Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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tes æquales. </
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<
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>Quoniam diſtantiæ
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CD, CI
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æquantur, erunt vi</
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res centripetæ in
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D
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&
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I
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æquales. </
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<
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>Exponantur hæ vires per æ
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quales lineolas
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DE, IN
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; & ſi vis una
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IN
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(per Legum Corol. </
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>2.)
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reſolvatur in duas
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NT
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&
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IT,
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vis
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NT,
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agendo ſecundum lineam
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NT
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corporis curſui
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ITK
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perpendicularem, nil mutabit velocita
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tem corporis in curſu illo, ſed retrahet ſolummodo corpus a cur
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ſu rectilineo, facietQ.E.I.ſum de Orbis tangente perpetuo deflecte
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re, inque via curvilinea
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ITKk
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progredi. </
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<
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>In hoc effectu produ
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cendo vis illa tota conſumetur: vis autem altera
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IT,
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ſecundum
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corporis curſum agendo, tota accelerabit illud, ac dato tem
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pore quam minimo accelerationem generabit ſibi ipſi proportiona
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lem. </
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>Proinde corporum in
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D
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&
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I
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accelerationes æqualibus tem
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poribus factæ (ſi ſumantur linearum naſcentium
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DE, IN, IK,
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IT, NT
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rationes primæ) ſunt ut lineæ
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DE, IT:
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temporibus au
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tem inæqualibus ut lineæ illæ & tempora conjunctim. </
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<
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>Tempora
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autem quibus
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DE
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&
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IK
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deſcribuntur, ob æqualitatem velocita
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tum ſunt ut viæ deſcriptæ
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DE
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&
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IK,
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adeoque accelerationes, in
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curſu corporum per lineas
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DE
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&
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IK,
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funt ut
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DE
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&
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IT, DE
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&
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IK
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conjunctim, id eſt ut
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DE quad
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&
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ITXIK rectangulum.
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Sed
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rectangulum ITXIK
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æquale eſt
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IN quadrato,
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hoc eſt, æquale
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DE quadrato;
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& propterea accelerationes in tranſitu corporum a
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D
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&
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I
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ad
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E
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&
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K
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æquales generantur. </
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<
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