Newton, Isaac, Philosophia naturalis principia mathematica, 1713

Table of figures

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              <subchap2>
                <p type="main">
                  <s>
                    <pb xlink:href="039/01/092.jpg" pagenum="64"/>
                    <arrow.to.target n="note40"/>
                  ad
                    <emph type="italics"/>
                  MA
                    <emph.end type="italics"/>
                  ut eſt
                    <emph type="italics"/>
                  MN
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  AB,
                    <emph.end type="italics"/>
                  & erecta
                    <emph type="italics"/>
                  PR
                    <emph.end type="italics"/>
                  perpendiculari ad
                    <emph type="italics"/>
                  AB,
                    <emph.end type="italics"/>
                    <lb/>
                  demiſſaque
                    <emph type="italics"/>
                  ZR
                    <emph.end type="italics"/>
                  perpendiculari ad
                    <emph type="italics"/>
                  PR
                    <emph.end type="italics"/>
                  ; erit, ex natura hujus Hy­
                    <lb/>
                  perbolæ,
                    <emph type="italics"/>
                  ZR
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  AZ
                    <emph.end type="italics"/>
                  ut eſt
                    <emph type="italics"/>
                  MN
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  AB.
                    <emph.end type="italics"/>
                  Simili diſcurſu punctum
                    <lb/>
                    <emph type="italics"/>
                  Z
                    <emph.end type="italics"/>
                  locabitur in alia Hyperbola, cujus umbilici ſunt
                    <emph type="italics"/>
                  A, C
                    <emph.end type="italics"/>
                  & princi­
                    <lb/>
                  palis axis differentia inter
                    <emph type="italics"/>
                  AZ
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  CZ,
                    <emph.end type="italics"/>
                  ducique poteſt
                    <emph type="italics"/>
                  QS
                    <emph.end type="italics"/>
                  ipſi
                    <emph type="italics"/>
                  AC
                    <emph.end type="italics"/>
                    <lb/>
                  perpendicularis, ad quam ſi ab Hyperbolæ hujus puncto quovis
                    <emph type="italics"/>
                  Z
                    <emph.end type="italics"/>
                    <lb/>
                  demittatur normalis
                    <emph type="italics"/>
                  ZS,
                    <emph.end type="italics"/>
                  hæc fuerit ad
                    <emph type="italics"/>
                  AZ
                    <emph.end type="italics"/>
                  ut eſt differentia inter
                    <lb/>
                    <emph type="italics"/>
                  AZ
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  CZ
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  AC.
                    <emph.end type="italics"/>
                  Dantur ergo rationes ipſarum
                    <emph type="italics"/>
                  ZR
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  ZS
                    <emph.end type="italics"/>
                    <lb/>
                  ad
                    <emph type="italics"/>
                  AZ,
                    <emph.end type="italics"/>
                  & idcirco datur earun­
                    <lb/>
                    <figure id="id.039.01.092.1.jpg" xlink:href="039/01/092/1.jpg" number="35"/>
                    <lb/>
                  dem
                    <emph type="italics"/>
                  ZR
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  ZS
                    <emph.end type="italics"/>
                  ratio ad invicem;
                    <lb/>
                  ideoque ſi rectæ
                    <emph type="italics"/>
                  RP, SQ
                    <emph.end type="italics"/>
                  concur­
                    <lb/>
                  rant in
                    <emph type="italics"/>
                  T,
                    <emph.end type="italics"/>
                  & agatur
                    <emph type="italics"/>
                  TZ,
                    <emph.end type="italics"/>
                  figura
                    <lb/>
                    <emph type="italics"/>
                  TRZS,
                    <emph.end type="italics"/>
                  dabitur ſpecie, & recta
                    <lb/>
                    <emph type="italics"/>
                  TZ
                    <emph.end type="italics"/>
                  in qua punctum
                    <emph type="italics"/>
                  Z
                    <emph.end type="italics"/>
                  alicubi lo­
                    <lb/>
                  catur, dabitur poſitione. </s>
                  <s>Eadem
                    <lb/>
                  methodo per Hyperbolam ter­
                    <lb/>
                  tiam, cujus umbilici ſunt
                    <emph type="italics"/>
                  B
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  C
                    <emph.end type="italics"/>
                    <lb/>
                  & axis principalis differentia re­
                    <lb/>
                  ctarum
                    <emph type="italics"/>
                  BZ, CZ,
                    <emph.end type="italics"/>
                  inveniri poteſt
                    <lb/>
                  alia recta in qua
                    <expan abbr="pũctum">punctum</expan>
                    <emph type="italics"/>
                  Z
                    <emph.end type="italics"/>
                  locatur. </s>
                  <s>
                    <lb/>
                  Habitis autem duobus Locis recti­
                    <lb/>
                  lineis, habetur punctum quæſitum
                    <emph type="italics"/>
                  Z
                    <emph.end type="italics"/>
                  in eorum interſectione.
