Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                <p type="main">
                  <s>
                    <pb xlink:href="039/01/298.jpg" pagenum="270"/>
                    <arrow.to.target n="note246"/>
                  tione diſtantiæ. </s>
                  <s>Fingatur quod vis comprimens ſit in duplicata
                    <lb/>
                  ratione denſitatis, & gravitas reciproce in ratione duplicata diſtan­
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                  tiæ, & denſitas erit reciproce ut diſtantia. </s>
                  <s>Caſus omnes percurre­
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                  re longum eſſet. </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note246"/>
                  DE MOTU
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                  CORPORUM</s>
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                <p type="main">
                  <s>
                    <emph type="center"/>
                  PROPOSITIO XXIII. THEOREMA XVIII.
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                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Si Fluidi ex particulis ſe mutuo fugientibus compoſiti denſitas ſit
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                  ut compreſſio, vires centrifugæ particularum ſunt reciproce pro­
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                  portionales diſtantiis centrorum ſuorum. </s>
                  <s>Et vice verſa, par­
                    <lb/>
                  ticulæ viribus quæ ſunt reciproce proportionales diſtantiis cen­
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                  trorum ſuorum ſe mutuo fugientes componunt Fluidum Elaſti­
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                  cum, cujus denſitas est compreſſioni proportionalis.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>Includi intelligatur Fluidum in ſpatio cubico
                    <emph type="italics"/>
                  ACE,
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                  dein com­
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                  preſſione redigi in ſpatium cubicum minus
                    <emph type="italics"/>
                  ace
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                  ; & particularum,
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                  ſimilem ſitum inter ſe in utro­
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                    <figure id="id.039.01.298.1.jpg" xlink:href="039/01/298/1.jpg" number="174"/>
                    <lb/>
                  que ſpatio obtinentium, diſtan­
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                  tiæ erunt ut cuborum latera
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                    <emph type="italics"/>
                  AB, ab
                    <emph.end type="italics"/>
                  ; & Medii denſitates
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                  reciproce ut ſpatia continentia
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                    <emph type="italics"/>
                  AB cub.
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  ab cub.
                    <emph.end type="italics"/>
                  In latere
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                  cubi majoris
                    <emph type="italics"/>
                  ABCD
                    <emph.end type="italics"/>
                  capiatur
                    <lb/>
                  quadratum
                    <emph type="italics"/>
                  DP
                    <emph.end type="italics"/>
                  æquale lateri
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                  cubi minoris
                    <emph type="italics"/>
                  db
                    <emph.end type="italics"/>
                  ; & ex Hypo­
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                  theſi, preſſio qua quadratum
                    <emph type="italics"/>
                  DP
                    <emph.end type="italics"/>
                  urget Fluidum incluſum, erit ad
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                  preſſionem qua latus illud quadratum
                    <emph type="italics"/>
                  db
                    <emph.end type="italics"/>
                  urget Fluidum incluſum
                    <lb/>
                  ut Medii denſitates ad invicem, hoc eſt, ut
                    <emph type="italics"/>
                  ab cub.
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  ABcub.
                    <emph.end type="italics"/>
                  Sed
                    <lb/>
                  preſſio qua quadratum
                    <emph type="italics"/>
                  DB
                    <emph.end type="italics"/>
                  urget Fluidum incluſum, eſt ad preſſi­
                    <lb/>
                  onem qua quadratum
                    <emph type="italics"/>
                  DP
                    <emph.end type="italics"/>
                  urget idem Fluidum, ut quadratum
                    <emph type="italics"/>
                  DB
                    <emph.end type="italics"/>
                    <lb/>
                  ad quadratum
                    <emph type="italics"/>
                  DP,
                    <emph.end type="italics"/>
                  hoc eſt, ut
                    <emph type="italics"/>
                  AB quad.
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  ab quad.
                    <emph.end type="italics"/>
                  Ergo, ex
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                  æquo, preſſio qua latus
                    <emph type="italics"/>
                  DB
                    <emph.end type="italics"/>
                  urget Fluidum, eſt ad preſſionem qua
                    <lb/>
                  latus
                    <emph type="italics"/>
                  db
                    <emph.end type="italics"/>
                  urget Fluidum, ut
                    <emph type="italics"/>
                  ab
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  AB.
                    <emph.end type="italics"/>
                  Planis
                    <emph type="italics"/>
                  FGH, fgh,
                    <emph.end type="italics"/>
                  per
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                  media cuborum ductis, diſtinguatur Fluidum in duas partes, & hæ
                    <lb/>
                  ſe mutuo prement iiſdem viribus, quibus premuntur a planis
                    <emph type="italics"/>
                  AC, ac,
                    <emph.end type="italics"/>
                    <lb/>
                  hoc eſt, in proportione
                    <emph type="italics"/>
                  ab
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  AB:
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                  adeoque vires centrifugæ, qui­
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                  bus hæ preſſiones ſuſtinentur, ſunt in eadem ratione. </s>
                  <s>Ob eundem
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                  particularum numerum ſimilemque ſitum in utroque cubo, vires
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                  quas particulæ omnes ſecundum plana
                    <emph type="italics"/>
                  FGH, fgh
                    <emph.end type="italics"/>
                  exercent in om-</s>
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