Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                <p type="main">
                  <s>
                    <pb xlink:href="039/01/115.jpg" pagenum="87"/>
                  gentes alias quaſvis duas
                    <emph type="italics"/>
                  GCD, FDE
                    <emph.end type="italics"/>
                  in
                    <emph type="italics"/>
                  L
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  K.
                    <emph.end type="italics"/>
                  Per harum
                    <lb/>
                    <arrow.to.target n="note63"/>
                  tangentium non parallelarum
                    <emph type="italics"/>
                  CL, FK
                    <emph.end type="italics"/>
                  cum parallelis
                    <emph type="italics"/>
                  CF, KL
                    <emph.end type="italics"/>
                    <lb/>
                  concurſus
                    <emph type="italics"/>
                  C
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  K, F
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  L
                    <emph.end type="italics"/>
                  age
                    <emph type="italics"/>
                  CK, FL
                    <emph.end type="italics"/>
                  concurrentes in
                    <emph type="italics"/>
                  R,
                    <emph.end type="italics"/>
                  & rec­
                    <lb/>
                  ta
                    <emph type="italics"/>
                  OR
                    <emph.end type="italics"/>
                  ducta & producta ſecabit tangentes parallelas
                    <emph type="italics"/>
                  CF, KL
                    <emph.end type="italics"/>
                  in
                    <lb/>
                  punctis contactuum. </s>
                  <s>Patet hoc per Corol. </s>
                  <s>2. Lem. </s>
                  <s>XXIV. </s>
                  <s>Ea­
                    <lb/>
                  dem methodo invenire licet alia contactuum puncta, & tum de­
                    <lb/>
                  mum per Probl. </s>
                  <s>XIV. &c. </s>
                  <s>Trajectoriam deſcribere.
                    <emph type="italics"/>
                  q.E.F.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note63"/>
                  LIBER
                    <lb/>
                  PRIMUS.</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>Problemata, ubi dantur Trajectoriarum vel centra vel Aſymp­
                    <lb/>
                  toti, includuntnr in præcedentibus. </s>
                  <s>Nam datis punctis & tangen­
                    <lb/>
                  tibus una cum centro, dantur alia totidem puncta aliæque tangen­
                    <lb/>
                  tes a centro ex altera ejus parte æqualiter diſtantes. </s>
                  <s>Aſymptotos
                    <lb/>
                  autem pro tangente habenda eſt, & ejus terminus infinite diſtans
                    <lb/>
                  (ſi ita loqui fas ſit) pro puncto contactus. </s>
                  <s>Concipe tangentis cu­
                    <lb/>
                  juſvis punctum contactus abire in infinitum, & tangens vertetur in
                    <lb/>
                  Aſymptoton, atque conſtructiones Problematis XIV & Caſus pri­
                    <lb/>
                  mi Problematis XV vertentur in conſtructiones Problematum ubi
                    <lb/>
                  Aſymptoti dantur. </s>
                </p>
                <p type="main">
                  <s>Poſtquam Trajectoria deſcripta eſt, invenire licet axes & umbi­
                    <lb/>
                  licos ejus hac methodo. </s>
                  <s>In conſtructione & figura Lemmatis XXI,
                    <lb/>
                  fac ut angulorum mobi­
                    <lb/>
                    <figure id="id.039.01.115.1.jpg" xlink:href="039/01/115/1.jpg" number="61"/>
                    <lb/>
                  lium
                    <emph type="italics"/>
                  PBN, PCN
                    <emph.end type="italics"/>
                  cru­
                    <lb/>
                  ra
                    <emph type="italics"/>
                  BP, CP,
                    <emph.end type="italics"/>
                  quorum
                    <lb/>
                  concurſu Trajectoria de­
                    <lb/>
                  ſcribebatur, ſint ſibi invi­
                    <lb/>
                  cem parallela, eumque
                    <lb/>
                  ſervantia ſitum revolvan­
                    <lb/>
                  tur circa polos ſuos
                    <emph type="italics"/>
                  B, C
                    <emph.end type="italics"/>
                    <lb/>
                  in figura illa. </s>
                  <s>Interea ve­
                    <lb/>
                  ro deſcribant altera an­
                    <lb/>
                  gulorum illorum crura
                    <lb/>
                    <emph type="italics"/>
                  CN, BN,
                    <emph.end type="italics"/>
                  concurſu
                    <lb/>
                  ſuo
                    <emph type="italics"/>
                  K
                    <emph.end type="italics"/>
                  vel
                    <emph type="italics"/>
                  k,
                    <emph.end type="italics"/>
                  Circulum
                    <lb/>
                    <emph type="italics"/>
                  IBKGC.
                    <emph.end type="italics"/>
                  Sit Circuli
                    <lb/>
                  hujus centrum
                    <emph type="italics"/>
                  O.
                    <emph.end type="italics"/>
                  Ab
                    <lb/>
                  hoc centro ad Regulam
                    <lb/>
                    <emph type="italics"/>
                  MN,
                    <emph.end type="italics"/>
                  ad quam altera illa crura
                    <emph type="italics"/>
                  CN, BN
                    <emph.end type="italics"/>
                  interea concurrebant </s>
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