Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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