Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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Dein junctis
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SI, SD,
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fiant ſegmentis
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SEIS, SEDS,
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ſec
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tores
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HSK, HSk
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æquales, & per Prop. </
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>XXXV, corpus
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G
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deſcri
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bet ſpatium
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GC
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eodem Tempore quo corpus
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K
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deſcribere po
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teſt arcum
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Kk. </
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E. F.
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LIBER
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PRIMUS.</
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PROPOSITIO XXXVIII. THEOREMA XII.
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Poſito quod Vis centripeta proportionalis ſit altitudini ſeu diſtantiæ lo
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eorum a centro, dico quod cadentium Tempora, Velocitates & Spa
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tia deſcripta ſunt arcubus, arcuumque finibus rectis & ſinibus
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verſis reſpective proportionalia.
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>Cadat corpus de loco quovis
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A
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ſecun
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dum rectam
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AS
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; & centro virium
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S,
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in
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tervallo
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AS,
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deſcribatur Circuli quadrans
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AE,
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ſitque
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CD
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ſinus rectus arcus cujuſ
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vis
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AD
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; & corpus
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A,
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Tempore
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AD,
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ca
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dendo deſcribet Spatium
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AC,
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inque loco
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C
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acquiret Velocitatem
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CD.
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<
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tione X, quo Propoſitio XXXII, ex Propo
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ſitione XI demonſtrata fuit. </
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Corol.
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1. Hinc æqualia ſunt Tempora quibus corpus unum de loco
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A
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cadendo pervenit ad centrum
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S,
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& corpus aliud revolvendo de
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ſcribit arcum quadrantalem
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ADE.
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Corol.
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2. Proinde æqualia ſunt Tempora omnia quibus corpora de
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locis quibuſvis ad uſque centrum cadunt. </
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pora omnia periodica (per Corol. </
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<
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>3. Prop. </
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<
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>IV.) æquantur. </
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