Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                <pb xlink:href="039/01/103.jpg" pagenum="75"/>
                <p type="main">
                  <s>
                    <emph type="center"/>
                    <emph type="italics"/>
                  Idem aliter.
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                    <emph.end type="center"/>
                    <lb/>
                    <arrow.to.target n="note51"/>
                  </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note51"/>
                  LIBER
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                  PRIMUS.</s>
                </p>
                <p type="main">
                  <s>E punctis datis junge tria quævis
                    <emph type="italics"/>
                  A, B, C
                    <emph.end type="italics"/>
                  ; &, circum duo eorum
                    <lb/>
                    <emph type="italics"/>
                  B, C
                    <emph.end type="italics"/>
                  ceu polos, rotando angulos magnitudine datos
                    <emph type="italics"/>
                  ABC,
                    <lb/>
                  ACB,
                    <emph.end type="italics"/>
                  applicentur cru­
                    <lb/>
                    <figure id="id.039.01.103.1.jpg" xlink:href="039/01/103/1.jpg" number="49"/>
                    <lb/>
                  ra
                    <emph type="italics"/>
                  BA, CA
                    <emph.end type="italics"/>
                  primo ad
                    <lb/>
                  punctum
                    <emph type="italics"/>
                  D,
                    <emph.end type="italics"/>
                  deinde
                    <lb/>
                  ad punctum
                    <emph type="italics"/>
                  P,
                    <emph.end type="italics"/>
                  & no­
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                  tentur puncta
                    <emph type="italics"/>
                  M, N
                    <emph.end type="italics"/>
                  in
                    <lb/>
                  quibus altera crura
                    <lb/>
                    <emph type="italics"/>
                  BL, CL
                    <emph.end type="italics"/>
                  caſu utroque
                    <lb/>
                  ſe decuſſant. </s>
                  <s>Agatur
                    <lb/>
                  recta infinita
                    <emph type="italics"/>
                  MN,
                    <emph.end type="italics"/>
                  &
                    <lb/>
                  rotentur anguli illi mo­
                    <lb/>
                  biles circum polos ſuos
                    <lb/>
                    <emph type="italics"/>
                  B, C,
                    <emph.end type="italics"/>
                  ea lege ut cru­
                    <lb/>
                  rum
                    <emph type="italics"/>
                  BL, CL
                    <emph.end type="italics"/>
                  vel
                    <lb/>
                    <emph type="italics"/>
                  BM, CM
                    <emph.end type="italics"/>
                  interſectio
                    <lb/>
                  quæ jam ſit
                    <emph type="italics"/>
                  m
                    <emph.end type="italics"/>
                  incidat
                    <lb/>
                  ſemper in rectam illam
                    <lb/>
                  infinitam
                    <emph type="italics"/>
                  MN
                    <emph.end type="italics"/>
                  & cru­
                    <lb/>
                  rum
                    <emph type="italics"/>
                  BA, CA,
                    <emph.end type="italics"/>
                  vel
                    <emph type="italics"/>
                  BD, CD
                    <emph.end type="italics"/>
                  interſectio, quæ jam ſit
                    <emph type="italics"/>
                  d,
                    <emph.end type="italics"/>
                  Trajecto­
                    <lb/>
                  riam quæſitam
                    <emph type="italics"/>
                  PAD dB
                    <emph.end type="italics"/>
                  delineabit. </s>
                  <s>Nam punctum
                    <emph type="italics"/>
                  d,
                    <emph.end type="italics"/>
                  per Lem. </s>
                  <s>
                    <lb/>
                  XXI, continget ſectionem Conicam per puncta
                    <emph type="italics"/>
                  B, C
                    <emph.end type="italics"/>
                  tranſeuntem; &
                    <lb/>
                  ubi punctum
                    <emph type="italics"/>
                  m
                    <emph.end type="italics"/>
                  accedit ad puncta
                    <emph type="italics"/>
                  L, M, N,
                    <emph.end type="italics"/>
                  punctum
                    <emph type="italics"/>
                  d
                    <emph.end type="italics"/>
                  (per con­
                    <lb/>
                  ſtructionem) accedet ad puncta
                    <emph type="italics"/>
                  A, D, P.
                    <emph.end type="italics"/>
                  Deſcribetur itaque ſec­
                    <lb/>
                  tio Conica tranſiens per puncta quinque
                    <emph type="italics"/>
                  A, B, C, P, D. q.E.F.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  1. Hinc recta expedite duci poteſt quæ Trajectoriam quæ­
                    <lb/>
                  ſitam, in puncto quovis dato
                    <emph type="italics"/>
                  B,
                    <emph.end type="italics"/>
                  continget. </s>
                  <s>Accedat punctum
                    <emph type="italics"/>
                  d
                    <emph.end type="italics"/>
                  ad
                    <lb/>
                  punctum
                    <emph type="italics"/>
                  B,
                    <emph.end type="italics"/>
                  & recta
                    <emph type="italics"/>
                  Bd
                    <emph.end type="italics"/>
                  evadet tangens quæſita. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  2. Unde etiam Trajectoriarum Centra, Diametri & Latera
                    <lb/>
                  recta inveniri poſſunt, ut in Corollario ſecundo Lemmatis XIX. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                    <emph type="italics"/>
                  Scholium.
                    <emph.end type="italics"/>
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>Conſtructio prior evadet paulo ſimplicior jungendo
                    <emph type="italics"/>
                  BP,
                    <emph.end type="italics"/>
                  & in ea,
                    <lb/>
                  ſi opus eſt, producta capiendo
                    <emph type="italics"/>
                  Bp
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  BP
                    <emph.end type="italics"/>
                  ut eſt
                    <emph type="italics"/>
                  PR
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  PT
                    <emph.end type="italics"/>
                  ; &
                    <lb/>
                  per
                    <emph type="italics"/>
                  p
                    <emph.end type="italics"/>
                  agendo rectam infinitam
                    <emph type="italics"/>
                  p
                    <emph.end type="italics"/>
                  d ipſi
                    <emph type="italics"/>
                  SPT
                    <emph.end type="italics"/>
                  parallelam, inque ea
                    <lb/>
                  capiendo ſemper
                    <emph type="italics"/>
                  p
                    <emph.end type="italics"/>
                  d æqualem
                    <emph type="italics"/>
                  Pr
                    <emph.end type="italics"/>
                  ; & agendo rectas
                    <emph type="italics"/>
                  Bd, Cr
                    <emph.end type="italics"/>
                  con­
                    <lb/>
                  currentes in
                    <emph type="italics"/>
                  d.
                    <emph.end type="italics"/>
                  Nam cum ſint
                    <emph type="italics"/>
                  Pr
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  Pt, PR
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  PT, pB
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  PB,
                    <lb/>
                  p
                    <emph.end type="italics"/>
                  d ad
                    <emph type="italics"/>
                  Pt
                    <emph.end type="italics"/>
                  in eadem ratione; erunt
                    <emph type="italics"/>
                  p
                    <emph.end type="italics"/>
                  d &
                    <emph type="italics"/>
                  Pr
                    <emph.end type="italics"/>
                  ſemper æqua-</s>
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