                    <emph type="italics"/>
                  Q.E.I.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note40"/>
                  DE MOTU
                    <lb/>
                  CORPORUM</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Cas.
                    <emph.end type="italics"/>
                  2. Si duæ ex tribus lineis, puta
                    <emph type="italics"/>
                  AZ
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  BZ
                    <emph.end type="italics"/>
                  æquantur, pun­
                    <lb/>
                  ctum
                    <emph type="italics"/>
                  Z
                    <emph.end type="italics"/>
                  locabitur in perpendiculo biſecante diſtantiam
                    <emph type="italics"/>
                  AB,
                    <emph.end type="italics"/>
                  & lo­
                    <lb/>
                  cus alius rectilineus invenietur ut ſupra.
                    <emph type="italics"/>
                  Q.E.I.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Cas.
                    <emph.end type="italics"/>
                  3. Si omnes tres æquantur, locabitur punctum
                    <emph type="italics"/>
                  Z
                    <emph.end type="italics"/>
                  in centro
                    <lb/>
                  Circuli per puncta
                    <emph type="italics"/>
                  A, B, C
                    <emph.end type="italics"/>
                  tranſeuntis.
                    <emph type="italics"/>
                  Q.E.I.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>Solvitur etiam hoc Lemma problematicum per Librum Tactio­
                    <lb/>
                  num
                    <emph type="italics"/>
                  Apollonii
                    <emph.end type="italics"/>
                  a
                    <emph type="italics"/>
                  Vieta
                    <emph.end type="italics"/>
                  reſtitutum. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                  PROPOSITIO XXI. PROBLEMA XIII.
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                    <emph type="italics"/>
                  Trajectoriam circa datum umbilicum deſcribere, quæ tranſibit per
                    <lb/>
                  puncta data & rectas poſitione datas continget.
                    <emph.end type="italics"/>
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>Detur umbilicus
                    <emph type="italics"/>
                  S,
                    <emph.end type="italics"/>
                  punctum
                    <emph type="italics"/>
                  P,
                    <emph.end type="italics"/>
                  & tangens
                    <emph type="italics"/>
                  TR,
                    <emph.end type="italics"/>
                  & invenien­
                    <lb/>
                  dus ſit umbilicus alter
                    <emph type="italics"/>
                  H.
                    <emph.end type="italics"/>
                  Ad tangentem demitte perpendiculum
                    <lb/>
                    <emph type="italics"/>
                  ST,
                    <emph.end type="italics"/>
                  & produc idem ad
                    <emph type="italics"/>
                  Y,
                    <emph.end type="italics"/>
                  ut ſit
                    <emph type="italics"/>
                  TY
                    <emph.end type="italics"/>
                  æqualis
                    <emph type="italics"/>
                  ST,
                    <emph.end type="italics"/>
                  & erit
                    <emph type="italics"/>
                  YH
                    <emph.end type="italics"/>
                  æ­
                    <lb/>
                  qualis axi principali. </s>
                  <s>Junge
                    <emph type="italics"/>
                  SP, HP,
                    <emph.end type="italics"/>
                  & erit
                    <emph type="italics"/>
                  SP
                    <emph.end type="italics"/>
                  differentia inter
                    <lb/>
                    <emph type="italics"/>
                  HP
                    <emph.end type="italics"/>
                  & axem principalem. </s>
                  <s>Hoc modo ſi dentur plures tangen-</s>
                </p>
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            </subchap1>
          </chap>
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