Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                  <s>
                    <pb xlink:href="039/01/066.jpg" pagenum="38"/>
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                  corpus alterum
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                  T,
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                  erunt areæ illæ temporibus quamproxime pro­
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                  portionales. </s>
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                  <s>
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                  DE MOTU
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                  CORPORUM</s>
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                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
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                  4. Si corpus
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                  L
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                  radio ad alterum corpus
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                  T
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                  ducto deſcri­
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                  bit areas quæ, cum temporibus collatæ, ſunt valde inæquales; &
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                  corpus illud alterum
                    <emph type="italics"/>
                  T
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                  vel quieſcit vel movetur uniformiter in di­
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                  rectum: actio vis centripetæ ad corpus illud alterum
                    <emph type="italics"/>
                  T
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                  tendentis,
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                  vel nulla eſt, vel miſcetur & componitur cum actionibus admodum
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                  potentibus aliarum virium: Viſque tota ex omnibus, ſi plures ſunt
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                  vires, compoſita, ad aliud (ſive immobile ſive mobile) centrum
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                  dirigitur. </s>
                  <s>Idem obtinet, ubi corpus alterum motu quocunque mo­
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                  vetur; ſi modo vis centripeta ſumatur, quæ reſtat poſt ſubductio­
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                  nem vis totius in corpus illud alterum
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                  T
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                  agentis. </s>
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                <p type="main">
                  <s>
                    <emph type="center"/>
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                  Scholium.
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                    <emph.end type="center"/>
                  </s>
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                  <s>Quoniam æquabilis arearum deſcriptio Index eſt Centri, quod
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                  vis illa reſpicit qua corpus maxime afficitur, quaque retrahitur a mo­
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                  tu rectilineo & in orbita ſua retinetur: quidni uſurpemus in ſequen­
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                  tibus æquabilem arearum deſcriptionem, ut Indicem Centri circum
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                  quod motus omnis circularis in ſpatiis liberis peragitur? </s>
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                  <s>
                    <emph type="center"/>
                  PROPOSITIO IV. THEOREMA IV.
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                  </s>
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                  <s>
                    <emph type="italics"/>
                  Corporum, quæ diverſos circulos æquabili motu deſcribunt, vires cen­
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                  tripetas ad centra eorundem circulorum tendere; & eſſe inter ſe,
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                  ut ſunt arcuum ſimul deſcriptorum quadrata applicata ad circulo­
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                  rum radios.
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                  </s>
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                <p type="main">
                  <s>Tendunt hæ vires ad centra circulorum per Prop.II. & Corol. </s>
                  <s>II.
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                  Prop. </s>
                  <s>1; & ſunt inter ſe ut arcuum æqualibus temporibus quam miNI­
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                  mis deſcriptorum ſinus verſi per Corol. </s>
                  <s>IV. Prop. </s>
                  <s>I; hoc eſt, ut qua­
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                  drata arcuum eorundem ad diametros circulorum applicata per
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                  Lem. </s>
                  <s>VII: & propterea, cum hi arcus ſint ut arcus temporibus
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                  quibuſvis æqualibus deſcripti, & diametri ſint ut eorum radii; vi­
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                  res erunt ut arcuum quorumvis ſimul deſcriptorum quadrata ap­
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                  plicata ad radios circulorum.
                    <emph type="italics"/>
                  Q.E.D.
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                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  1. Igitur, cum arcus illi ſint ut velocitates corporum, vi­
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                  res centripetæ ſunt ut velocitatum quadrata applicata ad radios
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                  circulorum: hoc eſt, ut cum Geometris loquar, vires ſunt in ra­
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                  tione compoſita ex duplicata ratione velocitatum directe & ratione
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                  ſimplici radiorum inverſe. </s>
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