Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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        <body>
          <chap>
            <subchap1>
              <subchap2>
                <p type="main">
                  <s>
                    <pb xlink:href="039/01/217.jpg" pagenum="189"/>
                    <arrow.to.target n="note165"/>
                  </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note165"/>
                  LIBER
                    <lb/>
                  PRIMUS.</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                  PROPOSITIO LXXXII. THEOREMA XLI.
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  In Sphæra centro
                    <emph.end type="italics"/>
                  S
                    <emph type="italics"/>
                  intervallo
                    <emph.end type="italics"/>
                  SA
                    <emph type="italics"/>
                  deſcripta, ſi capiantur
                    <emph.end type="italics"/>
                  SI, SA,
                    <lb/>
                  SP
                    <emph type="italics"/>
                  continue proportionales: dico quod corpuſculi intra Sphæ­
                    <lb/>
                  ram in loco quovis
                    <emph.end type="italics"/>
                  I
                    <emph type="italics"/>
                  attractio est ad attractionem ipſius extra
                    <lb/>
                  Sphæram in loco
                    <emph.end type="italics"/>
                  P,
                    <emph type="italics"/>
                  in ratione compoſita ex ſubduplicata ratione
                    <lb/>
                  diſtantiarum a centro
                    <emph.end type="italics"/>
                  IS, PS
                    <emph type="italics"/>
                  & ſubduplicata ratione virium
                    <lb/>
                  centripetarum, in locis illis
                    <emph.end type="italics"/>
                  P
                    <emph type="italics"/>
                  &
                    <emph.end type="italics"/>
                  I,
                    <emph type="italics"/>
                  ad centrum tendentium.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>Ut ſi vires centripetæ particularum Sphæræ ſint reciproce ut di­
                    <lb/>
                  ſtantiæ corpuſculi a ſe attracti; vis, qua corpuſculum ſitum in
                    <emph type="italics"/>
                  I
                    <emph.end type="italics"/>
                    <lb/>
                  trahitur a Sphæra tota, erit ad vim qua trahitur in
                    <emph type="italics"/>
                  P,
                    <emph.end type="italics"/>
                  in ratione
                    <lb/>
                    <figure id="id.039.01.217.1.jpg" xlink:href="039/01/217/1.jpg" number="124"/>
                    <lb/>
                  compoſita ex ſubduplicata ratione diſtantiæ
                    <emph type="italics"/>
                  SI
                    <emph.end type="italics"/>
                  ad diſtantiam
                    <emph type="italics"/>
                  SP
                    <emph.end type="italics"/>
                    <lb/>
                  & ratione ſubduplicata vis centripetæ in loco
                    <emph type="italics"/>
                  I,
                    <emph.end type="italics"/>
                  a particula aliqua
                    <lb/>
                  in centro oriundæ, ad vim centripetam in loco
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  ab eadem in cen­
                    <lb/>
                  tro particula oriundam, id eſt, ratione ſubduplicata diſtantiarum
                    <lb/>
                    <emph type="italics"/>
                  SI, SP
                    <emph.end type="italics"/>
                  ad invicem reciproce. </s>
                  <s>Hæ duæ rationes ſubduplicatæ
                    <lb/>
                  componunt rationem æqualitatis, & propterea attractiones in
                    <emph type="italics"/>
                  I
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                    <lb/>
                  a Sphæra tota factæ æquantur. </s>
                  <s>Simili computo, ſi vires particu­
                    <lb/>
                  larum Sphæræ ſunt reciproce in duplicata ratione diſtantiarum, col­
                    <lb/>
                  ligetur quod attractio in
                    <emph type="italics"/>
                  I
                    <emph.end type="italics"/>
                  ſit ad attractionem in
                    <emph type="italics"/>
                  P,
                    <emph.end type="italics"/>
                  ut diſtantia
                    <emph type="italics"/>
                  SP
                    <emph.end type="italics"/>
                    <lb/>
                  ad Sphæræ ſemidiametrum
                    <emph type="italics"/>
                  SA:
                    <emph.end type="italics"/>
                  Si vires illæ ſunt reciproce in tr­
                    <lb/>
                  plicata ratione diſtantiarum, attractiones in
                    <emph type="italics"/>
                  I
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  erunt ad invi-</s>
                </p>
              </subchap2>
            </subchap1>
          </chap>
        </body>
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