Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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DE MOTU
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CORPORUM</
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Corol.
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5. Et ſi Globi moveantur in Mediis diverſis; ſpatium in
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Medio, quod cæteris paribus magis reſiſtit, diminuendum erit in
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ratione majoris reſiſtentiæ. </
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nem) diminuetur in ratione reſiſtentiæ auctæ, & ſpatium in ra
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tione temporis. </
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LEMMA II.
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Momentum Genitæ æquatur Momentis laterum ſingulorum gene
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rantium in eorundem laterum indices dignitatum & coefficien
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tia continue ductis.
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<
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>Genitam voco quantitatem omnem quæ ex lateribus vel termi
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nis quibuſcunque, in Arithmetica per multiplicationem, diviſionem,
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& extractionem radicum; in Geometria per inventionem vel con
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tentorum & laterum, vel extremarum & mediarum proportionalium,
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abſque additione & ſubductione generatur. </
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>Ejuſmodi quantita
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tes ſunt Facti, Quoti, Radices, Rectangula, Quadrata, Cubi, Latera
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quadrata, Latera cubica, & ſimiles. </
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>Has quantitates ut indeterminatas
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& inſtabiles, & quaſi motu fluxuve perpetuo creſcentes vel decre
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ſcentes, hic conſidero; & earum incrementa vel decrementa momen
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tanea ſub nomine Momentorum intelligo: ita ut incrementa pro
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momentis addititiis ſeu affirmativis, ac decrementa pro ſubductitiis
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ſeu negativis habeantur. </
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<
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>Cave tamen intellexeris particulas fiNI
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tas. </
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>Particulæ finitæ non ſunt momenta, ſed quantitates ipſæ ex
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momentis genitæ. </
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>Intelligenda ſunt principia jamjam naſcentia fi
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nitarum magnitudinum. </
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>Neque enim ſpectatur in hoc Lemmate
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magnitudo momentorum, ſed prima naſcentium proportio. </
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>Eo
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dem recidit ſi loco momentorum uſurpentur vel velocitates incre
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mentorum ac decrementorum, (quas etiam motus, mutationes
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& fluxiones quantitatum nominare licet) vel finitæ quævis quanti
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tates velocitatibus hiſce proportionales. </
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<
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generantis Coefficiens eſt quantitas, quæ oritur applicando GeNI
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tam ad hoc latus. </
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<
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>Igitur ſenſus Lemmatis eſt, ut, ſi quantitatum quarumcunque
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perpetuo motu creſcentium vel decreſcentium A, B, C, &c. </
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menta, vel mutationum velocitates dicantur
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a, b, c,
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&c. </
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<
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vel mutatio geniti rectanguli AB fuerit
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a
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B+
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b
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A, & geniti con
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tenti ABC momentum fuerit
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a
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BC+
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b
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AC+
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c
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AB: & genitarum </
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