Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                  <s>
                    <pb xlink:href="039/01/110.jpg" pagenum="82"/>
                    <arrow.to.target n="note58"/>
                  hac figura tangentes illæ duæ evadent ſibi invicem parallelæ, & tan­
                    <lb/>
                  gens tertia fiet parallela rectæ per
                    <lb/>
                    <figure id="id.039.01.110.1.jpg" xlink:href="039/01/110/1.jpg" number="56"/>
                    <lb/>
                  puncta duo data tranſeunti. </s>
                  <s>Sunto
                    <lb/>
                    <emph type="italics"/>
                  hi, kl
                    <emph.end type="italics"/>
                  tangentes illæ duæ parallelæ,
                    <lb/>
                    <emph type="italics"/>
                  ik
                    <emph.end type="italics"/>
                  tangens tertia, &
                    <emph type="italics"/>
                  hl
                    <emph.end type="italics"/>
                  recta huic
                    <lb/>
                  parallela tranſiens per puncta illa
                    <lb/>
                    <emph type="italics"/>
                  a, b,
                    <emph.end type="italics"/>
                  per quæ Conica ſectio in hac
                    <lb/>
                  figura nova tranſire debet, & pa­
                    <lb/>
                  rallelogrammum
                    <emph type="italics"/>
                  hikl
                    <emph.end type="italics"/>
                  complens. </s>
                  <s>
                    <lb/>
                  Secentur rectæ
                    <emph type="italics"/>
                  hi, ik, kl
                    <emph.end type="italics"/>
                  in
                    <emph type="italics"/>
                  c, d, e,
                    <emph.end type="italics"/>
                    <lb/>
                  ita ut ſit
                    <emph type="italics"/>
                  hc
                    <emph.end type="italics"/>
                  ad latus quadratum
                    <lb/>
                  rectanguli
                    <emph type="italics"/>
                  ahb, ic
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  id,
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  ke
                    <emph.end type="italics"/>
                    <lb/>
                  ad
                    <emph type="italics"/>
                  kd
                    <emph.end type="italics"/>
                  ut eſt ſumma rectarum
                    <emph type="italics"/>
                  hi
                    <emph.end type="italics"/>
                    <lb/>
                  &
                    <emph type="italics"/>
                  kl
                    <emph.end type="italics"/>
                  ad ſummam trium linea­
                    <lb/>
                  rum quarum prima eſt recta
                    <emph type="italics"/>
                  ik,
                    <emph.end type="italics"/>
                  & alteræ duæ ſunt latera quadrata
                    <lb/>
                  rectangulorum
                    <emph type="italics"/>
                  ahb
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  alb
                    <emph.end type="italics"/>
                  & erunt
                    <emph type="italics"/>
                  c, d, e
                    <emph.end type="italics"/>
                  puncta contactuum. </s>
                  <s>Et­
                    <lb/>
                  enim, ex Conicis, ſunt
                    <emph type="italics"/>
                  hc
                    <emph.end type="italics"/>
                  quadratum ad rectangulum
                    <emph type="italics"/>
                  ahb,
                    <emph.end type="italics"/>
                  &
                    <lb/>
                    <emph type="italics"/>
                  ic
                    <emph.end type="italics"/>
                  quadratum ad
                    <emph type="italics"/>
                  id
                    <emph.end type="italics"/>
                  quadratum, &
                    <emph type="italics"/>
                  ke
                    <emph.end type="italics"/>
                  quadratum ad
                    <emph type="italics"/>
                  kd
                    <emph.end type="italics"/>
                  quadratum,
                    <lb/>
                  &
                    <emph type="italics"/>
                  el
                    <emph.end type="italics"/>
                  quadratum ad rectangulum
                    <emph type="italics"/>
                  alb
                    <emph.end type="italics"/>
                  in eadem ratione; & propter­
                    <lb/>
                  ea
                    <emph type="italics"/>
                  hc
                    <emph.end type="italics"/>
                  ad latus quadratum ipſius
                    <emph type="italics"/>
                  ahb, ic
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  id, ke
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  kd,
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  el
                    <emph.end type="italics"/>
                  ad
                    <lb/>
                  latus quadratum ipſius
                    <emph type="italics"/>
                  alb
                    <emph.end type="italics"/>
                  ſunt in ſubduplicata illa ratione, &
                    <lb/>
                  compoſite, in data ratione omnium antecedentium
                    <emph type="italics"/>
                  hi
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  kl
                    <emph.end type="italics"/>
                  ad
                    <lb/>
                  omnes conſequentes, quæ ſunt latus quadratum rectanguli
                    <emph type="italics"/>
                  ahb
                    <emph.end type="italics"/>
                  &
                    <lb/>
                  recta
                    <emph type="italics"/>
                  ik
                    <emph.end type="italics"/>
                  & latus quadratum rectanguli
                    <emph type="italics"/>
                  alb.
                    <emph.end type="italics"/>
                  Habentur igitur ex
                    <lb/>
                  data illa ratione puncta contactuum
                    <emph type="italics"/>
                  c, d, e,
                    <emph.end type="italics"/>
                  in figura nova. </s>
                  <s>Per
                    <lb/>
                  inverſas operationes Lemmatis noviſſimi transferantur hæc pun­
                    <lb/>
                  cta in figuram primam & ibi, per Probl. </s>
                  <s>XIV, deſcribetur
                    <lb/>
                  Trajectoria.
                    <emph type="italics"/>
                  q.E.F.
                    <emph.end type="italics"/>
                  Ceterum perinde ut puncta
                    <emph type="italics"/>
                  a, b
                    <emph.end type="italics"/>
                  ja­
                    <lb/>
                  cent vel inter puncta
                    <emph type="italics"/>
                  h, l,
                    <emph.end type="italics"/>
                  vel extra, debent puncta
                    <emph type="italics"/>
                  c, d, e
                    <emph.end type="italics"/>
                  vel
                    <lb/>
                  inter puncta
                    <emph type="italics"/>
                  h, i, k, l
                    <emph.end type="italics"/>
                  capi, vel extra. </s>
                  <s>Si punctorum
                    <emph type="italics"/>
                  a, b
                    <emph.end type="italics"/>
                  al­
                    <lb/>
                  terutrum cadit inter puncta
                    <emph type="italics"/>
                  h, l,
                    <emph.end type="italics"/>
                  & alterum extra, Problema im­
                    <lb/>
                  poſſibile eſt. </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note58"/>
                  DE MOTU
                    <lb/>
                  CORPORUM</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                  PROPOSITIO XXVI. PROBLEMA XVIII.
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                    <emph type="italics"/>
                  Trajectoriam deſcribere quæ tranſibit per punctum datum & rectas
                    <lb/>
                  quatuor poſitione datas continget.
                    <emph.end type="italics"/>
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>Ab interſectione communi duarum quarumlibet tangentium ad
                    <lb/>
                  interſectionem communem reliquarum duarum agatur recta infini-</s>
                </p>
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