Newton, Isaac, Philosophia naturalis principia mathematica, 1713

Table of figures

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          <chap>
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              <subchap2>
                <pb xlink:href="039/01/096.jpg" pagenum="68"/>
                <p type="main">
                  <s>Per puncta
                    <emph type="italics"/>
                  A, B, C, D
                    <emph.end type="italics"/>
                  & aliquod infinitorum punctorum
                    <emph type="italics"/>
                  P,
                    <emph.end type="italics"/>
                  pu­
                    <lb/>
                    <arrow.to.target n="note44"/>
                  ta
                    <emph type="italics"/>
                  p,
                    <emph.end type="italics"/>
                  concipe Conicam ſectionem deſcribi: dico punctum
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  hanc
                    <lb/>
                  ſemper tangere. </s>
                  <s>Si negas,
                    <lb/>
                    <figure id="id.039.01.096.1.jpg" xlink:href="039/01/096/1.jpg" number="41"/>
                    <lb/>
                  junge
                    <emph type="italics"/>
                  AP
                    <emph.end type="italics"/>
                  ſecantem hanc
                    <lb/>
                  Conicam ſectionem alibi
                    <lb/>
                  quam in
                    <emph type="italics"/>
                  P,
                    <emph.end type="italics"/>
                  ſi fieri poteſt,
                    <lb/>
                  puta in
                    <emph type="italics"/>
                  b.
                    <emph.end type="italics"/>
                  Ergo ſi ab his
                    <lb/>
                  punctis
                    <emph type="italics"/>
                  p
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  b
                    <emph.end type="italics"/>
                  ducantur in
                    <lb/>
                  datis angulis ad latera Tra­
                    <lb/>
                  pezii rectæ
                    <emph type="italics"/>
                  pq, pr, ps, pt
                    <emph.end type="italics"/>
                    <lb/>
                  &
                    <emph type="italics"/>
                  bk, br, bſ, bd
                    <emph.end type="italics"/>
                  ; erit
                    <lb/>
                  ut
                    <emph type="italics"/>
                  bkXb
                    <emph.end type="italics"/>
                  r ad
                    <emph type="italics"/>
                  bſXbd
                    <emph.end type="italics"/>
                  ita
                    <lb/>
                  (per Lem. </s>
                  <s>XVII)
                    <emph type="italics"/>
                  pqXpr
                    <emph.end type="italics"/>
                    <lb/>
                  ad
                    <emph type="italics"/>
                  psXpt,
                    <emph.end type="italics"/>
                  & ita (per
                    <lb/>
                  Hypoth.)
                    <emph type="italics"/>
                  PQXPR
                    <emph.end type="italics"/>
                  ad
                    <lb/>
                    <emph type="italics"/>
                  PSXPT.
                    <emph.end type="italics"/>
                  Eſt & prop­
                    <lb/>
                  ter ſimilitudinem Trapeziorum
                    <emph type="italics"/>
                  bkAſ, PQAS,
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  bk
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  bſ
                    <emph.end type="italics"/>
                  ita
                    <lb/>
                    <emph type="italics"/>
                  PQ
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  PS.
                    <emph.end type="italics"/>
                  Quare, applicando terminos prioris proportionis ad
                    <lb/>
                  terminos correſpondentes hujus, erit
                    <emph type="italics"/>
                  b
                    <emph.end type="italics"/>
                  r ad
                    <emph type="italics"/>
                  bd
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  PR
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  PT.
                    <emph.end type="italics"/>
                  Er­
                    <lb/>
                  go Trapezia æquiangula
                    <emph type="italics"/>
                  Dr bd, DRPT
                    <emph.end type="italics"/>
                  ſimilia ſunt, & eorum
                    <lb/>
                  diagonales
                    <emph type="italics"/>
                  Db, DP
                    <emph.end type="italics"/>
                  propterea coincidunt. </s>
                  <s>Incidit itaque
                    <emph type="italics"/>
                  b
                    <emph.end type="italics"/>
                  in
                    <lb/>
                  interſectionem rectarum
                    <emph type="italics"/>
                  AP, DP
                    <emph.end type="italics"/>
                  adeoque coincidit cum puncto
                    <lb/>
                    <emph type="italics"/>
                  P.
