Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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              <subchap2>
                <p type="main">
                  <s>
                    <pb xlink:href="039/01/297.jpg" pagenum="269"/>
                  tur jam diſtantiæ quælibet, puta
                    <emph type="italics"/>
                  SA, SD, SF
                    <emph.end type="italics"/>
                  in progreſſione Mu­
                    <lb/>
                    <arrow.to.target n="note245"/>
                  ſica, & differentiæ
                    <emph type="italics"/>
                  Aa-Dd, Dd-Ff
                    <emph.end type="italics"/>
                  erunt æquales; & propter­
                    <lb/>
                  ea differentiis hiſce proportionales areæ
                    <emph type="italics"/>
                  thlx, xlnz
                    <emph.end type="italics"/>
                  æquales erunt
                    <lb/>
                  inter ſe, & denſitates
                    <emph type="italics"/>
                  St, Sx, Sz,
                    <emph.end type="italics"/>
                  id eſt,
                    <emph type="italics"/>
                  AH, DL, FN,
                    <emph.end type="italics"/>
                  conti­
                    <lb/>
                  nue proportionales.
                    <emph type="italics"/>
                    <expan abbr="q.">que</expan>
                  E. D.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note244"/>
                  DE MOTU
                    <lb/>
                  CORPORUM</s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note245"/>
                  LIBER
                    <lb/>
                  SECUNDUS</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  Hinc ſi dentur Fluidi denſitates duæ quævis, puta
                    <emph type="italics"/>
                  AH
                    <emph.end type="italics"/>
                    <lb/>
                  &
                    <emph type="italics"/>
                  CK,
                    <emph.end type="italics"/>
                  dabitur area
                    <emph type="italics"/>
                  thkw
                    <emph.end type="italics"/>
                  harum differentiæ
                    <emph type="italics"/>
                  tw
                    <emph.end type="italics"/>
                  reſpondens; &
                    <lb/>
                  inde invenietur denſitas
                    <emph type="italics"/>
                  FN
                    <emph.end type="italics"/>
                  in altitudine quacunque
                    <emph type="italics"/>
                  SF,
                    <emph.end type="italics"/>
                  ſumen­
                    <lb/>
                  do aream
                    <emph type="italics"/>
                  thnz
                    <emph.end type="italics"/>
                  ad aream illam datam
                    <emph type="italics"/>
                  thkw
                    <emph.end type="italics"/>
                  ut eſt differentia
                    <lb/>
                    <emph type="italics"/>
                  Aa-Ff
                    <emph.end type="italics"/>
                  ad differentiam
                    <emph type="italics"/>
                  Aa-Cc.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                    <emph type="italics"/>
                  Scholium.
                    <emph.end type="italics"/>
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>Simili argumentatione probari poteſt, quod ſi gravitas particu­
                    <lb/>
                  larum Fluidi diminuatur in triplicata ratione diſtantiarum a centro;
                    <lb/>
                  & quadratorum diſtantiarum
                    <emph type="italics"/>
                  SA, SB, SC,
                    <emph.end type="italics"/>
                  &c. </s>
                  <s>reciproca (nem­
                    <lb/>
                  pe
                    <emph type="italics"/>
                  (SAcub./SAq), (SAcub./SBq), (SAcub./SCq)
                    <emph.end type="italics"/>
                  ) ſumantur in progreſſione Arithme­
                    <lb/>
                  tica; denſitates
                    <emph type="italics"/>
                  AH, BI, CK,
                    <emph.end type="italics"/>
                  &c. </s>
                  <s>erunt in progreſſione Geome­
                    <lb/>
                  trica. </s>
                  <s>Et ſi gravitas diminuatur in quadruplicata ratione diſtan­
                    <lb/>
                  tiarum, & cuborum diſtantiarum reciproca (puta
                    <emph type="italics"/>
                  (SAqq/SAcub), (SAqq/SBcub),
                    <lb/>
                  (SAqq/SCcub.),
                    <emph.end type="italics"/>
                  &c.) ſumantur in progreſſione Arithmetica; denſitates
                    <lb/>
                    <emph type="italics"/>
                  AH, BI, CK,
                    <emph.end type="italics"/>
                  &c. </s>
                  <s>erunt in progreſſione Geometrica. </s>
                  <s>Et ſic in
                    <lb/>
                  infinitum. </s>
                  <s>Rurſus. </s>
                  <s>ſi gravitas particularum Fluidi in omnibus di­
                    <lb/>
                  ſtantiis eadem ſit, & diſtantiæ ſint in progreſſione Arithmetica,
                    <lb/>
                  denſitates erunt in progreſſione Geometrica, uti Vir Cl.
                    <emph type="italics"/>
                  Edmundus
                    <lb/>
                  Hælleius
                    <emph.end type="italics"/>
                  invenit. </s>
                  <s>Si gravitas ſit ut diſtantia, & quadrata diſtantia­
                    <lb/>
                  rum ſint in progreſſione Arithmetica, denſitates erunt in progreſ­
                    <lb/>
                  ſione Geometrica. </s>
                  <s>Et ſic in infinitum. </s>
                  <s>Hæc ita ſe habent ubi Fluidi
                    <lb/>
                  compreſſione condenſati denſitas eſt ut vis compreſſionis, vel, quod
                    <lb/>
                  perinde eſt, ſpatium a Fluido occupatum reciproce ut hæc vis. </s>
                  <s>
                    <lb/>
                  Fingi poſſunt aliæ condenſationis Leges, ut quod cubus vis com­
                    <lb/>
                  primentis ſit ut quadrato-quadratum denſitatis, feu triplicata ra­
                    <lb/>
                  tio Vis æqualis quadruplicatæ rationi denſitatis. </s>
                  <s>Quo in caſu, ſi gra­
                    <lb/>
                  vitas eſt reciproce ut quadratum diſtantiæ a centro, denſitas erit
                    <lb/>
                  reciproce ut cubus diſtantiæ. </s>
                  <s>Fingatur quod cubus vis compri­
                    <lb/>
                  mentis ſit ut quadrato-cubus denſitatis, & ſi gravitas eſt reciproce
                    <lb/>
                  ut quadratum diſtantiæ, denſitas erit reciproce in ſuſquiplicata ra-</s>
                </p>
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          </chap>
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