Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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        <body>
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              <subchap2>
                <p type="main">
                  <s>
                    <pb xlink:href="039/01/107.jpg" pagenum="79"/>
                  &
                    <emph type="italics"/>
                  LD.
                    <emph.end type="italics"/>
                  Seca autem pro lubitu vel inter puncta
                    <emph type="italics"/>
                  K
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  H,
                    <emph.end type="italics"/>
                    <lb/>
                    <arrow.to.target n="note55"/>
                    <emph type="italics"/>
                  I
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  L,
                    <emph.end type="italics"/>
                  vel extra eadem: dein age
                    <emph type="italics"/>
                  RS
                    <emph.end type="italics"/>
                  ſecantem tangentes in
                    <emph type="italics"/>
                  A
                    <emph.end type="italics"/>
                    <lb/>
                  &
                    <emph type="italics"/>
                  P,
                    <emph.end type="italics"/>
                  & erunt
                    <emph type="italics"/>
                  A
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  puncta contactuum. </s>
                  <s>Nam ſi
                    <emph type="italics"/>
                  A
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                    <lb/>
                  ſupponantur eſſe puncta contactuum alicubi in tangentibus ſi­
                    <lb/>
                  ta; & per punctorum
                    <emph type="italics"/>
                  H, I, K, L
                    <emph.end type="italics"/>
                  quodvis
                    <emph type="italics"/>
                  I,
                    <emph.end type="italics"/>
                  in tangente al­
                    <lb/>
                  terutra
                    <emph type="italics"/>
                  HI
                    <emph.end type="italics"/>
                  ſitum, agatur recta
                    <emph type="italics"/>
                  IY
                    <emph.end type="italics"/>
                  tangenti alteri
                    <emph type="italics"/>
                  KL
                    <emph.end type="italics"/>
                  paral­
                    <lb/>
                  lela, quæ occurrat curvæ in
                    <emph type="italics"/>
                  X
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  Y,
                    <emph.end type="italics"/>
                  & in ea ſumatur
                    <emph type="italics"/>
                  IZ
                    <emph.end type="italics"/>
                  me­
                    <lb/>
                  dia proportionalis inter
                    <emph type="italics"/>
                  IX
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  IY:
                    <emph.end type="italics"/>
                  erit, ex Conicis, rectangulum
                    <lb/>
                    <emph type="italics"/>
                  XIY
                    <emph.end type="italics"/>
                  ſeu
                    <emph type="italics"/>
                  IZ quad.
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  LP quad.
                    <emph.end type="italics"/>
                  ut rectangulum
                    <emph type="italics"/>
                  CID
                    <emph.end type="italics"/>
                  ad rectan­
                    <lb/>
                  gulum
                    <emph type="italics"/>
                  CLD,
                    <emph.end type="italics"/>
                  id eſt (per conſtructionem) ut
                    <emph type="italics"/>
                  SI quad.
                    <emph.end type="italics"/>
                  ad
                    <lb/>
                    <emph type="italics"/>
                  SL quad:
                    <emph.end type="italics"/>
                  atque adeo
                    <emph type="italics"/>
                  IZ
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  LP
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  SI
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  SL.
                    <emph.end type="italics"/>
                  Jacent ergo punc­
                    <lb/>
                  ta
                    <emph type="italics"/>
                  S, P, Z
                    <emph.end type="italics"/>
                  in una recta. </s>
                  <s>Porro tangentibus concurrentibus in
                    <emph type="italics"/>
                  G,
                    <emph.end type="italics"/>
                  e­
                    <lb/>
                  rit (ex Conicis) rectangulum
                    <emph type="italics"/>
                  XIY
                    <emph.end type="italics"/>
                  ſeu
                    <emph type="italics"/>
                  IZ quad.
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  IA quad.
                    <emph.end type="italics"/>
                  ut
                    <lb/>
                    <emph type="italics"/>
                  GP quad
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  GA quad:
                    <emph.end type="italics"/>
                  adeoque
                    <emph type="italics"/>
                  IZ
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  IA
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  GP
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  GA.
