Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                <p type="main">
                  <s>
                    <pb xlink:href="039/01/159.jpg" pagenum="131"/>
                  A
                    <emph type="sup"/>
                  (11/9)
                    <emph.end type="sup"/>
                  vel A
                    <emph type="sup"/>
                  1/4
                    <emph.end type="sup"/>
                  , aut directe ut A
                    <emph type="sup"/>
                  6
                    <emph.end type="sup"/>
                  vel A
                    <emph type="sup"/>
                  13
                    <emph.end type="sup"/>
                  . </s>
                  <s>Denique ſi corpus pergendo
                    <lb/>
                    <arrow.to.target n="note107"/>
                  ab Apſide ſumma ad Apſidem ſummam confecerit revolutionem in­
                    <lb/>
                  tegram, & præterea gradus tres, adeoque Apſis illa ſingulis corporis
                    <lb/>
                  revolutionibus confecerit in conſequentia gradus tres; erit
                    <emph type="italics"/>
                  m
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  n
                    <emph.end type="italics"/>
                  ut
                    <lb/>
                  363
                    <emph type="italics"/>
                  gr.
                    <emph.end type="italics"/>
                  ad 360
                    <emph type="italics"/>
                  gr.
                    <emph.end type="italics"/>
                  ſive ut 121 ad 120, adeoque A
                    <emph type="sup"/>
                  (
                    <emph type="italics"/>
                  nn/mm
                    <emph.end type="italics"/>
                  )-3
                    <emph.end type="sup"/>
                  erit æquale
                    <lb/>
                  A
                    <emph type="sup"/>
                  -(29523/14641)
                    <emph.end type="sup"/>
                  ; & propterea vis centripeta reciproce ut A
                    <emph type="sup"/>
                  (29523/14641)
                    <emph.end type="sup"/>
                  ſeu re­
                    <lb/>
                  ciproce ut A
                    <emph type="sup"/>
                  2 (4/2+3)
                    <emph.end type="sup"/>
                  proxime. </s>
                  <s>Decreſcit igitur vis centripeta in ratio­
                    <lb/>
                  ne paulo majore quam duplicata, ſed quæ vicibus 59 3/4 propius ad
                    <lb/>
                  duplicatam quam ad triplicatam accedit. </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note106"/>
                  DE MOTU
                    <lb/>
                  CORPORUM</s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note107"/>
                  LIBER
                    <lb/>
                  PRIMUS.</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  2. Hinc etiam ſi corpus, vi centripeta quæ ſit reciproce
                    <lb/>
                  ut quadratum altitudinis, revolvatur in Ellipſi umbilicum haben­
                    <lb/>
                  te in centro virium, & huic vi centripetæ addatur vel auferatur
                    <lb/>
                  vis alia quævis extranea; cognoſci poteſt (per Exempla tertia)
                    <lb/>
                  motus Apſidum qui ex vi illa extranea orietur: & contra. </s>
                  <s>Ut ſi
                    <lb/>
                  vis qua corpus revolvitur in Ellipſi ſit ut (1/AA), & vis extranea ab­
                    <lb/>
                  lata ut
                    <emph type="italics"/>
                  c
                    <emph.end type="italics"/>
                  A, adeoque vis reliqua ut (A-
                    <emph type="italics"/>
                  c
                    <emph.end type="italics"/>
                  A
                    <emph type="sup"/>
                  4
                    <emph.end type="sup"/>
                  /A
                    <emph type="italics"/>
                  cub.
                    <emph.end type="italics"/>
                  ); erit (in Exemplis ter­
                    <lb/>
                  tiis)
                    <emph type="italics"/>
                  b
                    <emph.end type="italics"/>
                  æqualis 1,
                    <emph type="italics"/>
                  m
                    <emph.end type="italics"/>
                  æqualis 1,
                    <emph type="italics"/>
                  n
                    <emph.end type="italics"/>
                  æqualis 4, adeoque angulus revo­
                    <lb/>
                  lutionis inter Apſides æqualis angulo graduum 180 √(1-
                    <emph type="italics"/>
                  c
                    <emph.end type="italics"/>
                  /1-4
                    <emph type="sup"/>
                    <emph type="italics"/>
                  c
                    <emph.end type="italics"/>
                    <emph.end type="sup"/>
                  ). Po­
                    <lb/>
                  natur vim illam extraneam eſſe 357,
                    <emph type="sup"/>
                  45
                    <emph.end type="sup"/>
                  partibus minorem quam vis
                    <lb/>
                  altera qua corpus revolvitur in Ellipſi, id eſt
                    <emph type="italics"/>
                  c
                    <emph.end type="italics"/>
                  eſſe (100/35745), exiſtente A
                    <lb/>
                  vel T æquali 1; & 180 √(1-
                    <emph type="italics"/>
                  c
                    <emph.end type="italics"/>
                  /1-4
                    <emph type="sup"/>
                    <emph type="italics"/>
                  c
                    <emph.end type="italics"/>
                    <emph.end type="sup"/>
                  ) evadet 180 √(35645/35345), ſeu 180, 7623,
                    <lb/>
                  id eſt, 180
                    <emph type="italics"/>
                  gr.
                    <emph.end type="italics"/>
                  45
                    <emph type="italics"/>
                  m.
                    <emph.end type="italics"/>
                  44
                    <emph type="italics"/>
                  ſ.
                    <emph.end type="italics"/>
                  Igitur corpus de Apſide ſumma diſce­
                    <lb/>
                  dens, motu angulari 180
                    <emph type="italics"/>
                  gr.
                    <emph.end type="italics"/>
                  45
                    <emph type="italics"/>
                  m.
                    <emph.end type="italics"/>
                  44.
                    <emph type="italics"/>
                  ſ.
                    <emph.end type="italics"/>
                  perveniet ad Apſidem
                    <lb/>
                  imam, & hoc motu duplicato ad Apſidem ſummam redibit: adeo­
                    <lb/>
                  que Apſis ſumma ſingulis revolutionibus progrediendo conficiet
                    <lb/>
                  1
                    <emph type="italics"/>
                  gr.
                    <emph.end type="italics"/>
                  31
                    <emph type="italics"/>
                  m.
                    <emph.end type="italics"/>
                  28
                    <emph type="italics"/>
                  ſec.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>Hactenus de Motu corporum in Orbibus quorum plana per
                    <lb/>
                  centrum Virium tranſeunt. </s>
                  <s>Supereſt ut Motus etiam determine­
                    <lb/>
                  mus in planis excentricis. </s>
                  <s>Nam Scriptores qui Motum gravium
                    <lb/>
                  tractant, conſiderare ſolent aſcenſus & deſcenſus ponderum,
                    <lb/>
                  tam obliquos in planis quibuſcunQ.E.D.tis, quam perpendicu­
                    <lb/>
                  lares: & pari jure Motus corporum Viribus quibuſcunque cen-</s>
                </p>
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            </subchap1>
          </chap>
        </body>
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