Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                  <s>
                    <pb xlink:href="039/01/085.jpg" pagenum="57"/>
                  De loco
                    <emph type="italics"/>
                  P,
                    <emph.end type="italics"/>
                  ſecundum lineam
                    <emph type="italics"/>
                  PR,
                    <emph.end type="italics"/>
                  exeat corpus
                    <emph type="italics"/>
                  P,
                    <emph.end type="italics"/>
                  cum data velo­
                    <lb/>
                    <arrow.to.target n="note33"/>
                  citate, & mox inde, cogente vi centripeta, deflectat illud in CoNI­
                    <lb/>
                  ſectionem
                    <emph type="italics"/>
                    <expan abbr="Pq.">Pque</expan>
                    <emph.end type="italics"/>
                  Hanc igitur recta
                    <emph type="italics"/>
                  PR
                    <emph.end type="italics"/>
                  tanget in
                    <emph type="italics"/>
                  P.
                    <emph.end type="italics"/>
                  Tangat itidem
                    <lb/>
                  recta aliqua
                    <emph type="italics"/>
                  pr
                    <emph.end type="italics"/>
                  Orbitam
                    <emph type="italics"/>
                  pq
                    <emph.end type="italics"/>
                  in
                    <emph type="italics"/>
                  p,
                    <emph.end type="italics"/>
                  & ſi ab
                    <emph type="italics"/>
                  S
                    <emph.end type="italics"/>
                  ad eas tangentes demitti
                    <lb/>
                  intelligantur perpendicula, erit (per Corol. </s>
                  <s>1. Prop. </s>
                  <s>XVI.) latus re­
                    <lb/>
                  ctum principale Coniſectionis ad latus rectum principale Orbitæ, in
                    <lb/>
                  ratione compoſita ex duplicata ratione perpendiculorum & dupli­
                    <lb/>
                  cata ratione velocitatum, atque adeo datur. </s>
                  <s>Sit iſtud
                    <emph type="italics"/>
                  L.
                    <emph.end type="italics"/>
                  Da­
                    <lb/>
                  tur præterea Coniſe­
                    <lb/>
                    <figure id="id.039.01.085.1.jpg" xlink:href="039/01/085/1.jpg" number="26"/>
                    <lb/>
                  ctionis umbilicus
                    <emph type="italics"/>
                  S.
                    <emph.end type="italics"/>
                    <lb/>
                  Anguli
                    <emph type="italics"/>
                  RPS
                    <emph.end type="italics"/>
                  com­
                    <lb/>
                  plementum ad du­
                    <lb/>
                  os rectos fiat angu­
                    <lb/>
                  lus
                    <emph type="italics"/>
                  RPH,
                    <emph.end type="italics"/>
                  & dabi­
                    <lb/>
                  tur poſitione linea
                    <lb/>
                    <emph type="italics"/>
                  PH,
                    <emph.end type="italics"/>
                  in qua umbilicus
                    <lb/>
                  alter
                    <emph type="italics"/>
                  H
                    <emph.end type="italics"/>
                  locatur. </s>
                  <s>De­
                    <lb/>
                  miſſo ad
                    <emph type="italics"/>
                  PH
                    <emph.end type="italics"/>
                  perpen­
                    <lb/>
                  diculo
                    <emph type="italics"/>
                  SK,
                    <emph.end type="italics"/>
                  erigi intelligatur ſemiaxis conjugatus
                    <emph type="italics"/>
                  BC,
                    <emph.end type="italics"/>
                  & erit
                    <lb/>
                    <emph type="italics"/>
                  SPq.-2KPH+PHq.=SHq.=4CHq.=4BHq-4BCq.=
                    <lb/>
                  —SP+PH: quad. -LX—SP+PH=SPq.+2SPH+PHq.
                    <lb/>
                  -LX—SP+PH.
                    <emph.end type="italics"/>
                  Addantur utrobique 2
                    <emph type="italics"/>
                  KPH-SPq-PHq
                    <lb/>
                  +LX—SP+PH,
                    <emph.end type="italics"/>
                  & fiet
                    <emph type="italics"/>
                  LX—SP+PH=2SPH+2KPH,
                    <emph.end type="italics"/>
                    <lb/>
                  ſeu
                    <emph type="italics"/>
                  SP+PH,
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  PH,
                    <emph.end type="italics"/>
                  ut 2
                    <emph type="italics"/>
                  SP+2KP
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  L.
