Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                  <s>
                    <pb xlink:href="039/01/205.jpg" pagenum="177"/>
                  nihili ſit; nimirum Orbes evaneſcentes ex quibus Sphæra ultimo
                    <lb/>
                    <arrow.to.target n="note153"/>
                  conſtat, ubi Orbium illorum numerus augetur & craſſitudo minui­
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                  tur in infinitum. </s>
                  <s>Similiter per Puncta, ex quibus lineæ, ſuperficies
                    <lb/>
                  & ſolida componi dicuntur, intelligendæ ſunt particulæ æquales
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                  magnitudinis contemnendæ. </s>
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                  LIBER
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                  PRIMUS.</s>
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                  <s>
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                  PROPOSITIO LXXIV. THEOREMA XXXIV.
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                  Iiſdem poſitis, dico quod corpuſculum extra Sphæram conſtitutum
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                  attrabitur vi reciproce proportionali quadrato diſtantiæ ſuæ ab
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                  ipſius centro.
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                  <s>Nam diſtinguatur Sphæra in ſuperficies Sphæricas innumeras
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                  concentricas, & attractiones corpuſculi a ſingulis ſuperficiebus
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                  oriundæ erunt reciproce proportionales quadrato diſtantiæ cor­
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                  puſculi a centro, per Prop. </s>
                  <s>LXXI. </s>
                  <s>Et componendo, fiet ſum­
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                  ma attractionum, hoc eſt attractio corpuſculi in Sphæram totam, in
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                  eadem ratione.
                    <emph type="italics"/>
                    <expan abbr="q.">que</expan>
                  E. D.
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                  </s>
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                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
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                  1. Hinc in æqualibus diſtantiis a centris homogenearum
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                  Sphærarum, attractiones ſunt ut Sphæræ. </s>
                  <s>Nam per Prop. </s>
                  <s>LXXII,
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                  ſi diſtantiæ ſunt proportionales diametris Sphærarum, vires erunt
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                  ut diametri. </s>
                  <s>Minuatur diſtantia major in illa ratione; &, diſtan­
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                  tiis jam factis æqualibus, augebitur attractio in duplicata illa ratio­
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                  ne, adeoque erit ad attractionem alteram in triplicata illa ratione,
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                  hoc eſt, in ratione Sphærarum. </s>
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                  <s>
                    <emph type="italics"/>
                  Corol.
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                  2. In diſtantiis quibuſvis attractiones ſunt ut Sphæræ ap­
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                  plicatæ ad quadrata diſtantiarum. </s>
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                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
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                  3. Si corpuſculum, extra Sphæram homogeneam poſitum,
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                  trahitur vi reciproce proportionali quadrato diſtantiæ ſuæ ab ipſius
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                  centro, conſtet autem Sphæra ex particulis attractivis; decreſcet vis
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                  particulæ cujuſQ.E.I. duplicata ratione diſtantiæ a particula. </s>
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                  <s>
                    <emph type="center"/>
                  PROPOSITIO LXXV. THEOREMA XXXV.
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                  </s>
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                  <s>
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                  Si ad Sphæræ datæ puncta ſingula tendant vires æquales centripe­
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                  tæ, decreſcentes in duplicata ratione diſtantiarum a punctis; dico
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                  quod Sphæra quævis alia ſimilaris ab eadem attrahitur vi reci­
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                  proce proportionali quadrato diſtantiæ centrorum.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>Nam particulæ cujuſvis attractio eſt reciproce ut quadratum di­
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                  ſtantiæ ſuæ a centro Sphæræ trahentis, (per Prop. </s>
                  <s>LXXIV) & prop-</s>
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