                  P,
                    <emph.end type="italics"/>
                  & vi centripeta quæ ſit re­
                    <lb/>
                  ciproce proportionalis quadrato diſtantiæ loeorum a centro, ſimul
                    <lb/>
                  agitetur; movebitur hoc corpus in aliqua ſectionum Conicarum
                    <lb/>
                  umbilicum habente in centro virium; & contra. </s>
                  <s>Nam datis umbi­
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                  lico & puncto contactus & poſitione tangentis, deſcribi poteſt ſectio
                    <lb/>
                  Conica quæ curvaturam datam ad punctum illud habebit. </s>
                  <s>Datur
                    <lb/>
                  autem curvatura ex data vi centripeta: & Orbes duo ſe mutuo tan­
                    <lb/>
                  gentes, eadem vi centripeta deſcribi non poſſunt. </s>
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                <p type="margin">
                  <s>
                    <margin.target id="note29"/>
                  LIBER
                    <lb/>
                  PRIMUS.</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  2. Si velocitas, quacum corpus exit de loco ſuo
                    <emph type="italics"/>
                  P,
                    <emph.end type="italics"/>
                  ea
                    <lb/>
                  ſit, qua lineola
                    <emph type="italics"/>
                  PR
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                  in minima aliqua temporis particula deſcribi
                    <lb/>
                  poſſit, & vis centripeta potis ſit eodem tempore corpus idem mo­
                    <lb/>
                  vere per ſpatium
                    <emph type="italics"/>
                  QR:
                    <emph.end type="italics"/>
                  movebitur hoc corpus in Conica aliqua ſe­
                    <lb/>
                  ctione, cujus latus rectum principale eſt quantitas illa (
                    <emph type="italics"/>
                  QTq./QR
                    <emph.end type="italics"/>
                  ) quæ
                    <lb/>
                  ultimo fit ubi lineolæ
                    <emph type="italics"/>
                  PR, QR
                    <emph.end type="italics"/>
                  in infinitum diminuuntur. </s>
                  <s>Circu­
                    <lb/>
                  lum in his Corollariis refero ad Ellipſin, & caſum excipio ubi cor­
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                  pus recta deſcendit ad centrum. </s>
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                <p type="main">
                  <s>
                    <emph type="center"/>
                  PROPOSITIO XIV. THEOREMA VI.
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                  </s>
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                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Si corpora plura revolvantur circa centrum commune, & vis centri­
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                  peta ſit reciproce in duplicata ratione diſtantiæ loeorum a centro;
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                  dico quod Orbium Latera recta principalia ſunt in duplicata ratio­
                    <lb/>
                  one arearum quas corpora, radiis ad centrum ductis, eodem tempore
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                  deſcribunt.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>Nam, per Corol. </s>
                  <s>2. Prop. </s>
                  <s>XIII, Latus rectum
                    <emph type="italics"/>
                  L
                    <emph.end type="italics"/>
                  æquale eſt quan­
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                  titati (
                    <emph type="italics"/>
                  QTq./QR
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                  ) quæ ultimo fit ubi coeunt puncta
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                    <expan abbr="q.">que</expan>
                    <emph.end type="italics"/>
                  Sed linea
                    <lb/>
                  minima
                    <emph type="italics"/>
                  QR,
                    <emph.end type="italics"/>
                  dato tempore, eſt ut vis centripeta generans, hoc
                    <lb/>
                  eſt (per Hypotheſin) reciproce ut
                    <emph type="italics"/>
                    <expan abbr="SPq.">SPque</expan>
                    <emph.end type="italics"/>
                  Ergo (
                    <emph type="italics"/>
                  QTq./QR
                    <emph.end type="italics"/>
                  ) eſt ut
                    <lb/>
                    <emph type="italics"/>
                    <expan abbr="QTq.XSPq.">QTq.XSPque</expan>
                    <emph.end type="italics"/>
                  hoc eſt, latus rectum
                    <emph type="italics"/>
                  L
                    <emph.end type="italics"/>
                  in duplicata ratione areæ
                    <lb/>
                    <emph type="italics"/>
                  QTXSP. Q.E.D.
                    <emph.end type="italics"/>
                  </s>
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