                    <emph.end type="italics"/>
                  Unde datur
                    <emph type="italics"/>
                  PH
                    <emph.end type="italics"/>
                    <lb/>
                  tam longitudine quam poſitione. </s>
                  <s>Nimirum ſi ea fit corporis &c. </s>
                  <s>in
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                    <lb/>
                  velocitas, ut latus rectum
                    <emph type="italics"/>
                  L
                    <emph.end type="italics"/>
                  minus fuerit quam 2
                    <emph type="italics"/>
                  SP+2KP,
                    <emph.end type="italics"/>
                    <lb/>
                  jacebit
                    <emph type="italics"/>
                  PH
                    <emph.end type="italics"/>
                  ad eandem partem tangentis
                    <emph type="italics"/>
                  PR
                    <emph.end type="italics"/>
                  cum linea
                    <emph type="italics"/>
                  PS,
                    <emph.end type="italics"/>
                    <lb/>
                  adeoque figura erit Ellipſis, & ex datis umbilicis
                    <emph type="italics"/>
                  S, H,
                    <emph.end type="italics"/>
                  & axe
                    <lb/>
                  principali
                    <emph type="italics"/>
                  SP+PH,
                    <emph.end type="italics"/>
                  dabitur: Sin tanta ſit corporis velocitas ut
                    <lb/>
                  latus rectum
                    <emph type="italics"/>
                  L
                    <emph.end type="italics"/>
                  æquale fuerit 2
                    <emph type="italics"/>
                  SP+2KP,
                    <emph.end type="italics"/>
                  longitudo
                    <emph type="italics"/>
                  PH
                    <emph.end type="italics"/>
                  infi­
                    <lb/>
                  nita erit, & propterea figura erit Parabola axem habens
                    <emph type="italics"/>
                  SH
                    <emph.end type="italics"/>
                  paral­
                    <lb/>
                  lelum lineæ
                    <emph type="italics"/>
                  PK,
                    <emph.end type="italics"/>
                  & inde dabitur. </s>
                  <s>Quod ſi corpus majori adhuc
                    <lb/>
                  cum velocitate de loco ſuo
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  exeat, capienda erit longitudo
                    <emph type="italics"/>
                  PH
                    <emph.end type="italics"/>
                    <lb/>
                  ad alteram partem tangentis, adeoque tangente inter umbilicos per­
                    <lb/>
                  gente, figura erit Hyperbola axem habens principalem æqualem dif­
                    <lb/>
                  ferentiæ linearum
                    <emph type="italics"/>
                  SP
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  PH,
                    <emph.end type="italics"/>
                  & inde dabitur.
                    <emph type="italics"/>
                  Q.E.I.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note33"/>
                  LIBER
                    <lb/>
                  PRIMUS.</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  1. Hinc in omni Coniſectione ex dato vertice principali
                    <emph type="italics"/>
                  D,
                    <emph.end type="italics"/>
                    <lb/>
                  latere recto
                    <emph type="italics"/>
                  L,
                    <emph.end type="italics"/>
                  & umbilico
                    <emph type="italics"/>
                  S,
                    <emph.end type="italics"/>
                  datur umbilicus alter
                    <emph type="italics"/>
                  H
                    <emph.end type="italics"/>
                  capiendo
                    <emph type="italics"/>
                  DH,
                    <emph.end type="italics"/>
                    <lb/>
                  ad
                    <emph type="italics"/>
                  DS
                    <emph.end type="italics"/>
                  ut eſt latus rectum ad differentiam inter latus rectum &
                    <lb/>
                  4
                    <emph type="italics"/>
                  DS.
                    <emph.end type="italics"/>
                  Nam proportio
                    <emph type="italics"/>
                  SP+PH
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  PH
                    <emph.end type="italics"/>
                  ut 2
                    <emph type="italics"/>
                  SP+2KP
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  L,
                    <emph.end type="italics"/>
                  </s>
                </p>
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        </body>
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