Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                <pb xlink:href="039/01/070.jpg" pagenum="42"/>
                <p type="main">
                  <s>
                    <arrow.to.target n="note20"/>
                  eſt ſagittæ dupli arcus
                    <emph type="italics"/>
                  QP,
                    <emph.end type="italics"/>
                  in cujus medio eſt
                    <emph type="italics"/>
                  P,
                    <emph.end type="italics"/>
                  & duplum trian­
                    <lb/>
                  guli
                    <emph type="italics"/>
                  SQP
                    <emph.end type="italics"/>
                  ſive
                    <emph type="italics"/>
                  SPXQT,
                    <emph.end type="italics"/>
                  tempori quo arcus iſte duplus deſcribitur
                    <lb/>
                  proportionale eſt, ideoque pro temporis exponente ſcribi poteſt. </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note20"/>
                  DE MOTU
                    <lb/>
                  CORPORUM</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  2. Eodem argumento vis centripeta eſt reciprocè ut ſolidum
                    <lb/>
                  (
                    <emph type="italics"/>
                  SYqXQPq/QR
                    <emph.end type="italics"/>
                  ), ſi modo
                    <emph type="italics"/>
                  SY
                    <emph.end type="italics"/>
                  perpendiculum ſit a centro virium in Or­
                    <lb/>
                  bis tangentem
                    <emph type="italics"/>
                  PR
                    <emph.end type="italics"/>
                  demiſſum. </s>
                  <s>Nam rectangula
                    <emph type="italics"/>
                  SYXQP
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  SPXQT
                    <emph.end type="italics"/>
                    <lb/>
                  æquantur. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  3. Si Orbis vel circulus eſt, vel angulum contactus cum cir­
                    <lb/>
                  culo quam minimum continet, eandem habens curvaturam eundem­
                    <lb/>
                  que radium curvaturæ ad punctum contactus
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  ; & ſi
                    <emph type="italics"/>
                  PV
                    <emph.end type="italics"/>
                  chorda
                    <lb/>
                  ſit circuli hujus a corpore per centrum virium acta: erit vis centri­
                    <lb/>
                  peta reciproce ut ſolidum
                    <emph type="italics"/>
                  SYqXPV.
                    <emph.end type="italics"/>
                  Nam
                    <emph type="italics"/>
                  PV
                    <emph.end type="italics"/>
                  eſt (
                    <emph type="italics"/>
                  QPq/QR
                    <emph.end type="italics"/>
                  ). </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  4. Iiſdem poſitis, eſt vis centripeta ut velocitas bis directe,
                    <lb/>
                  & chorda illa inverſe. </s>
                  <s>Nam velocitas eſt reciproce ut perpendicu­
                    <lb/>
                  lum
                    <emph type="italics"/>
                  SY
                    <emph.end type="italics"/>
                  per Corol. </s>
                  <s>I Prop. </s>
                  <s>I. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  5. Hinc ſi detur figura quævis curvilinea
                    <emph type="italics"/>
                  APQ,
                    <emph.end type="italics"/>
                  & in ea
                    <lb/>
                  detur etiam punctum
                    <emph type="italics"/>
                  S
                    <emph.end type="italics"/>
                  ad quod vis centripeta perpetuo dirigitur,
                    <lb/>
                  inveniri poteſt lex vis centripetæ, qua corpus quodvis
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  a curſu
                    <lb/>
                  rectilineo perpetuò retractum in figuræ illius perimetro detinebitur
                    <lb/>
                  eamque revolvendo deſcribet. </s>
                  <s>Nimirum computandum eſt vel ſo­
                    <lb/>
                  lidum (
                    <emph type="italics"/>
                  SPqXQTq/QR
                    <emph.end type="italics"/>
                  ) vel ſolidum
                    <emph type="italics"/>
                  SYqXPV
                    <emph.end type="italics"/>
                  huic vi reciproce pro­
                    <lb/>
                  portionale. </s>
                  <s>Ejus rei dabimus exempla in Problematis ſequentibus. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                  PROPOSITIO VII. PROBLEMA II.
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                    <emph type="italics"/>
                  Gyretur corpus in circumferentia Circuli, requiritur Lex vis centri­
                    <lb/>
                  petæ tendentis ad punctum quodcunQ.E.D.tum.
                    <emph.end type="italics"/>
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>Eſto Circuli circumferentia
                    <lb/>
                    <figure id="id.039.01.070.1.jpg" xlink:href="039/01/070/1.jpg" number="16"/>
                    <lb/>
                    <emph type="italics"/>
                  VQPA,
                    <emph.end type="italics"/>
                  punctum datum ad
                    <lb/>
                  quod vis ceu ad
                    <expan abbr="centrũ">centrum</expan>
                    <expan abbr="ſuũ">ſuum</expan>
                  ten­
                    <lb/>
                  dit
                    <emph type="italics"/>
                  S,
                    <emph.end type="italics"/>
                  corpus in circumferentia
                    <lb/>
                  latum
                    <emph type="italics"/>
                  P,
                    <emph.end type="italics"/>
                  locus proximus in quem
                    <lb/>
                  movebitur
                    <emph type="italics"/>
                  Q,
                    <emph.end type="italics"/>
                  & circuli tangens
                    <lb/>
                  ad locum priorem
                    <emph type="italics"/>
                  PRZ.
                    <emph.end type="italics"/>
                  Per
                    <lb/>
                  punctum
                    <emph type="italics"/>
                  S
                    <emph.end type="italics"/>
                  ducatur chorda
                    <emph type="italics"/>
                  PV,
                    <emph.end type="italics"/>
                    <lb/>
                  & acta circuli diametro
                    <emph type="italics"/>
                  VA
                    <emph.end type="italics"/>
                  jun­
                    <lb/>
                  gatur
                    <emph type="italics"/>
                  AP,
                    <emph.end type="italics"/>
                  & ad
                    <emph type="italics"/>
                  SP
                    <emph.end type="italics"/>
                  demittatur
                    <lb/>
                  perpendiculum
                    <emph type="italics"/>
                  QT,
                    <emph.end type="italics"/>
                  quod productum occurrat tangenti
                    <emph type="italics"/>
                  PR
                    <emph.end type="italics"/>
                  in
                    <emph type="italics"/>
                  Z,
                    <emph.end type="italics"/>
                  </s>
                </p>
              </subchap2>
            </subchap1>
          </chap>
        </body>
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