Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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ut velocitas & pars altera ut
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velocitatis quadratum, fit re
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ſiſtentia tota in
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ut
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AP quad
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+2
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BAP.
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Jungantur
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DA,
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DP
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Circulum ſecantes in
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E
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ac
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T,
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& exponatur gravitas per
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DA quad,
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ita ut ſit gravitas ad
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reſiſtentiam in
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P
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ut
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DAq
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ad
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APq
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+2
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BAP:
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& tempus
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aſcenſus omnis ſuturi erit ut
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Circuli ſector
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EDTE.
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DE MOTU
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CORPORUM</
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<
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DVQ,
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ab
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ſcindens & velocitatis
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AP
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momentum
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PQ,
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& Sectoris
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DET
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momentum
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DTV
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da
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to temporis momento reſpondens: & velocitatis decrementum il
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lud
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PQ
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erit ut ſumma virium gravitatis
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DAq
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& reſiſtentiæ
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APq
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+2
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BAP,
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id eſt (per Prop. </
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>2. Elem.) ut
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DPquad.
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Proinde area
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DPQ,
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ipſi
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PQ
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proportionalis, eſt ut
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DP quad
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;
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& area
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DTV,
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(quæ eſt ad aream
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DPQ
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ut
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DTq
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ad
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DPq
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)
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eſt ut datum
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DTQ
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Decreſcit igitur area
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EDT
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uniformiter ad mo
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dum temporis futuri, per ſubductionem datarum particularum
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DTV,
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& propterea tempori aſcenſus futuri proportionalis eſt.
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Q.E.D.
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Caſ.
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2. Si veloci
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tas in aſcenſu cor
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poris exponatur per
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longitudinem
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AP
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ut prius, & reſiſten
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tia ponatur eſſe ut
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APq
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+2
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BAP,
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&
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ſi vis gravitatis mi
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nor ſit quam quæ per
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DAq
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exponi poſ
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ſit; capiatur
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BD
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e
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jus longitudinis, ut
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ſit
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ABq-BDq
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gravitati proportio
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nale, ſitque
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DF
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ipſi
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DB
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perpendicularis & æqualis, & per verticem
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F
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deſcribatur Hy
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perbola
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FTVE
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cujus ſemidiametri conjugatæ ſint
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DB
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&
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DF,
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quæque ſecet
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DA
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in
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E,
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&
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DP, DQ
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in
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T
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&
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V
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; & crit tempus
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aſcenſus futuri ut Hyperbolæ ſector
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TDE.
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