Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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Corol.
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4. Unde cum quadrata temporum, cæteris paribus, ſint ut
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longitudines pendulorum; ſi & tempora & quantitates materiæ æ
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qualia ſunt, pondera erunt ut longitudines pendulorum. </
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LIBER
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SECUNDUS.</
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Corol.
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5. Et univerſaliter, quantitas materiæ pendulæ eſt ut pon
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dus & quadratum temporis directe, & longitudo penduli inverſe. </
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Corol.
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6. Sed & in Medio non reſiſtente quantitas materiæ pen
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dulæ eſt ut pondus comparativum & quadratum temporis directe
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& longitudo penduli inverſe. </
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>Nam pondus comparativum eſt vis
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motrix corporis in Medio quovis gravi, ut ſupra explicui; adeoque
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idem præſtat in tali Medio non reſiſtente atque pondus abſolutum
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in vacuo. </
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Corol.
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7. Et hinc liquet ratio tum comparandi corpora inter ſe,
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quoad quantitatem materiæ in ſingulis; tum comparandi pondera
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ejuſdem corporis in diverſis locis, ad cognoſcendam variationem
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gravitatis. </
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ſemper quantitatem materiæ in corporibus ſingulis eorum ponderi
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proportionalem eſſe. </
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PROPOSITIO XXV. THEOREMA XX:
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Corpora Funependula quibus, in Medio quovis, reſiſtitur in ratione
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momentorum temporis, & corpora Funependula quæ in ejuſdem
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gravitatis ſpecificæ Medio non reſiſtente moventur, oſcillatio
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nes in Cycloide eodem tempore peragunt, & arcuum partes pro
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portionales ſimul deſcribunt.
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AB
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Cycloidis
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arcus, quem corpus
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D
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tempore quovis in
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Medio non reſiſtente
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oſcillando deſcribit. </
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Biſecetur idem in
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C,
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ita ut
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C
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ſit infimum
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ejus punctum; & erit
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vis acceleratrix qua
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corpus urgetur in lo
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co quovis
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D
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vel
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d
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vel
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E
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ut longitudo arcus
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CD
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vel
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Cd
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vel
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CE.
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Exponatur vis illa per eundem arcum; &
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cum reſiſtentia ſit ut momentum temporis, adeoQ.E.D.tur, expona-</
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