Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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dex eſt (
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)-3. Id quod per Exempla ſecunda manifeſtum eſt. </
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Unde liquet vim illam in majore quam triplicata altitudinis ratione,
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in receſſu a centro, decreſcere non poſſe: Corpus tali vi revolvens
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deque Apſide diſcedens, ſi cæperit deſcendere nunquam perveniet
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ad Apſidem imam ſeu altitudinem minimam, ſed deſcendet uſque ad
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centrum, deſcribens Curvam illam lineam de qua egimus in Cor. </
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<
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>3.
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Prop. </
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<
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>XLI. </
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>Sin cæperit illud, de Apſide diſcedens, vel minimum
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aſcendere; aſcendet in infinitum, neque unquam perveniet ad Ap
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ſidem ſummam. </
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<
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>Deſcribet enim Curvam illam lineam de qua ac
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tum eſt in eodem Corol. </
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<
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>& in Corol. </
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<
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>6, Prop. </
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>XLIV. </
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>Sic & ubi
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vis, in receſſu a centro, decreſcit in majore quam triplicata ratione
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altitudinis, corpus de Apſide diſcedens, perinde ut cæperit deſcen
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dere vel aſcendere, vel deſcendet ad centrum uſque vel aſcendet
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in infinitum. </
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<
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>At ſi vis, in receſſu a centro, vel decreſcat in minore
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quam triplicata ratione altitudinis, vel creſcat in altitudinis ratione
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quacunque; corpus nunquam deſcendet ad centrum uſque, ſed ad
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Apſidem imam aliquando perveniet: & contra, ſi corpus de Apſi
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de ad Apſidem alternis vicibus deſcendens & aſcendens nunquam
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appellat ad centrum; vis in receſſu a centro aut augebitur, aut in
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minore quam triplicata altitudinis ratione decreſcet: & quo ci
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tius corpus de Apſide ad Apſidem redierit, eo longius ratio virium
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recedet a ratione illa triplicata. </
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<
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>Ut ſi corpus revolutionibus 8 vel
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4 vel 2 vel 1 1/2 de Apſide ſumma ad Apſidem ſummam alterno de
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ſcenſu & aſcenſu redierit; hoc eſt, ſi fuerit
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m
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ad
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ut 8 vel 4 vel
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2 vel 1 1/2 ad 1, adeoque (
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nn/mm
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)-3 valeat (1/64)-3 vel (1/16) -3 vel 1/4-3
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vel 4/9-3: erit vis ut A
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(1/64)-3
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vel A
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(1/16)-3
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vel A
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1/4-3
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vel A
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4/9-3
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,
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id eſt, reciproce ut A
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3-(1/64)
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vel A
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3-(1/16)
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vel A
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3-1/4
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vel A
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3-4/9
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. </
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Si corpus ſingulis revolutionibus redierit ad Apſidem eandem immo
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tam; erit
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ad
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ut 1 ad 1, adeoque A (
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nn/mm
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)-3 æqualis A
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-2
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ſeu (1/AA
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& propterea decrementum virium in ratione duplicata altitudinis,
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ut in præcedentibus demonſtratum eſt. </
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<
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>Si corpus partibus revo
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lutionis unius vel tribus quartis, vel duabus tertiis, vel una ter
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tia, vel una quarta, ad Apſidem eandem redierit; erit
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m
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ad
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ut
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1/4 vel 2/3 vel 1/3 vel 1/4 ad 1, adeoque A(
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nn/mm
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)-3 æqualis A
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(16/9)-3
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vel
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A
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9/4-3
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vel A
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9-3
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vel A
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16-3
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; & propterea vis aut reciproce ut </
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