Newton, Isaac, Philosophia naturalis principia mathematica, 1713
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                    <pb xlink:href="039/01/075.jpg" pagenum="47"/>
                  dæ arcus
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                  PQ
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                  erit æquale rectangulo
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                  VPv
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                  ; adeoque Circulus qui
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                    <arrow.to.target n="note23"/>
                  tangit Sectionem Conicam in
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                  P
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                  & tranſit per punctum
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                  Q,
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                  tranſibit
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                  etiam per punctum
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                  V.
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                  Coeant puncta
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                  P
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                  &
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                  Q,
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                  & hic circulus
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                  ejuſdem erit curvaturæ cum ſectione conica in
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                  P,
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                  &
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                  PV
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                  æqualis erit
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                  (2
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                  DCq/PC
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                  ). Proinde vis qua corpus
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                  P
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                  in Ellipſi revolvitur, erit reci­
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                  proce ut (2
                    <emph type="italics"/>
                  DCq/PC
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                  ) in
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                  PFq
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                  (per Corol. </s>
                  <s>3 Prop. </s>
                  <s>VI.) hoc eſt (ob
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                  datum 2
                    <emph type="italics"/>
                  DCq
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                  in
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                  PFq
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                  ) directe ut
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                  PC.
                    <expan abbr="q.">que</expan>
                  E. I.
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                  </s>
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                <p type="margin">
                  <s>
                    <margin.target id="note23"/>
                  LIBER
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                  PRIMUS.</s>
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                  <s>
                    <emph type="italics"/>
                  Corol.
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                  1. Eſt igitur vis ut diſtantia corporis a centro Ellipſeos: &
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                  viciſſim, ſi vis ſit ut diſtantia, movebitur corpus in Ellipſi centrum
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                  habente in centro virium, aut forte in Circulo, in quem utique
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                  Ellipſis migrare poteſt. </s>
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                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
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                  2. Et æqualia erunt revolutionum in Ellipſibus univerſis cir­
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                  cum centrum idem factarum periodica tempora. </s>
                  <s>Nam tempora
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                  illa in Ellipſibus ſimilibus æqualia ſunt per Corol. </s>
                  <s>3 & 8, Prop. </s>
                  <s>IV:
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                  in Ellipſibus autem communem habentibus axem majorem, ſunt ad
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                  invicem ut Ellipſeon areæ totæ directe & arearum particulæ ſimul
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                  deſcriptæ inverſe; id eſt, ut axes minores directe & corporum ve­
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                  locitates in verticibus principalibus inverſe; hoc eſt, ut axes illi mi­
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                  nores directe & ordinatim applicatæ ad axes alteros inverſe; & prop­
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                  terea (ob æqualitatem rationum directarum & inverſarum) in ra­
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                  tione æqualitatis. </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>Si Ellipſis, centro in infinitum abeunte vertatur in Parabolam,
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                  corpus movebitur in hac Parabola; & vis ad centrum infinite di­
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                  ſtans jam tendens evadet æquabilis. </s>
                  <s>Hoc eſt Theorema
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                  Galilæi.
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                  Et ſi coni ſectio Parabolica, inclinatione plani ad conum ſectum
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                  mutata, vertatur in Hyperbolam, movebitur corpus in hujus pe­
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                  rimetro, vi centripeta in centrifugam verſa. </s>
                  <s>Et quemadmo­
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                  dum in Circulo vel Ellipſi, ſi vires tendunt ad centrum figuræ
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                  in Abſciſſa poſitum, hæ vires augendo vel diminuendo Ordinatas in
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                  ratione quacunQ.E.D.ta, vel etiam mutando angulum inclinationis
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                  Ordinatarum ad Abſciſſam, ſemper augentur vel diminuuntur in
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                  ratione diſtantiarum a centro, ſi modo tempora periodica maneant
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                  æqualia: ſic etiam in figuris univerſis, ſi Ordinatæ augeantur vel di­
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                  minuantur in ratione quacunQ.E.D.ta, vel angulus ordinationis ut­
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                  cunque mutetur, manente tempore periodico; vires ad centrum
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                  quodcunQ.E.I. Abſciſſa poſitum tendentes a binis quibuſvis figurarum locis, ad quæ termi­
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                  nantur Ordinatæ correſpondentibus Abſciſſarum punctis inſiſtentes, augentur vel &c. </s>
                  <s>augentur vel diminuun­
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                  tur in ratione diſtantiarum a centro. </s>
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