Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                  <s>
                    <pb xlink:href="039/01/064.jpg" pagenum="36"/>
                    <arrow.to.target n="note17"/>
                  ubi arcus illi in infinitum diminuuntur. </s>
                  <s>Nam hæ ſagittæ ſunt ſe­
                    <lb/>
                  miſſes diagonalium de quibus egimus in Corollario tertio. </s>
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                <p type="margin">
                  <s>
                    <margin.target id="note17"/>
                  DE MOTU
                    <lb/>
                  CORPORUM</s>
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                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  5. Ideoque vires eædem ſunt ad vim gravitatis, ut hæ ſa­
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                  gittæ ad ſagittas horizonti perpendiculares arcuum Parabolieorum
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                  quos projectilia eodem tempore deſcribunt. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  6. Eadem omnia obtinent per Legum Corol. </s>
                  <s>IV, ubi plana
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                  in quibus corpora moventur, una cum centris virium quæ in ipſis
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                  fita ſunt, non quieſcunt, ſed moventur uniformiter in directum. </s>
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                <p type="main">
                  <s>
                    <emph type="center"/>
                  PROPOSITIO II. THEOREMA II.
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                  </s>
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                  <s>
                    <emph type="italics"/>
                  Corpus omne, quod movetur in linea aliqua curva in plano de­
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                  ſcripta, & radio ducto ad punctum vel immobile, vel motu rectili­
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                  neo uniformiter progrediens, deſcribit areas circa punctum illud
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                  temporibus proportionales, urgetur a vi centripeta tendente ad idem
                    <lb/>
                  punctum.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Cas.
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                  1. Nam corpus omne quod movetur in linea curva, detor­
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                  quetur de curſu rectilineo per vim aliquam in ipſum agentem (per
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                  Leg. </s>
                  <s>1.) Et vis illa qua corpus de curſu rectilineo detorquetur, &
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                  cogitur triangula quam minima
                    <emph type="italics"/>
                  SAB, SBC, SCD,
                    <emph.end type="italics"/>
                  &c. </s>
                  <s>circa
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                  punctum immobile
                    <emph type="italics"/>
                  S
                    <emph.end type="italics"/>
                  temporibus æqualibus æqualia deſcribere, a­
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                  git in loco
                    <emph type="italics"/>
                  B
                    <emph.end type="italics"/>
                  ſecundum lineam parallelam ipſi
                    <emph type="italics"/>
                  cC
                    <emph.end type="italics"/>
                  (per Prop. </s>
                  <s>XL,
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                  Lib. </s>
                  <s>1 Elem. </s>
                  <s>& Leg. </s>
                  <s>11.) hoc eſt, ſecundum lineam
                    <emph type="italics"/>
                  BS
                    <emph.end type="italics"/>
                  ; & in loco
                    <lb/>
                    <emph type="italics"/>
                  C
                    <emph.end type="italics"/>
                  ſecundum lineam ipſi
                    <emph type="italics"/>
                  dD
                    <emph.end type="italics"/>
                  parallelam, hoc eſt, ſecundum lineam
                    <lb/>
                    <emph type="italics"/>
                  SC,
                    <emph.end type="italics"/>
                  &c. </s>
                  <s>Agit ergo ſemper ſecundum lineas tendentes ad punctum
                    <lb/>
                  illud immobile
                    <emph type="italics"/>
                  S.
                    <expan abbr="q.">que</expan>
                  E. D.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Cas.
                    <emph.end type="italics"/>
                  2. Et, per Legum Corollarium quintum, perinde eſt ſive
                    <lb/>
                  quieſcat ſuperficies in qua corpus deſcribit figuram curvilineam,
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                  ſive moveatur eadem una cum corpore, figura deſcripta, & puncto
                    <lb/>
                  ſuo
                    <emph type="italics"/>
                  S
                    <emph.end type="italics"/>
                  uniformiter in directum. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  1. In Spatiis vel Mediis non reſiſtentibus, ſi areæ non ſunt
                    <lb/>
                  temporibus proportionales, vires non tendunt ad concurſum radio­
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                  rum; ſed inde declinant in conſequentia ſeu verſus plagam in quam
                    <lb/>
                  fit motus, ſi modo arearum deſcriptio acceleratur: ſin retardatur, de­
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                  clinant in antecedentia. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  2. In Mediis etiam reſiſtentibus, ſi arearum deſcriptio accele­
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                  ratur, virium directiones declinant a concurſu radiorum verſus plagam
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                  in quam ſit motus. </s>
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