Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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DE MOTU
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CORPORUM</
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PROPOSITIO XCII. PROBLEMA XLVI.
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Dato Corpore attractivo, invenire rationem decrementi virium cen
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tripetarum in ejus puncta ſingula tendentium.
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>E Corpore dato formanda eſt Sphæra vel Cylindrus aliave figu
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ra regularis, cujus lex attractionis, cuivis decrementi rationi con
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gruens (per Prop. </
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>LXXX, LXXXI, & XCI) inveniri poteſt. </
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ctis experimentis invenienda eſt vis attractionis in diverſis diſtan
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tiis, & lex attractionis in totum inde patefacta dabit rationem de
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crementi virium partium ſingularum, quam invenire oportuit. </
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PROPOSITIO XCIII. THEOREMA XLVII.
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Si Solidum ex una parte planum, ex reliquis autem partibus infiNI
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tum, conſtet ex particulis æqualibus æqualiter attractivis, qua
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rum vires in receſſu a Solido decreſcunt in ratione poteſtatis cu
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juſvis diſtantiarum pluſquam quadraticæ, & vi Solidi totius cor
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puſculum ad utramvis plani partem conſtitutum trahatur: dico
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quod Solidi vis illa attractiva, in receſſu ab ejus ſuperficie pla
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na, decreſcet in ratione poteſtatis, cujus latus est diſtantia cor
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puſculi a plano, & Index ternario minor quam Index poteſta
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tis diſtantiarum.
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Cas.
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1. Sit
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LGl
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planum
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quo Solidum terminatur. </
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Jaceat Solidum autem ex
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parte plani hujus verſus
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I,
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inque plana innumera
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mHM, nIN,
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&c. </
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GL
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parallela reſolvatur. </
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>Et
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primo collocetur corpus at
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tractum
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C
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extra Solidum. </
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Agatur autem
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CGHI
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pla
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nis illis innumeris perpendicularis, & decreſcant vires attractivæ
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punctorum Solidi in ratione poteſtatis diſtantiarum, cujus index ſit
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numerus
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n
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ternario non minor. </
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<
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>XC) </
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