Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                <p type="main">
                  <s>
                    <pb xlink:href="039/01/299.jpg" pagenum="271"/>
                  nes, ſunt ut vires quas ſingulæ exercent in ſingulas. </s>
                  <s>Ergo vires,
                    <lb/>
                    <arrow.to.target n="note247"/>
                  quas ſingulæ exercent in ſingulas ſecundum planum
                    <emph type="italics"/>
                  FGH
                    <emph.end type="italics"/>
                  in cubo
                    <lb/>
                  majore, ſunt ad vires quas ſingulæ exercent in ſingulas ſecundum
                    <lb/>
                  planum
                    <emph type="italics"/>
                  fgh
                    <emph.end type="italics"/>
                  in cubo minore ut
                    <emph type="italics"/>
                  ab
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  AB,
                    <emph.end type="italics"/>
                  hoc eſt, reciproce ut
                    <lb/>
                  diſtantiæ particularum ad invicem.
                    <emph type="italics"/>
                    <expan abbr="q.">que</expan>
                  E. D.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note247"/>
                  LIBER
                    <lb/>
                  SECUNDUS.</s>
                </p>
                <p type="main">
                  <s>Et vice verſa, ſi vires particularum ſingularum ſunt reciproce
                    <lb/>
                  ut diſtantiæ, id eſt, reciproce ut cuborum latera
                    <emph type="italics"/>
                  AB, ab
                    <emph.end type="italics"/>
                  ; ſummæ
                    <lb/>
                  virium erunt in eadem ratione, & preſſiones laterum
                    <emph type="italics"/>
                  DB, db
                    <emph.end type="italics"/>
                  ut
                    <lb/>
                  ſummæ virium; & preſſio quadrati
                    <emph type="italics"/>
                  DP
                    <emph.end type="italics"/>
                  ad preſſionem lateris
                    <emph type="italics"/>
                  DB
                    <emph.end type="italics"/>
                    <lb/>
                  ut
                    <emph type="italics"/>
                  ab quad.
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  AB quad.
                    <emph.end type="italics"/>
                  Et, ex æquo, preſſio quadrati
                    <emph type="italics"/>
                  DP
                    <emph.end type="italics"/>
                  ad preſ­
                    <lb/>
                  ſionem lateris
                    <emph type="italics"/>
                  db
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  ab cub.
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  AB cub.
                    <emph.end type="italics"/>
                  id eſt, vis compreſſionis ad
                    <lb/>
                  vim compreſſionis ut denſitas ad denſitatem.
                    <emph type="italics"/>
                    <expan abbr="q.">que</expan>
                  E. D.
                    <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 argumento, ſi particularum vires centrifugæ ſint reciproce
                    <lb/>
                  in duplicata ratione diſtantiarum inter centra, cubi virium compri­
                    <lb/>
                  mentium erunt ut quadrato-quadrata denſitarum. </s>
                  <s>Si vires centri­
                    <lb/>
                  fugæ ſint reciproce in triplicata vel quadruplicata ratione diſtantia­
                    <lb/>
                  rum, cubi virium comprimentium erunt ut quadrato-cubi vel cubo­
                    <lb/>
                  cubi denſitatum. </s>
                  <s>Et univerſaliter, ſi D ponatur pro diſtantia, &
                    <lb/>
                  E pro denſitate Fluidi compreſſi, & vires centrifugæ ſint reciproce
                    <lb/>
                  ut diſtantiæ dignitas quælibet D
                    <emph type="sup"/>
                    <emph type="italics"/>
                  n
                    <emph.end type="italics"/>
                    <emph.end type="sup"/>
                  , cujus index eſt numerus
                    <emph type="italics"/>
                  n
                    <emph.end type="italics"/>
                  ; vi­
                    <lb/>
                  res comprimentes erunt ut latera cubica dignitatis E
                    <emph type="sup"/>
                    <emph type="italics"/>
                  n
                    <emph.end type="italics"/>
                  +2
                    <emph.end type="sup"/>
                  , cujus
                    <lb/>
                  index eſt numerus
                    <emph type="italics"/>
                  n
                    <emph.end type="italics"/>
                  +2: & contra. </s>
                  <s>Intelligenda vero ſunt hæc
                    <lb/>
                  omnia de particularum Viribus centrifugis quæ terminantur in par­
                    <lb/>
                  ticulis proximis, aut non longe ultra diffunduntur. </s>
                  <s>Exemplum
                    <lb/>
                  habemus in corporibus Magneticis. </s>
                  <s>Horum Virtus attractiva ter­
                    <lb/>
                  minatur fere in ſui generis corporibus ſibi proximis. </s>
                  <s>Magnetis
                    <lb/>
                  virtus per interpoſitam laminam ferri contrahitur, & in lamina fere
                    <lb/>
                  terminatur. </s>
                  <s>Nam corpora ulteriora non tam a Magnete quam a
                    <lb/>
                  lamina trahuntur. </s>
                  <s>Ad eundem modum ſi particulæ fugant alias ſui
                    <lb/>
                  generis particulas ſibi proximas, in particulas autem remotiores
                    <lb/>
                  virtutem nullam exerceant, ex hujuſmodi particulis componentur
                    <lb/>
                  Fluida de quibus actum eſt in hac Propoſitione. </s>
                  <s>Quod ſi particulæ
                    <lb/>
                  cujuſque virtus in infinitum propagetur, opus erit vi majori ad æqua­
                    <lb/>
                  lem condenſationem majoris quantitatis Fluidi. </s>
                  <s>An vero Fluida
                    <lb/>
                  Elaſtica ex particulis ſe mutuo fugantibus conſtent, Quæſtio Phy­
                    <lb/>
                  ſica eſt. </s>
                  <s>Nos proprietatem Fluidorum ex ejuſmodi particulis con­
                    <lb/>
                  ſtantium Mathematice demonſtravimus, ut Philoſophis anſam præ­
                    <lb/>
                  beamus Quæſtionem illam tractandi. </s>
                </p>
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