Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                  <s>
                    <pb xlink:href="039/01/207.jpg" pagenum="179"/>
                  denſiorem verſus centrum, vel ſubductæ relinquant tenuiorem; &
                    <lb/>
                    <arrow.to.target n="note155"/>
                  hæ (per Prop. </s>
                  <s>LXXV) trahent Sphæras alias quotcunque concentri­
                    <lb/>
                  cas ſimilares
                    <emph type="italics"/>
                  GH, IK, LM,
                    <emph.end type="italics"/>
                  &c. </s>
                  <s>ſingulæ ſingulas, viribus reci­
                    <lb/>
                  proce proportionalibus quadrato diſtantiæ
                    <emph type="italics"/>
                  SP.
                    <emph.end type="italics"/>
                  Et componendo
                    <lb/>
                  vel dividendo, ſumma virium illarum omnium, vel exceſſus ali­
                    <lb/>
                  quarum ſupra alias, hoc eſt, vis quas Sphæra tota ex concen­
                    <lb/>
                  tricis quibuſcunque vel concentricarum differentiis compoſita
                    <emph type="italics"/>
                  AB,
                    <emph.end type="italics"/>
                    <lb/>
                  trahit totam ex concentricis quibuſcunque vel concentricarum dif­
                    <lb/>
                  ferentiis compoſitam
                    <emph type="italics"/>
                  GH,
                    <emph.end type="italics"/>
                  erit in eadem ratione. </s>
                  <s>Augeatur nu­
                    <lb/>
                  merus Sphærarum concentricarum in infinitum ſic, ut materiæ den­
                    <lb/>
                  ſitas una cum vi attractiva, in progreſſu a circumferentia ad cen­
                    <lb/>
                  trum, ſecundum Legem quamcunque creſcat vel decreſcat: &, ad­
                    <lb/>
                    <figure id="id.039.01.207.1.jpg" xlink:href="039/01/207/1.jpg" number="117"/>
                    <lb/>
                  dita materia non attractiva, compleatur ubivis denſitas deficiens, eo
                    <lb/>
                  ut Sphæræ acquirant formam quamvis optatam; & vis qua harum
                    <lb/>
                  una attrahet alteram erit etiamnum (per argumentum ſuperius) in
                    <lb/>
                  eadem illa diſtantiæ quadratæ ratione inverſa.
                    <emph type="italics"/>
                    <expan abbr="q.">que</expan>
                  E. D.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note155"/>
                  LIBER
                    <lb/>
                  PRIMUS.</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  1. Hinc ſi ejuſmodi Sphæræ complures, ſibi invicem per
                    <lb/>
                  omnia ſimiles, ſe mutuo trahant; attractiones acceleratrices ſingula­
                    <lb/>
                  rum in ſingulas erunt, in æqualibus quibuſvis centrorum diſtantiis,
                    <lb/>
                  ut Sphæræ attrahentes. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  2. InQ.E.D.ſtantiis quibuſvis inæqualibus, ut Sphæræ attra­
                    <lb/>
                  hentes applicatæ ad quadrata diſtantiarum inter centra. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  3. Attractiones vero motrices, ſeu pondera Sphærarum in
                    <lb/>
                  Sphæras erunt, in æqualibus centrorum diſtantiis, ut Sphæræ attra­
                    <lb/>
                  hentes & attractæ conjunctim, id eſt, ut contenta ſub Sphæris per
                    <lb/>
                  multiplicationem producta. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  4. InQ.E.D.ſtantiis inæqualibus, ut contenta illa applicata
                    <lb/>
                  ad quadrata diſtantiarum inter centra. </s>
                </p>
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          </chap>
        </body>
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