Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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dentibus Corollariis: manifeſtum eſt quod effectus illi omnes, ſtan
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te corporum
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T
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&
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P
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Syſtemate, & mutatis tantum diſtantia
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ST
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&
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vi abſoluta corporis
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S,
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ſint quamproxime in ratione compoſita ex
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ratione directa vis abſolutæ corporis
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S
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& ratione triplicata inverſa
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diſtantiæ
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ST.
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Unde ſi Syſtema corporum
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&
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P
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revolvatur cir
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ca corpus longinquum
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S,
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vires illæ
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NM, ML
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& earum effectus
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erunt (per Corol. </
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>2. & 6. Prop. </
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<
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>IV.) reciproce in duplicata ratione
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temporis periodici. </
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>Et inde etiam, ſi magnitudo corporis
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S
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propor
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tionalis ſit ipſius vi abſolutæ, erunt vires illæ
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NM, ML
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& earum
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effectus directe ut cubus diametri apparentis longinqui corporis
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e
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corpore
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ſpectati, & vice verſa. </
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<
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>Namque hæ rationes eædem ſunt
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atque ratio ſuperior compoſita. </
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LIBER
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PRIMUS.</
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Corol.
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15. Et quoniam ſi, manentibus Orbium
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ESE
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&
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PAB
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forma, proportionibus & inclinatione ad invicem, mutetur eorum
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magnitudo, & ſi corporum
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S
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&
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T
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vel maneant vel mutentur vires
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in data quavis ratio
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ne, hæ vires (hoc eſt,
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vis corporis
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qua cor
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pus
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P
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de recto trami
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te in Orbitam
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PAB
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deflectere, & vis cor
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poris
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qua corpus
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idem
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P
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de Orbita illa
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deviare cogitur) agunt
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ſemper eodem mo
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do & eadem proportione: neceſſe eſt ut ſimiles & proportiona
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les ſint effectus omnes & proportionalia effectuum tempora; hoc
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eſt, ut errores omnes lineares ſint ut Orbium diametri, angulares
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vero iidem qui prius, & errorum linearium ſimilium vel angularium
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æqualium tempora ut Orbium tempora periodica. </
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Corol.
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16. Unde, ſi dentur Orbium formæ & inclinatio ad invi
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cem, & mutentur utcunque corporum magnitudines, vires & di
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ſtantiæ; ex datis erroribus & errorum temporibus in uno Caſu, col
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ligi poſſunt errores & errorum tempora in alio quovis, quam pro
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xime: Sed brevius hac Methodo. </
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<
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>Vires
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NM, ML,
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cæteris ſtan
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tibus, ſunt ut Radius
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TP,
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& harum effectus periodici (per Corol.2,
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Lem. </
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<
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>X) ut vires & quadratum temporis periodici corporis
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P
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con
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junctim. </
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<
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>Hi ſunt errores lineares corporis
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P
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; & hinc errores an
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gulares e centro
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T
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ſpectati (id eſt, tam motus Augis & Nodorum,
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quam omnes in Longitudinem & Latitudinem errores apparentes)
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ſunt, in qualibet revolutione corporis
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P,
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ut quadratum temporis </
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