Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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DE MOTU
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CORPORUM</
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PROPOSITIO LVII. THEOREMA XX.
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Corpora duo ſe invicem trahentia deſcribunt, & circum commune
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centrum gravitatis, & circum ſe mutuo, Figuras ſimiles.
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>Sunt enim diſtantiæ a communi gravitatis centro reciproce pro
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portionales corporibus, atque adeo in data ratione ad invicem, &
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componendo, in data ratione ad diſtantiam totam inter corpora. </
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Feruntur autem hæ diſtantiæ circum terminos ſuos communi motu
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angulari, propterea quod in directum ſemper jacentes non mutant
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inclinationem ad ſe mutuo. </
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<
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>Lineæ autem rectæ, quæ ſunt in data
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ratione ad invicem, & æquali motu angulari circum terminos ſuos
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feruntur, Figuras circum eoſdem terminos (in planis quæ una cum
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his terminis vel quieſcunt vel motu quovis non angulari moven
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tur) deſcribunt omnino ſimiles. </
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<
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>Proinde ſimiles ſunt Figuræ quæ
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his diſtantiis circumactis deſcribuntur.
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Q.E.D.
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PROPOSITIO LVIII. THEOREMA XXI.
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Si corpora duo Viribus quibuſvis ſe mutuo trahunt, & interea re
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volvuntur circa gravitatis centrum commune: dico quod Fi
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guris, quas corpora ſic mota deſcribunt circum ſe mutuo, potest
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Figura ſimilis & æqualis, circum corpus alterutrum immotum,
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Viribus iiſdem deſcribi.
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<
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>Revolvantur corpora
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S, P
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circa commune gravitatis centrum
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C,
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pergendo de
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S
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ad
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T
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deque
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P
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ad
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A dato puncto
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s
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ipſis
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SP, TQ
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æquales & parallelæ ducantur ſemper
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sp, sq
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; & Curva
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pqv
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quam punctum
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p,
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revolvendo circum punctum immotum
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s,
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