Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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DE MOTU
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CORPORUM</
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<
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>Si longitudo Cylindri augeatur vel minuatur: motus ejus ut &
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tempus quo quadruplum longitudinis ſuæ deſcribit, augebitur vel
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minuetur in eadem ratione; adeoque Vis illa qua motus auctus vel
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diminutus, tempore pariter aucto vel diminuto, generari vel tolli
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poſſit, non mutabitur; ac proinde etiamnum æqualis eſt reſi
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ſtentiæ Cylindri, nam & hæc quoQ.E.I.mutata manet per Lem
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ma IV.
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<
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>Si denſitas Cylindri augeatur vel minuatur: motus ejus ut &
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Vis qua motus eodem tempore generari vel tolli poteſt, in eadem
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ratione augebitur vel minuetur. </
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>Reſiſtentia itaque Cylindri cu
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juſcunque erit ad Vim qua totus ejus motus, interea dum quadru
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plum longitudinis ſuæ deſcribit, vel generari poſſit vel tolli, ut
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denſitas Medii ad denſitatem Cylindri quamproxime.
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Q.E.D.
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<
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>Fluidum autem comprimi debet ut ſit continuum, continuum
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vero eſſe & non elaſticum ut preſſio omnis quæ ab ejus compreſſi
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one oritur propagetur in inſtanti &, in omnes moti corporis partes
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æqualiter agendo, reſiſtentiam non mutet. </
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>Preſſio utique quæ a
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motu corporis oritur, impenditur in motum partium fluidi gene
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randum & Reſiſtentiam creat. </
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>Preſſio autem quæ oritur a com
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preſſione fluidi, utcunque fortis ſit, ſi propagetur in inſtanti, nul
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lum generat motum in partibus fluidi continui, nullam omnino in
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ducit motus mutationem; ideoque reſiſtentiam nec auget nec mi
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nuit. </
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<
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>Certe Actio fluidi, quæ ab ejus compreſſione oritur, fortior
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eſſe non poteſt in partes poſticas corporis moti quam in ejus par
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tes anticas, ideoque reſiſtentiam in hac Propoſitione deſcriptam
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minuere non poteſt: & fortior non erit in partes anticas quam in
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poſticas, ſi modo propagatio ejus infinite velocior ſit quam motus
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corporis preſſi. </
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<
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>Infinite autem velocior erit & propagabitur in in
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ſtanti, ſi modo fluidum ſit continuum & non elaſticum.
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Corol.
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1. Cylindrorum, qui ſecundum longitudines ſuas in Mediis
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continuis infinitis uniformiter progrediuntur, reſiſtentiæ ſunt in ra
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tione quæ componitur ex duplicata ratione velocitatum & dupli
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cata ratione diametrorum & ratione denſitatis Mediorum.
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Corol.
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2. Si amplitudo canalis non augeatur in infinitum, ſed Cy
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lindrus in Medio quieſcente incluſo ſecundum longitudinem ſuam
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progrediatur, & interea axis ejus cum axe canalis coincidat: Reſi
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ſtentia ejus erit ad vim qua totus ejus motus, quo tempore qua
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druplum longitudinis ſuæ deſcribit, vel generari poſſit vel tolli,
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in ratione quæ componitur ex ratione
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EFq
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ad
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-1/2
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PQq
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