Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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DE MOTU
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CORPORUM</
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SECTIO VI.
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De Motu & Reſiſtentia Corporum Funependulorum.
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PROPOSITIO XXIV. THEOREMA XIX.
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Quantitates materiæ in corporibus funependulis, quorum centra
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oſcillationum a centro ſuſpenſionis æqualiter diſtant, ſunt in ra
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tione compoſita ex ratione ponderum & ratione duplicata tem
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porum oſcillationum in vacuo.
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>Nam velocitas, quam data vis in data materia dato tempore ge
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nerare poteſt, eſt ut vis & tempus directe, & materia inverſe. </
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>Quo
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major eſt vis vel majus tempus vel minor materia, eo major gene
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rabitur velocitas. </
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>Id quod per motus Legem ſecundam manife
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ſtum eſt. </
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>Jam vero ſi Pendula ejuſdem ſint longitudinis, vires mo
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trices in locis a perpendiculo æqualiter diſtantibus ſunt ut ponde
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ra: ideoque ſi corpora duo oſcillando deſcribant arcus æquales, &
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arcus illi dividantur in partes æquales; cum tempora quibus cor
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pora deſcribant ſingulas arcuum partes correſpondentes ſint ut
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tempora oſcillationum totarum, erunt velocitates ad invicem in
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correſpondentibus oſcillationum partibus, ut vires motrices & tota
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oſcillationum tempora directe & quantitates materiæ reciproce:
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adeoque quantitates materiæ ut vires & oſcillationum tempora di
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recte & velocitates reciproce. </
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<
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>Sed velocitates reciproce ſunt ut
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tempora, atque adeo tempora directe & velocitates reciproce ſunt
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ut quadrata temporum, & propterea quantitates materiæ ſunt ut
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vires motrices & quadrata temporum, id eſt, ut pondera & quadra
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ta temporum.
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E. D.
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Corol.
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1. Ideoque ſi tempora ſunt æqualia, quantitates materiæ
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in ſingulis corporibus erunt ut pondera. </
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Corol.
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2. Si pondera ſunt æqualia, quantitates materiæ erunt ut
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quadrata temporum. </
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Corol.
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3. Si quantitates materiæ æquantur, pondera erunt reci
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proce ut quadrata temporum. </
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