                    <emph.end type="italics"/>
                  Jacent
                    <lb/>
                  ergo puncta
                    <emph type="italics"/>
                  P, Z
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  A
                    <emph.end type="italics"/>
                  in una recta, adeoque puncta
                    <emph type="italics"/>
                  S, P
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  A
                    <emph.end type="italics"/>
                    <lb/>
                  ſunt in una recta. </s>
                  <s>Et eodem argumento probabitur quod puncta
                    <lb/>
                    <emph type="italics"/>
                  R, P
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  A
                    <emph.end type="italics"/>
                  ſunt in una recta. </s>
                  <s>Jacent igitur puncta contactuum
                    <emph type="italics"/>
                  A
                    <emph.end type="italics"/>
                    <lb/>
                  &
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  in recta
                    <emph type="italics"/>
                  RS.
                    <emph.end type="italics"/>
                  Hiſce autem inventis, Trajectoria deſeribetur
                    <lb/>
                  ut in caſu primo Problematis ſuperioris.
                    <emph type="italics"/>
                  q.E.F.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note55"/>
                  LIBER
                    <lb/>
                  PRIMUS.</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                  LEMMA XXII.
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                    <emph type="italics"/>
                  Figuras in alias ejuſdem generis figur as mutare.
                    <emph.end type="italics"/>
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>Tranſmutanda ſit figura quævis
                    <emph type="italics"/>
                  HGI.
                    <emph.end type="italics"/>
                  Ducantur pro lubitu
                    <lb/>
                  rectæ duæ parallelæ
                    <emph type="italics"/>
                  AO, BL
                    <emph.end type="italics"/>
                  tertiam quamvis poſitione datam
                    <lb/>
                    <emph type="italics"/>
                  AB
                    <emph.end type="italics"/>
                  ſecantes in
                    <emph type="italics"/>
                  A
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  B,
                    <emph.end type="italics"/>
                    <lb/>
                    <figure id="id.039.01.107.1.jpg" xlink:href="039/01/107/1.jpg" number="54"/>
                    <lb/>
                  & a figuræ puncto quo­
                    <lb/>
                  vis
                    <emph type="italics"/>
                  G,
                    <emph.end type="italics"/>
                  ad rectam
                    <emph type="italics"/>
                  AB
                    <emph.end type="italics"/>
                    <lb/>
                  ducatur quævis
                    <emph type="italics"/>
                  GD,
                    <emph.end type="italics"/>
                    <lb/>
                  ipſi
                    <emph type="italics"/>
                  OA
                    <emph.end type="italics"/>
                  parallela. </s>
                  <s>De­
                    <lb/>
                  inde a puncto aliquo
                    <emph type="italics"/>
                  O,
                    <emph.end type="italics"/>
                    <lb/>
                  in linea
                    <emph type="italics"/>
                  OA
                    <emph.end type="italics"/>
                  dato, ad
                    <lb/>
                  punctum
                    <emph type="italics"/>
                  D
                    <emph.end type="italics"/>
                  ducatur
                    <lb/>
                  recta
                    <emph type="italics"/>
                  OD,
                    <emph.end type="italics"/>
                  ipſi
                    <emph type="italics"/>
                  BL
                    <emph.end type="italics"/>
                  oc­
                    <lb/>
                  currens in
                    <emph type="italics"/>
                  d,
                    <emph.end type="italics"/>
                  & a puncto
                    <lb/>
                  occurſus erigatur recta
                    <lb/>
                    <emph type="italics"/>
                  dg
                    <emph.end type="italics"/>
                  datum quemvis angulum cum recta
                    <emph type="italics"/>
                  BL
                    <emph.end type="italics"/>
                  continens, atque eam
                    <lb/>
                  habens rationem ad
                    <emph type="italics"/>
                  Od
                    <emph.end type="italics"/>
                  quam habet
                    <emph type="italics"/>
                  DG
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  OD
                    <emph.end type="italics"/>
                  ; & erit
                    <emph type="italics"/>
                  g
                    <emph.end type="italics"/>
                  punc­
                    <lb/>
                  tum in figura nova
                    <emph type="italics"/>
                  hgi
                    <emph.end type="italics"/>
                  puncto
                    <emph type="italics"/>
                  G
                    <emph.end type="italics"/>
                  reſpondens. </s>
                  <s>Eadem ratione
                    <lb/>
                  puncta ſingula figuræ primæ dabunt puncta totidem figura novæ. </s>
                </p>
              </subchap2>
            </subchap1>
          </chap>
        </body>
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