Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                  <s>
                    <pb xlink:href="039/01/125.jpg" pagenum="97"/>
                    <arrow.to.target n="note73"/>
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              <subchap2>
                <p type="margin">
                  <s>
                    <margin.target id="note73"/>
                  LIBER
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                  PRIMUS.</s>
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                <p type="main">
                  <s>
                    <emph type="center"/>
                  SECTIO VI.
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                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                    <emph type="italics"/>
                  De Inventione Motuum in Orbibus datis.
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                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                  PROPOSITIO XXX. PROBLEMA XXII.
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                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                    <emph type="italics"/>
                  Corporis in data Trajectoria Parabolica moti invenire locum ad
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                  tempus aſſignatum.
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                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>Sit
                    <emph type="italics"/>
                  S
                    <emph.end type="italics"/>
                  umbilicus &
                    <emph type="italics"/>
                  A
                    <emph.end type="italics"/>
                  vertex principa­
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                    <figure id="id.039.01.125.1.jpg" xlink:href="039/01/125/1.jpg" number="73"/>
                    <lb/>
                  lis Parabolæ, ſitque 4
                    <emph type="italics"/>
                  ASXM
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                  æquale
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                  areæ Parabolicæ abſcindendæ
                    <emph type="italics"/>
                  APS,
                    <emph.end type="italics"/>
                    <lb/>
                  quæ radio
                    <emph type="italics"/>
                  SP,
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                  vel poſt exceſſum cor­
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                  poris de vertice deſcripta fuit, vel an­
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                  te appulſum ejus ad verticem deſcri­
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                  benda eſt. </s>
                  <s>Innoteſcit quantitas areæ il­
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                  lius abſcindendæ ex tempore ipſi pro­
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                  portionali. </s>
                  <s>Biſeca
                    <emph type="italics"/>
                  AS
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                  in
                    <emph type="italics"/>
                  G,
                    <emph.end type="italics"/>
                  erigeque
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                  perpendiculum
                    <emph type="italics"/>
                  GH
                    <emph.end type="italics"/>
                  æquale 3 M, &
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                  Circulus centro
                    <emph type="italics"/>
                  H,
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                  intervallo
                    <emph type="italics"/>
                  HS
                    <emph.end type="italics"/>
                    <lb/>
                  deſcriptus ſecabit Parabolam in loco
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                  quæſito
                    <emph type="italics"/>
                  P.
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                  Nam, demiſſa ad axem
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                  perpendiculari
                    <emph type="italics"/>
                  PO
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                  & ducta
                    <emph type="italics"/>
                  PH,
                    <emph.end type="italics"/>
                  eſt
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                    <emph type="italics"/>
                  AGq+GHq (=HP q=—AO-AG: quad.+—PO-GH: quad.)=
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                  AOq+POq-2
                    <expan abbr="GAO-2GHXPO+AGq+GHq.">GAO-2GHXPO+AGq+GHque</expan>
                    <emph.end type="italics"/>
                  Unde
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                  2
                    <emph type="italics"/>
                  GHXPO (=AOq+POq-2GAO)=AOq+1/4
                    <expan abbr="POq.">POque</expan>
                    <emph.end type="italics"/>
                    <lb/>
                  Pro
                    <emph type="italics"/>
                  AOq
                    <emph.end type="italics"/>
                  ſcribe (
                    <emph type="italics"/>
                  AOXPOq/4AS
                    <emph.end type="italics"/>
                  ); &, applicatis terminis omnibus ad
                    <lb/>
                  3
                    <emph type="italics"/>
                  PO
                    <emph.end type="italics"/>
                  ductiſQ.E.I. 2
                    <emph type="italics"/>
                  AS,
                    <emph.end type="italics"/>
                  fiet 4/3
                    <emph type="italics"/>
                  GHXAS(=1/6AOXPO+1/2 ASXPO
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                  =(AO+3AS/6)XPO=(4AO-3SO/6)XPO
                    <emph.end type="italics"/>
                  =areæ —
                    <emph type="italics"/>
                  APO-SPO)
                    <emph.end type="italics"/>
                    <lb/>
                  =areæ
                    <emph type="italics"/>
                  APS.
                    <emph.end type="italics"/>
                  Sed
                    <emph type="italics"/>
                  GH
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                  erat 3 M, & inde 4/3
                    <emph type="italics"/>
                  GHXAS
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                  eſt 4
                    <emph type="italics"/>
                  AS
                    <emph.end type="italics"/>
                  XM. </s>
                  <s>
                    <lb/>
                  Ergo area abſciſſa
                    <emph type="italics"/>
                  APS
                    <emph.end type="italics"/>
                  æqualis eſt abſcindendæ 4
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                  ASXM. Q.E.D.
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                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
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                  1. Hinc
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                  GH
                    <emph.end type="italics"/>
                  eſt ad
                    <emph type="italics"/>
                  AS,
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                  ut tempus quo corpùs deſcrip­
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                  ſit arcum
                    <emph type="italics"/>
                  AP
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                  ad tempus quo corpus deſcripſit arcum inter verti­
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                  cem
                    <emph type="italics"/>
                  A
                    <emph.end type="italics"/>
                  & perpendiculum ad axem ab umbilico
                    <emph type="italics"/>
                  S
                    <emph.end type="italics"/>
                  erectum. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
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                  2. Et Circulo
                    <emph type="italics"/>
                  ASP
                    <emph.end type="italics"/>
                  per corpus motum
                    <emph type="italics"/>
                  P
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                  perpetuo tranſ­
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                  eunte, velocitas puncti
                    <emph type="italics"/>
                  H
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                  eſt ad velocitatem quam corpus habuit </s>
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