Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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Scholium.
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<
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>Urgeri poteſt corpus a vi centripeta compoſita ex pluribus viri
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bus. </
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>In hoc caſu ſenſus Propoſitionis eſt, quod vis illa quæ ex om
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nibus componitur, tendit ad punctum
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S.
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Porro ſi vis aliqua agat
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perpetuo ſecundum lineam ſuperficiei deſcriptæ perpendicularem;
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hæc faciet ut corpus deflectatur a plano ſui motus: ſed quantita
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tem ſuperficiei deſcriptæ nec augebit nec minuet, & propterea in
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compoſitione virium negligenda eſt. </
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PROPOSITIO III. THEOREMA III.
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Corpus omne, quod radio ad centrum corporis alterius utcunque moti
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ducto deſcribit areas circa centrum illud temporibus proportiona
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les, urgetur vi compoſita ex vi centripeta tendente ad corpus il
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lud alterum, & ex vi omni acceleratrice qua corpus illud alterum
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urgetur.
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<
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>Sit corpus primum
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L
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& corpus alterum
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T:
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& (per Legum Corol. </
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VI.) ſi vi nova, quæ æqualis & contraria ſit illi qua corpus alterum
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urgetur, urgeatur corpus utrumque ſecundum lineas parallelas;
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perget corpus primum
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L
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deſcribere circa corpus alterum
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areas
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eaſdem ac prius: vis autem, qua corpus alterum
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urgebatur, jam
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deſtruetur per vim ſibi æqualem & contrariam; & propterea (per
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Leg. </
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>1.) corpus illud alterum
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ſibimet ipſi jam relictum vel qui
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eſcet vel movebitur uniformiter in directum: & corpus primum
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L
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urgente differentia virium, id eſt, urgente vi reliqua perget areas
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temporibus proportionales circa corpus alterum
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deſcribere. </
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dit igitur (per Theor. </
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>11.) differentia virium ad corpus illud alte
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rum
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ut centrum.
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E. D.
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Corol.
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1. Hinc ſi corpus unum
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radio ad alterum
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ducto de
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ſcribit areas temporibus proportionales; atQ.E.D. vi tota (ſive ſim
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plici, ſive ex viribus pluribus, juxta Legum Corollarium ſecundum,
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compoſita,) qua corpus prius
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L
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urgetur, ſubducatur (per idem Le
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gum Corollarium) vis tota acceleratrix qua corpus alterum urgetur:
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vis omnis reliqua qua corpus prius urgetur tendet ad corpus alte
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rum
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ut centrum. </
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Corol.
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2. Et, ſi areæ illæ ſunt temporibus quamproxime propor
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tionales, vis reliqua tendet ad corpus alterum
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quamproxime. </
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Corol.
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3. Et vice verſa, ſi vis reliqua tendit quamproxime ad </
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