Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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nes, ſunt ut vires quas ſingulæ exercent in ſingulas. </
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>Ergo vires,
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quas ſingulæ exercent in ſingulas ſecundum planum
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FGH
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in cubo
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majore, ſunt ad vires quas ſingulæ exercent in ſingulas ſecundum
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planum
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fgh
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in cubo minore ut
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ab
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ad
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AB,
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hoc eſt, reciproce ut
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diſtantiæ particularum ad invicem.
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E. D.
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LIBER
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SECUNDUS.</
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<
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>Et vice verſa, ſi vires particularum ſingularum ſunt reciproce
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ut diſtantiæ, id eſt, reciproce ut cuborum latera
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AB, ab
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; ſummæ
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virium erunt in eadem ratione, & preſſiones laterum
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DB, db
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ut
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ſummæ virium; & preſſio quadrati
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DP
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ad preſſionem lateris
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DB
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ut
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ab quad.
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ad
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AB quad.
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Et, ex æquo, preſſio quadrati
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DP
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ad preſ
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ſionem lateris
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db
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ut
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ab cub.
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ad
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AB cub.
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id eſt, vis compreſſionis ad
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vim compreſſionis ut denſitas ad denſitatem.
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E. D.
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Scholium.
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<
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>Simili argumento, ſi particularum vires centrifugæ ſint reciproce
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in duplicata ratione diſtantiarum inter centra, cubi virium compri
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mentium erunt ut quadrato-quadrata denſitarum. </
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>Si vires centri
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fugæ ſint reciproce in triplicata vel quadruplicata ratione diſtantia
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rum, cubi virium comprimentium erunt ut quadrato-cubi vel cubo
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cubi denſitatum. </
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>Et univerſaliter, ſi D ponatur pro diſtantia, &
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E pro denſitate Fluidi compreſſi, & vires centrifugæ ſint reciproce
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ut diſtantiæ dignitas quælibet D
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n
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, cujus index eſt numerus
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n
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; vi
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res comprimentes erunt ut latera cubica dignitatis E
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+2
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, cujus
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index eſt numerus
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+2: & contra. </
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<
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>Intelligenda vero ſunt hæc
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omnia de particularum Viribus centrifugis quæ terminantur in par
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ticulis proximis, aut non longe ultra diffunduntur. </
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>Exemplum
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habemus in corporibus Magneticis. </
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minatur fere in ſui generis corporibus ſibi proximis. </
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>Magnetis
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virtus per interpoſitam laminam ferri contrahitur, & in lamina fere
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terminatur. </
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>Nam corpora ulteriora non tam a Magnete quam a
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lamina trahuntur. </
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>Ad eundem modum ſi particulæ fugant alias ſui
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generis particulas ſibi proximas, in particulas autem remotiores
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virtutem nullam exerceant, ex hujuſmodi particulis componentur
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Fluida de quibus actum eſt in hac Propoſitione. </
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<
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>Quod ſi particulæ
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cujuſque virtus in infinitum propagetur, opus erit vi majori ad æqua
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lem condenſationem majoris quantitatis Fluidi. </
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<
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>An vero Fluida
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Elaſtica ex particulis ſe mutuo fugantibus conſtent, Quæſtio Phy
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ſica eſt. </
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<
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>Nos proprietatem Fluidorum ex ejuſmodi particulis con
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ſtantium Mathematice demonſtravimus, ut Philoſophis anſam præ
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beamus Quæſtionem illam tractandi. </
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