Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                  <s>
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                  tra petentium, & planis excentricis innitentium hic conſiderandus
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                  venit. </s>
                  <s>Plana autem ſupponimus eſſe politiſſima & abſolute lubrica
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                  ne corpora retardent. </s>
                  <s>Quinimo, in his demonſtrationibus, vi­
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                  ce planorum quibus corpora incumbunt quæque tangunt incum­
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                  bendo, uſurpamus plana his parallela, in quibus centra corpo­
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                  rum moventur & Orbitas movendo deſcribunt. </s>
                  <s>Et eadem lege
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                  Motus corporum in ſuperficiebus Curvis peractos ſubinde de­
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                  terminamus. </s>
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                <p type="margin">
                  <s>
                    <margin.target id="note108"/>
                  DE MOTU
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                  CORPORUM</s>
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                  <s>
                    <emph type="center"/>
                  SECTIO X.
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                  </s>
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                  <s>
                    <emph type="center"/>
                    <emph type="italics"/>
                  De Motu Corporum in Superficiebus datis, deque Funipendulorum
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                  Motu reciproco.
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                    <emph.end type="center"/>
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                  <s>
                    <emph type="center"/>
                  PROPOSITIO XLVI. PROBLEMA XXXII.
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                  <s>
                    <emph type="italics"/>
                  Poſita cujuſcunque generis Vi centripeta, datoque tum Virium cen­
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                  tro tum Plano quocunQ.E.I. quo corpus revolvitur, & conceſ­
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                  ſis Figurarum curvilinearum quadraturis: requiritur Motus cor­
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                  poris de loco dato, data cum Velocitate, ſecundum rectam in
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                  Plano illo datam egreſſi.
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                  </s>
                </p>
                <p type="main">
                  <s>Sit
                    <emph type="italics"/>
                  S
                    <emph.end type="italics"/>
                  centrum Virium,
                    <emph type="italics"/>
                  SC
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                  diſtantia minima centri hujus a Plano
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                  dato,
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  corpus de loco
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  ſecundum rectam
                    <emph type="italics"/>
                  PZ
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                  egrediens,
                    <emph type="italics"/>
                  Q
                    <emph.end type="italics"/>
                    <lb/>
                  corpus idem in Trajectoria ſua revolvens, &
                    <emph type="italics"/>
                  PQR
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                  Trajectoria
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                  illa, in Plano dato deſcripta, quam invenire oportet. </s>
                  <s>Jungantur
                    <emph type="italics"/>
                  CQ
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                  QS,
                    <emph.end type="italics"/>
                  & ſi in
                    <emph type="italics"/>
                  QS
                    <emph.end type="italics"/>
                  capiatur
                    <emph type="italics"/>
                  SV
                    <emph.end type="italics"/>
                  proportionalis vi centripetæ qua
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                  corpus trahitur verſus centrum
                    <emph type="italics"/>
                  S,
                    <emph.end type="italics"/>
                  & agatur
                    <emph type="italics"/>
                  VT
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                  quæ fit parallela
                    <lb/>
                    <emph type="italics"/>
                  CQ
                    <emph.end type="italics"/>
                  & occurrat
                    <emph type="italics"/>
                  SC
                    <emph.end type="italics"/>
                  in
                    <emph type="italics"/>
                  T:
                    <emph.end type="italics"/>
                  Vis
                    <emph type="italics"/>
                  SV
                    <emph.end type="italics"/>
                  reſolvetur (per Legum Corol. </s>
                  <s>2.)
                    <lb/>
                  in vires
                    <emph type="italics"/>
                  ST, TV;
                    <emph.end type="italics"/>
                  quarum
                    <emph type="italics"/>
                  ST
                    <emph.end type="italics"/>
                  trahendo corpus ſecundum lineam
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                  plano perpendicularem, nil mutat motum ejus in hoc plano. </s>
                  <s>Vis
                    <lb/>
                  autem altera
                    <emph type="italics"/>
                  TV,
                    <emph.end type="italics"/>
                  agendo ſecundum poſitionem plani, trahit cor­
                    <lb/>
                  pus directe verſus punctum
                    <emph type="italics"/>
                  C
                    <emph.end type="italics"/>
                  in plano datum, adeoque facit illud
                    <lb/>
                  in hoc plano perinde moveri ac ſi vis
                    <emph type="italics"/>
                  ST
                    <emph.end type="italics"/>
                  tolleretur, & corpus vi
                    <lb/>
                  ſola
                    <emph type="italics"/>
                  TV
                    <emph.end type="italics"/>
                  revolveretur circa centrum
                    <emph type="italics"/>
                  C
                    <emph.end type="italics"/>
                  in ſpatio libero. </s>
                  <s>Data autem </s>
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