Newton, Isaac, Philosophia naturalis principia mathematica, 1713

Table of figures

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                  <s>
                    <pb xlink:href="039/01/266.jpg" pagenum="238"/>
                    <arrow.to.target n="note214"/>
                  ut (
                    <emph type="italics"/>
                  (bb/a
                    <emph type="sup"/>
                  4
                    <emph.end type="sup"/>
                  )/(bb/a
                    <emph type="sup"/>
                  3
                    <emph.end type="sup"/>
                  )√1+(mm/nn)-(2mbb/naa)+(b
                    <emph type="sup"/>
                  4
                    <emph.end type="sup"/>
                  /a
                    <emph type="sup"/>
                  4
                    <emph.end type="sup"/>
                  )
                    <emph.end type="italics"/>
                  ) ſeu (1/
                    <emph type="italics"/>
                  √aa+(mm/nn)aa-(2mbb/n)+(b
                    <emph type="sup"/>
                  4
                    <emph.end type="sup"/>
                  /aa)
                    <emph.end type="italics"/>
                  ) id
                    <lb/>
                  eſt, ſi in
                    <emph type="italics"/>
                  VZ
                    <emph.end type="italics"/>
                  ſumatur
                    <emph type="italics"/>
                  VY
                    <emph.end type="italics"/>
                  æqualis
                    <emph type="italics"/>
                  VG,
                    <emph.end type="italics"/>
                  ut (1/
                    <emph type="italics"/>
                  XY
                    <emph.end type="italics"/>
                  ). Namque
                    <emph type="italics"/>
                  aa
                    <emph.end type="italics"/>
                  &
                    <lb/>
                    <emph type="italics"/>
                  (mm/nn)aa-(2mbb/n)+(b
                    <emph type="sup"/>
                  4
                    <emph.end type="sup"/>
                  /aa)
                    <emph.end type="italics"/>
                  ſunt ipſarum
                    <emph type="italics"/>
                  XZ
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  ZY
                    <emph.end type="italics"/>
                  quadrata. </s>
                  <s>Reſiſten­
                    <lb/>
                  tia autem invenitur in ratione ad gravitatem quam habet 3
                    <emph type="italics"/>
                  XY
                    <emph.end type="italics"/>
                  ad
                    <lb/>
                    <figure id="id.039.01.266.1.jpg" xlink:href="039/01/266/1.jpg" number="155"/>
                    <lb/>
                  2
                    <emph type="italics"/>
                  YG
                    <emph.end type="italics"/>
                  & velocitas ea eſt quacum corpus in Parabola pergeret verti­
                    <lb/>
                  cem
                    <emph type="italics"/>
                  G,
                    <emph.end type="italics"/>
                  diametrum
                    <emph type="italics"/>
                  DG,
                    <emph.end type="italics"/>
                  & latus rectum (
                    <emph type="italics"/>
                  XYquad./VG
                    <emph.end type="italics"/>
                  ) habente. </s>
                  <s>Pona­
                    <lb/>
                  tur itaque quod Medii denſitates in locis ſingulis
                    <emph type="italics"/>
                  G
                    <emph.end type="italics"/>
                  ſint reciproce
                    <lb/>
                  ut diſtantiæ
                    <emph type="italics"/>
                  XY,
                    <emph.end type="italics"/>
                  quodque reſiſtentia in loco aliquo
                    <emph type="italics"/>
                  G
                    <emph.end type="italics"/>
                  ſit ad gra­
                    <lb/>
                  vitatem ut 3
                    <emph type="italics"/>
                  XY
                    <emph.end type="italics"/>
                  ad 2
                    <emph type="italics"/>
                  YG
                    <emph.end type="italics"/>
                  ; & corpus de loco
                    <emph type="italics"/>
                  A,
                    <emph.end type="italics"/>
                  juſta cum veloci­
                    <lb/>
                  tate emiſſum, deſcribet Hyperbolam illam
                    <emph type="italics"/>
                  AGK. Q.E.I.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note214"/>
                  DE MOTU
                    <lb/>
                  CORPORUM</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Exempl.
                    <emph.end type="italics"/>
                  4. Ponatur indefinite, quod linea
                    <emph type="italics"/>
                  AGK
                    <emph.end type="italics"/>
                  Hyperbola ſit,
                    <lb/>
                  centro
                    <emph type="italics"/>
                  X
                    <emph.end type="italics"/>
                  Aſymptotis
                    <emph type="italics"/>
                  MX, NX
                    <emph.end type="italics"/>
                  ea lege deſcripta, ut conſtructo
                    <lb/>
                  rectangulo
                    <emph type="italics"/>
                  XZDN
                    <emph.end type="italics"/>
                  cujus latus
                    <emph type="italics"/>
                  ZD
                    <emph.end type="italics"/>
                  ſecet Hyperbolam in
                    <emph type="italics"/>
                  G
                    <emph.end type="italics"/>
                  & </s>
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