Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                <pb xlink:href="039/01/065.jpg" pagenum="37"/>
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                  <s>
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                  Scholium.
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                  <s>Urgeri poteſt corpus a vi centripeta compoſita ex pluribus viri­
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                  bus. </s>
                  <s>In hoc caſu ſenſus Propoſitionis eſt, quod vis illa quæ ex om­
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                  nibus componitur, tendit ad punctum
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                  S.
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                  Porro ſi vis aliqua agat
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                  perpetuo ſecundum lineam ſuperficiei deſcriptæ perpendicularem;
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                  hæc faciet ut corpus deflectatur a plano ſui motus: ſed quantita­
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                  tem ſuperficiei deſcriptæ nec augebit nec minuet, & propterea in
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                  compoſitione virium negligenda eſt. </s>
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                  PROPOSITIO III. THEOREMA III.
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                  Corpus omne, quod radio ad centrum corporis alterius utcunque moti
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                  ducto deſcribit areas circa centrum illud temporibus proportiona­
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                  les, urgetur vi compoſita ex vi centripeta tendente ad corpus il­
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                  lud alterum, & ex vi omni acceleratrice qua corpus illud alterum
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                  urgetur.
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                  </s>
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                <p type="main">
                  <s>Sit corpus primum
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                  L
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                  & corpus alterum
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                  T:
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                  & (per Legum Corol. </s>
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                  VI.) ſi vi nova, quæ æqualis & contraria ſit illi qua corpus alterum
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                    <emph type="italics"/>
                  T
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                  urgetur, urgeatur corpus utrumque ſecundum lineas parallelas;
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                  perget corpus primum
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                  L
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                  deſcribere circa corpus alterum
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                  T
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                  areas
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                  eaſdem ac prius: vis autem, qua corpus alterum
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                  T
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                  urgebatur, jam
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                  deſtruetur per vim ſibi æqualem & contrariam; & propterea (per
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                  Leg. </s>
                  <s>1.) corpus illud alterum
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                  T
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                  ſibimet ipſi jam relictum vel qui­
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                  eſcet vel movebitur uniformiter in directum: & corpus primum
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                  L
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                    <lb/>
                  urgente differentia virium, id eſt, urgente vi reliqua perget areas
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                  temporibus proportionales circa corpus alterum
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                  T
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                  deſcribere. </s>
                  <s>Ten­
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                  dit igitur (per Theor. </s>
                  <s>11.) differentia virium ad corpus illud alte­
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                  rum
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                  T
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                  ut centrum.
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                    <expan abbr="q.">que</expan>
                  E. D.
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                  </s>
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                  <s>
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                  Corol.
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                  1. Hinc ſi corpus unum
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                  L
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                  radio ad alterum
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                  T
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                  ducto de­
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                  ſcribit areas temporibus proportionales; atQ.E.D. vi tota (ſive ſim­
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                  plici, ſive ex viribus pluribus, juxta Legum Corollarium ſecundum,
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                  compoſita,) qua corpus prius
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                  L
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                  urgetur, ſubducatur (per idem Le­
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                  gum Corollarium) vis tota acceleratrix qua corpus alterum urgetur:
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                  vis omnis reliqua qua corpus prius urgetur tendet ad corpus alte­
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                  rum
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                  T
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                  ut centrum. </s>
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                <p type="main">
                  <s>
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                  Corol.
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                  2. Et, ſi areæ illæ ſunt temporibus quamproxime propor­
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                  tionales, vis reliqua tendet ad corpus alterum
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                  quamproxime. </s>
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                <p type="main">
                  <s>
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                  Corol.
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                  3. Et vice verſa, ſi vis reliqua tendit quamproxime ad </s>
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