Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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LIBER
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PRIMUS.</
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SECTIO VII.
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De Corporum Aſcenſu & Deſcenſu Rectilineo.
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PROPOSITIO XXXII. PROBLEMA XXIV.
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Poſito quod Vis centripeta ſit reciproce proportionalis quadrato di
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ſtantiæ loeorum a centro, Spatia definire quæ corpus recta cadendo
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datis temporibus deſcribit.
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Cas.
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1. Si Corpus non cadit perpendicu
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lariter deſcribet id, per Corol. </
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>1. Prop. </
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>XIII,
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Sectionem aliquam Conicam cujus umbili
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cus congruit cum centro virium. </
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tio illa Conica
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ARPB
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& umbilicus ejus
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S.
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Et primo ſi Figura Ellipſis eſt, ſuper hu
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jus axe majore
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AB
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deſcribatur Semicirculus
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ADB,
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& per corpus decidens tranſeat rec
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ta
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DPC
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perpendicularis ad axem; actiſque
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DS, PS
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erit area
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ASD
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areæ
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ASP
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at
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que adeo etiam tempori proportionalis. </
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<
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>Ma
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nente axe
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AB
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minuatur perpetuo latitudo
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Ellipſeos, & ſemper manebit area
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ASD
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tempori proportionalis. </
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<
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>Minuatur latitudo
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illa in infinitum: &, Orbe
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APB
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jam coin
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cidente cum axe
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AB
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& umbilico
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S
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cum
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axis termino
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B,
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deſcendet corpus in recta
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AC,
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& area
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ABD
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evadet tempori pro
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portionalis. </
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<
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>Dabitur itaque Spatium
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AC,
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quod corpus de loco
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A
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perpendiculariter
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cadendo tempore dato deſcribit, ſi modo tempori proportiona
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lis capiatur area
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ABD,
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& a puncto
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D
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ad rectam
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AB
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demit
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tatur perpendicularis
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DC.
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E. I.
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