Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                  latera recta principalia ſunt æqualia, velocitas corporis eſt reciproce
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                  ut perpendiculum demiſſum ab umbilico ad tangentem. </s>
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                  DE MOTU
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                  CORPORUM</s>
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                  <s>
                    <emph type="italics"/>
                  Corol.
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                  6. In Parabola, velocitas eſt reciproce in ſubduplicata ra­
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                  tione diſtantiæ corporis ab umbilico figuræ; in Ellipſi magis varia­
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                  tur, in Hyperbola minus, quam in hac ratione. </s>
                  <s>Nam (per Corol. </s>
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                  2. Lem. </s>
                  <s>XIV.) perpendiculum demiſſum ab umbilico ad tangentem
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                  Parabolæ eſt in ſubduplicata ratione diſtantiæ. </s>
                  <s>In Hyperbola per­
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                  pendiculum minus variatur, in Ellipſi magis. </s>
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                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
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                  7. In Parabola, velocitas corporis ad quamvis ab umbili­
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                  co diſtantiam, eſt ad velocitatem corporis revolventis in Circulo
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                  ad eandem a centro diſtantiam, in ſubduplicata ratione numeri bi­
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                  narii ad unitatem; in Ellipſi minor eſt, in Hyperbola major quam
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                  in hac ratione. </s>
                  <s>Nam per hujus Corollarium ſecundum, velocitas
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                  in vertice Parabolæ eſt in hac ratione, & per Corollaria ſexta hu­
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                  jus & Propoſitionis quartæ, ſervatur eadem proportio in omnibus
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                  diſtantiis. </s>
                  <s>Hinc etiam in Parabola velocitas ubique æqualis eſt ve­
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                  locitati corporis revolventis in Circulo ad dimidiam diſtantiam, in
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                  Ellipſi minor eſt, in Hyperbola major. </s>
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                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
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                  8. Velocitas gyrantis in Sectione quavis Conica eſt ad ve­
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                  locitatem gyrantis in Circulo in diſtantia dimidii lateris recti princi­
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                  palis Sectionis, ut diſtantia illa ad perpendiculum ab umbilico in
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                  tangentem Sectionis demiſſum. </s>
                  <s>Patet per Corollarium quintum. </s>
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                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
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                  9. Unde cum (per Corol. </s>
                  <s>6. Prop. </s>
                  <s>IV.) velocitas gyrantis
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                  in hoc Circulo ſit ad velocitatem gyrantis in Circulo quovis alio,
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                  reciproce in ſubduplicata ratione diſtantiarum; fiet ex æquo velo­
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                  citas gyrantis in Conica ſectione ad velocitatem gyrantis in Circulo
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                  in eadem diſtantia, ut media proportionalis inter diſtantiam illam
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                  communem & ſemiſſem principalis lateris recti ſectionis, ad per­
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                  pendiculum ab umbilico communi in tangentem ſectionis de­
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                  miſſum. </s>
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                  PROPOSITIO XVII. PROBLEMA. IX.
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                  Poſito quod vis centripeta ſit reciproce proportionalis quadrato diſtan­
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                  ſtantiæ loeorum a centro, & quod vis illius quantitas abſoluta ſit
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                  cognita; requiritur Linea quam corpus deſcribit, de loco dato, cum
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                  data velocitate, ſecundum datam rectam egrediens.
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                  </s>
                </p>
                <p type="main">
                  <s>Vis centripeta tendens ad punctum
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                  S
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                  ea ſit qua corpus
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                  p
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                  in or­
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                  bita quavis data
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                  pq
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                  gyretur, & cognoſcatur hujus velocitas in loco
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                  p.
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                  </s>
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