Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                    <pb xlink:href="039/01/174.jpg" pagenum="146"/>
                    <arrow.to.target n="note122"/>
                  a ſuperficie, proportiona­
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                    <figure id="id.039.01.174.1.jpg" xlink:href="039/01/174/1.jpg" number="103"/>
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                  lis;
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                  PHTF
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                  recta axi
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                  parallela per corpus tran­
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                  ſiens, &
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                  GF, IH
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                  rectæ
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                  a punctis
                    <emph type="italics"/>
                  G
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                  &
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                  I
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                  in pa­
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                  rallelam illam
                    <emph type="italics"/>
                  PHTF
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                    <lb/>
                  perpendiculariter demiſ­
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                  ſæ. </s>
                  <s>Dico jam quod area
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                    <emph type="italics"/>
                  AOP,
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                  radio
                    <emph type="italics"/>
                  OP
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                  ab iNI­
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                  tio motus deſcripta, ſit
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                  tempori proportionalis. </s>
                  <s>
                    <lb/>
                  Nam vis
                    <emph type="italics"/>
                  TG
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                  (per Le­
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                  gum Corol. </s>
                  <s>2.) reſolvitur
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                  in vires
                    <emph type="italics"/>
                  TF, FG
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                  ; & vis
                    <lb/>
                    <emph type="italics"/>
                  TI
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                  in vires
                    <emph type="italics"/>
                  TH, HI:
                    <emph.end type="italics"/>
                    <lb/>
                  Vires autem
                    <emph type="italics"/>
                  TF, TH
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                    <lb/>
                  agendo ſecundum lineam
                    <lb/>
                    <emph type="italics"/>
                  PF
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                  plano
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                  AOP
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                  per­
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                  pendicularem mutant ſo­
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                  lummodo motum cor­
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                  poris quatenus huic plano perpendicularem. </s>
                  <s>Ideoque motus ejus
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                  quatenus ſecundum poſitionem plani factus, hoc eſt, motus pun­
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                  cti
                    <emph type="italics"/>
                  P
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                  quo Trajectoriæ veſtigium
                    <emph type="italics"/>
                  AP
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                  in hoc plano deſcri­
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                  bitur, idem eſt ac ſi vires
                    <emph type="italics"/>
                  TF, TH
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                  tollerentur, & corpus ſolis vi­
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                  ribus
                    <emph type="italics"/>
                  FG, HI
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                  agitaretur; hoc eſt, idem ac ſi corpus in plano
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                    <emph type="italics"/>
                  AOP,
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                  vi centripeta ad centrum
                    <emph type="italics"/>
                  O
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                  tendente & ſummam virium
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                    <emph type="italics"/>
                  FG
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                  &
                    <emph type="italics"/>
                  HI
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                  æquante, deſcriberet curvam
                    <emph type="italics"/>
                  AP.
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                  Sed vi tali deſcribi­
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                  tur area
                    <emph type="italics"/>
                  AOP
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                  (per Prop. </s>
                  <s>1.) tempori proportionalis.
                    <emph type="italics"/>
                  Q.E.D.
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                  </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note122"/>
                  DE MOTU
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                  CORPORUM</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  Eodem argumento ſi corpus a viribus agitatum ad centra
                    <lb/>
                  duo vel plura in eadem quavis recta
                    <emph type="italics"/>
                  CO
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                  data tendentibus, deſcri­
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                  beret in ſpatio libero lineam quamcunque curvam
                    <emph type="italics"/>
                  ST
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                  ; foret area
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                    <emph type="italics"/>
                  AOP
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                  tempori ſemper proportionalis. </s>
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                <p type="main">
                  <s>
                    <emph type="center"/>
                  PROPOSITIO LVI. PROBLEMA XXXVII.
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                  </s>
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                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Conceſſis Figurarum curvilinearum quadraturis, datiſque tum lege
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                  Vis centripetæ ad centrum datum tendentis, tum ſuperficie cur­
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                  va cujus axis per centrum illud trænſit; invenieuda est Traje­
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                  ctoria quam corpus in eadem ſuperficie deſcribet, de loco dato, data
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                  cum Velocitate, verſus plagam in ſuperficie illa datam egreſſum.
                    <emph.end type="italics"/>
                  </s>
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