Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                    <pb xlink:href="039/01/232.jpg" pagenum="204"/>
                    <arrow.to.target n="note180"/>
                  ſecans tam
                    <emph type="italics"/>
                  HM
                    <emph.end type="italics"/>
                  in
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  Q,
                    <emph.end type="italics"/>
                  quam
                    <emph type="italics"/>
                  MI
                    <emph.end type="italics"/>
                  productam in
                    <emph type="italics"/>
                  N,
                    <emph.end type="italics"/>
                  & primo
                    <lb/>
                  ſi attractio vel impulſus ponatur uniformis, erit (ex demonſtratis
                    <lb/>
                    <emph type="italics"/>
                  Galilæi
                    <emph.end type="italics"/>
                  ) curva
                    <emph type="italics"/>
                  HI
                    <emph.end type="italics"/>
                  Parabola, cujus hæc eſt proprietas, ut rectan­
                    <lb/>
                  gulum ſub dato latere recto & linea
                    <emph type="italics"/>
                  IM
                    <emph.end type="italics"/>
                  æquale ſit
                    <emph type="italics"/>
                  HM
                    <emph.end type="italics"/>
                  quadrato;
                    <lb/>
                  ſed & linea
                    <emph type="italics"/>
                  HM
                    <emph.end type="italics"/>
                  biſecabitur in
                    <emph type="italics"/>
                  L.
                    <emph.end type="italics"/>
                  Unde ſi ad
                    <emph type="italics"/>
                  MI
                    <emph.end type="italics"/>
                  demittatur
                    <lb/>
                  perpendiculum
                    <emph type="italics"/>
                  LO,
                    <emph.end type="italics"/>
                  æ­
                    <lb/>
                    <figure id="id.039.01.232.1.jpg" xlink:href="039/01/232/1.jpg" number="134"/>
                    <lb/>
                  quales erunt
                    <emph type="italics"/>
                  MO, OR
                    <emph.end type="italics"/>
                  ;
                    <lb/>
                  & additis æqualibus
                    <emph type="italics"/>
                  ON,
                    <lb/>
                  OI,
                    <emph.end type="italics"/>
                  fient totæ æquales
                    <lb/>
                    <emph type="italics"/>
                  MN, IR.
                    <emph.end type="italics"/>
                  Proinde cum
                    <lb/>
                    <emph type="italics"/>
                  IR
                    <emph.end type="italics"/>
                  detur, datur etiam
                    <lb/>
                    <emph type="italics"/>
                  MN
                    <emph.end type="italics"/>
                  ; eſtque rectangu­
                    <lb/>
                  lum
                    <emph type="italics"/>
                  NMI
                    <emph.end type="italics"/>
                  ad rectangu­
                    <lb/>
                  lum ſub latere recto &
                    <lb/>
                    <emph type="italics"/>
                  IM,
                    <emph.end type="italics"/>
                  hoc eſt, ad
                    <emph type="italics"/>
                  HMq,
                    <emph.end type="italics"/>
                    <lb/>
                  in data ratione. </s>
                  <s>Sed rect­
                    <lb/>
                  angulum
                    <emph type="italics"/>
                  NMI
                    <emph.end type="italics"/>
                  æquale
                    <lb/>
                  eſt rectangulo
                    <emph type="italics"/>
                  PMQ,
                    <emph.end type="italics"/>
                  id
                    <lb/>
                  eſt, differentiæ quadrato­
                    <lb/>
                  rum
                    <emph type="italics"/>
                  MLq,
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  PLq
                    <emph.end type="italics"/>
                  ſeu
                    <lb/>
                    <emph type="italics"/>
                  LIq
                    <emph.end type="italics"/>
                  ; &
                    <emph type="italics"/>
                  HMq
                    <emph.end type="italics"/>
                  datam
                    <lb/>
                  rationem habet ad ſui ipſius quartam partem
                    <emph type="italics"/>
                  MLq:
                    <emph.end type="italics"/>
                  ergo datur
                    <lb/>
                  ratio
                    <emph type="italics"/>
                  MLq-LIq
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  MLq,
                    <emph.end type="italics"/>
                  & diviſim, ratio
                    <emph type="italics"/>
                  LIq
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  MLq,
                    <emph.end type="italics"/>
                  &
                    <lb/>
                  ratio dimidiata
                    <emph type="italics"/>
                  LI
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  ML.
                    <emph.end type="italics"/>
                  Sed in omni triangulo
                    <emph type="italics"/>
                  LMI,
                    <emph.end type="italics"/>
                  ſinus
                    <lb/>
                  angulorum ſunt proportionales lateribus oppoſitis. </s>
                  <s>Ergo datur
                    <lb/>
                  ratio ſinus anguli incidentiæ
                    <emph type="italics"/>
                  LMR
                    <emph.end type="italics"/>
                  ad ſinum anguli emergen­
                    <lb/>
                  tiæ
                    <emph type="italics"/>
                  LIR.
                    <expan abbr="q.">que</expan>
                  E. D.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note180"/>
                  DE MOTU
                    <lb/>
                  CORPORUM</s>
                </p>
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                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Cas.
                    <emph.end type="italics"/>
                  2. Tranſeat jam corpus ſucceſſive per ſpatia plura paralle­
                    <lb/>
                  lis planis terminata,
                    <emph type="italics"/>
                  AabB, BbcC,
                    <emph.end type="italics"/>
                  &c. </s>
                  <s>& agitetur vi quæ ſit in </s>
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