Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                  una tendente ad
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                  T
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                  & oriunda a mutua attractione corporum
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                  T
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                  &
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                  P.
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                    <lb/>
                  Hac vi ſola corpus
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                  P
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                  circum corpus
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                  T,
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                  ſive immotum ſive hac
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                  attractione agitatum, deſcribere deberet & areas, radio
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                  PT,
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                  tem­
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                  poribus proportionales, & Ellipſin cui umbilicus eſt in centro cor­
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                  poris
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                  T.
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                  Patet hoc per Prop. </s>
                  <s>XI. & Corollaria 2 & 3 Theor. </s>
                  <s>XXI. </s>
                  <s>Vis
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                  altera eſt attractionis
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                  LM,
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                  quæ quoniam tendit a
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                  P
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                  ad
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                  T,
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                  ſuperad­
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                  dita vi priori coincidet cum ipſa, & ſic faciet ut areæ etiamnum tem­
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                  poribus proportionales deſcribantur per Corol. </s>
                  <s>3. Theor. </s>
                  <s>XXI. </s>
                  <s>At
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                  quoniam non eſt quadrato diſtantiæ
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                  PT
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                  reciproce proportionalis,
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                  componet ea cum vi priore vim ab hac proportione aberrantem, id­
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                  que eo magis quo major eſt proportio hujus vis ad vim priorem,
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                  cæteris paribus. </s>
                  <s>Proinde cum (per Prop. </s>
                  <s>XI, & per Corol. </s>
                  <s>2.
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                  Theor. </s>
                  <s>XXI) vis qua Ellipſis circa umbilicum
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                  T
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                  deſcribitur tendere
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                  debeat ad umbilicum illum, & eſſe quadrato diſtantiæ
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                  PT
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                  reciproce
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                  proportionalis; vis illa
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                    <figure id="id.039.01.186.1.jpg" xlink:href="039/01/186/1.jpg" number="108"/>
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                  compoſita, aberrando
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                  ab hac proportione, fa­
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                  ciet ut Orbis
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                  PAB
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                    <lb/>
                  aberret a forma Ellip­
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                  ſeos umbilicum haben­
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                  tis in
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                  S;
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                  idque eo ma­
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                  gis quo major eſt ab­
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                  erratio ab hac propor­
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                  tione; atque adeo eti­
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                  am quo major eſt proportio vis ſecundæ
                    <emph type="italics"/>
                  LM
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                  ad vim primam, cæ­
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                  teris paribus. </s>
                  <s>Jam vero vis tertia
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                  SM,
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                  trahendo corpus
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                  P
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                  ſecun­
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                  dum lineam ipſi
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                  ST
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                  parallelam, componet cum viribus prioribus
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                  vim quæ non amplius dirigitur a
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                  P
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                  in
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                  T,
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                  quæque ab hac determi­
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                  natione tanto magis aberrat, quanto major eſt proportio hujus ter­
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                  tiæ vis ad vires priores, cæteris paribus; atque adeo quæ faciet ut
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                  corpus
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                  P,
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                  radio
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                  TP,
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                  areas non amplius temporibus proportiona­
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                  les deſcribat, atque aberratio ab hac proportionalitate ut tanto ma­
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                  jor ſit, quanto major eſt proportio vis hujus tertiæ ad vires cæte­
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                  ras. </s>
                  <s>Orbis vero
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                  PAB
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                  aberrationem a forma Elliptica præfata hæc­
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                  vis tertia duplici de cauſa adaugebit, tum quod non dirigatur a
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                  P
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                    <lb/>
                  ad
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                  T,
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                  tum etiam quod non ſit proportionalis quadrato diſtantiæ
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                  PT.
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                  Quibus intellectis, manifeſtum eſt quod areæ temporibus tum max­
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                  ime fiunt proportionales, ubi vis tertia, manentibus viribus cæte­
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                  ris, fit minima; & quod Orbis
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                  PAB
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                  tum maxime accedit ad præ­
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                  fatam formam Ellipticam, ubi vis tam ſecunda quam tertia, ſed præ­
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                  cipue vis tertia, fit minima, vi prima manente. </s>
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