Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                <p type="main">
                  <s>
                    <pb xlink:href="039/01/088.jpg" pagenum="60"/>
                    <arrow.to.target n="note36"/>
                  methodo ſive dentur duo puncta
                    <emph type="italics"/>
                  P, p,
                    <emph.end type="italics"/>
                  ſive duæ tangentes
                    <emph type="italics"/>
                  TR,
                    <lb/>
                  tr,
                    <emph.end type="italics"/>
                  ſive punctum
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  & tangens
                    <lb/>
                    <figure id="id.039.01.088.1.jpg" xlink:href="039/01/088/1.jpg" number="29"/>
                    <lb/>
                    <emph type="italics"/>
                  TR,
                    <emph.end type="italics"/>
                  deſcribendi ſunt circuli duo. </s>
                  <s>
                    <lb/>
                  Sit
                    <emph type="italics"/>
                  H
                    <emph.end type="italics"/>
                  eorum interſectio com­
                    <lb/>
                  munis, & umbilicis
                    <emph type="italics"/>
                  S, H,
                    <emph.end type="italics"/>
                  axe illo
                    <lb/>
                  dato deſcribatur Trajectoria. </s>
                  <s>
                    <lb/>
                  Dico factum. </s>
                  <s>Nam Trajecto­
                    <lb/>
                  ctoria deſcripta (eo quod
                    <emph type="italics"/>
                  PH
                    <lb/>
                  +SP
                    <emph.end type="italics"/>
                  in Ellipſi, &
                    <emph type="italics"/>
                  PH-SP
                    <emph.end type="italics"/>
                    <lb/>
                  in Hyperbola æquatur axi)
                    <lb/>
                  tranſibit per punctum
                    <emph type="italics"/>
                  P,
                    <emph.end type="italics"/>
                  &
                    <lb/>
                  (per Lemma ſuperius) tanget
                    <lb/>
                  rectam
                    <emph type="italics"/>
                  TR.
                    <emph.end type="italics"/>
                  Et eodem argu­
                    <lb/>
                  mento vel tranſibit eadem per
                    <lb/>
                  puncta duo
                    <emph type="italics"/>
                  P, p,
                    <emph.end type="italics"/>
                  vel tanget re­
                    <lb/>
                  ctas duas
                    <emph type="italics"/>
                  TR, tr. </s>
                  <s>q.E.F.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note36"/>
                  DE MOTU
                    <lb/>
                  CORPORUM</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                  PROPOSITIO XIX. PROBLEMA XI.
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                    <emph type="italics"/>
                  Circa datum umbilicum Trajectoriam Parabolicam deſcribere, quæ
                    <lb/>
                  tranſibit per puncta data, & rectas poſitione datas continget.
                    <emph.end type="italics"/>
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>Sit
                    <emph type="italics"/>
                  S
                    <emph.end type="italics"/>
                  umbilicus,
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  punctum &
                    <emph type="italics"/>
                  TR
                    <emph.end type="italics"/>
                  tangens Trajectoriæ deſcri­
                    <lb/>
                  bendæ. </s>
                  <s>Centro
                    <emph type="italics"/>
                  P,
                    <emph.end type="italics"/>
                  intervallo
                    <emph type="italics"/>
                  PS
                    <emph.end type="italics"/>
                  deſcribe cir­
                    <lb/>
                    <figure id="id.039.01.088.2.jpg" xlink:href="039/01/088/2.jpg" number="30"/>
                    <lb/>
                  culum
                    <emph type="italics"/>
                  FG.
                    <emph.end type="italics"/>
                  Ab umbilico ad tangentem demit­
                    <lb/>
                  te perpendicularem
                    <emph type="italics"/>
                  ST,
                    <emph.end type="italics"/>
                  & produc eam ad
                    <emph type="italics"/>
                  V,
                    <emph.end type="italics"/>
                    <lb/>
                  ut ſit
                    <emph type="italics"/>
                  TV
                    <emph.end type="italics"/>
                  æqualis
                    <emph type="italics"/>
                  ST.
                    <emph.end type="italics"/>
                  Eodem modo deſcri­
                    <lb/>
                  bendus eſt alter circulus
                    <emph type="italics"/>
                  fg,
                    <emph.end type="italics"/>
                  ſi datur alterum
                    <lb/>
                  punctum
                    <emph type="italics"/>
                  p
                    <emph.end type="italics"/>
                  ; vel inveniendum alterum punctum
                    <lb/>
                    <emph type="italics"/>
                  v,
                    <emph.end type="italics"/>
                  ſi datur altera tangens
                    <emph type="italics"/>
                  tr
                    <emph.end type="italics"/>
                  ; dein ducenda re­
                    <lb/>
                  cta
                    <emph type="italics"/>
                  IF
                    <emph.end type="italics"/>
                  quæ tangat duos circulos
                    <emph type="italics"/>
                  FG, fg
                    <emph.end type="italics"/>
                  ſi
                    <lb/>
                  dantur duo puncta
                    <emph type="italics"/>
                  P, p,
                    <emph.end type="italics"/>
                  vel tranſeat per duo
                    <lb/>
                  puncta
                    <emph type="italics"/>
                  V, v,
                    <emph.end type="italics"/>
                  ſi dantur duæ tangentes
                    <emph type="italics"/>
                  TR, tr,
                    <emph.end type="italics"/>
                  vel
                    <lb/>
                  tangat circulum
                    <emph type="italics"/>
                  FG
                    <emph.end type="italics"/>
                  & tranſeat per punctum
                    <emph type="italics"/>
                  V,
                    <emph.end type="italics"/>
                    <lb/>
                  ſi datur punctum
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  & tangens
                    <emph type="italics"/>
                  TR.
                    <emph.end type="italics"/>
                  Ad
                    <emph type="italics"/>
                  FI
                    <emph.end type="italics"/>
                  demitte perpendicula­
                    <lb/>
                  rem
                    <emph type="italics"/>
                  SI,
                    <emph.end type="italics"/>
                  eamque biſeca in
                    <emph type="italics"/>
                  K
                    <emph.end type="italics"/>
                  ; & axe
                    <emph type="italics"/>
                  SK,
                    <emph.end type="italics"/>
                  vertice principali
                    <emph type="italics"/>
                  K
                    <emph.end type="italics"/>
                  de­
                    <lb/>
                  ſcribatur Parabola. </s>
                  <s>Dico factum. </s>
                  <s>Nam Parabola, ob æquales
                    <lb/>
                    <emph type="italics"/>
                  SK
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  IK, SP
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  FP,
                    <emph.end type="italics"/>
                  tranſibit per punctum
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  ; & (per Lem­
                    <lb/>
                  matis XIV. Corol. </s>
                  <s>3.) ob æquales
                    <emph type="italics"/>
                  ST
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  TV
                    <emph.end type="italics"/>
                  & angulum rectum
                    <lb/>
                    <emph type="italics"/>
                  STR,
                    <emph.end type="italics"/>
                  tanget rectam
                    <emph type="italics"/>
                  TR. q.E.F.
                    <emph.end type="italics"/>
                  </s>
                </p>
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