                    <emph.end type="italics"/>
                  Quare punctum
                    <emph type="italics"/>
                  P,
                    <emph.end type="italics"/>
                  ubicunque ſumatur, incidit in aſſignatam
                    <lb/>
                  Conicam ſectionem.
                    <emph type="italics"/>
                  Q.E.D.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note44"/>
                  DE MOTU
                    <lb/>
                  CORPORUM</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  Hinc ſi rectæ tres
                    <emph type="italics"/>
                  PQ, PR, PS
                    <emph.end type="italics"/>
                  a puncto communi
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                    <lb/>
                  ad alias totidem poſitione datas rectas
                    <emph type="italics"/>
                  AB, CD, AC,
                    <emph.end type="italics"/>
                  ſingulæ ad
                    <lb/>
                  ſingulas, in datis angulis ducantur, ſitque rectangulum ſub duabus
                    <lb/>
                  ductis
                    <emph type="italics"/>
                  PQXPR
                    <emph.end type="italics"/>
                  ad quadratum tertiæ
                    <emph type="italics"/>
                  PS quad.
                    <emph.end type="italics"/>
                  in data ratione:
                    <lb/>
                  punctum
                    <emph type="italics"/>
                  P,
                    <emph.end type="italics"/>
                  a quibus rectæ ducuntur, locabitur in ſectione Conica
                    <lb/>
                  quæ tangit lineas
                    <emph type="italics"/>
                  AB, CD
                    <emph.end type="italics"/>
                  in
                    <emph type="italics"/>
                  A
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  C
                    <emph.end type="italics"/>
                  ; & contra. </s>
                  <s>Nam coeat linea
                    <lb/>
                    <emph type="italics"/>
                  BD
                    <emph.end type="italics"/>
                  cum linea
                    <emph type="italics"/>
                  AC
                    <emph.end type="italics"/>
                  manente poſitione trium
                    <emph type="italics"/>
                  AB, CD, AC
                    <emph.end type="italics"/>
                  ; de­
                    <lb/>
                  in coeat etiam linea
                    <emph type="italics"/>
                  PT
                    <emph.end type="italics"/>
                  cum linea
                    <emph type="italics"/>
                  PS:
                    <emph.end type="italics"/>
                  & rectangulum
                    <emph type="italics"/>
                  PSXPT
                    <emph.end type="italics"/>
                    <lb/>
                  evadet
                    <emph type="italics"/>
                  PS quad.
                    <emph.end type="italics"/>
                  rectæque
                    <emph type="italics"/>
                  AB, CD
                    <emph.end type="italics"/>
                  quæ curvam in punctis
                    <emph type="italics"/>
                  A
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                  &
                    <emph type="italics"/>
                  B,
                    <lb/>
                  C
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  D
                    <emph.end type="italics"/>
                  ſecabant, jam Curvam in punctis illis coeuntibus non am­
                    <lb/>
                  plius ſecare poſſunt ſed tantum tangent. </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>Nomen Conicæ ſectionis in hoc Lemmate late ſumitur, ita ut
                    <lb/>
                  ſectio tam Rectilinea per verticem Coni tranſiens, quam Circularis
                    <lb/>
                  baſi parallela includatur. </s>
                  <s>Nam ſi punctum
                    <emph type="italics"/>
                  p
                    <emph.end type="italics"/>
                  incidit in rectam, qua
                    <lb/>
                  quævis ex punctis quatuor
                    <emph type="italics"/>
                  A, B, C, D
                    <emph.end type="italics"/>
                  junguntur, Conica ſectio </s>
                </p>
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