Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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1
DE MOTU
CORPORUM
PROPOSITIO LVII. THEOREMA XX.
Corpora duo ſe invicem trahentia deſcribunt, & circum commune
centrum gravitatis, & circum ſe mutuo, Figuras ſimiles.
Sunt enim diſtantiæ a communi gravitatis centro reciproce pro­
portionales corporibus, atque adeo in data ratione ad invicem, &
componendo, in data ratione ad diſtantiam totam inter corpora.

Feruntur autem hæ diſtantiæ circum terminos ſuos communi motu
angulari, propterea quod in directum ſemper jacentes non mutant
inclinationem ad ſe mutuo.
Lineæ autem rectæ, quæ ſunt in data
ratione ad invicem, & æquali motu angulari circum terminos ſuos
feruntur, Figuras circum eoſdem terminos (in planis quæ una cum
his terminis vel quieſcunt vel motu quovis non angulari moven­
tur) deſcribunt omnino ſimiles.
Proinde ſimiles ſunt Figuræ quæ
his diſtantiis circumactis deſcribuntur. Q.E.D.
PROPOSITIO LVIII. THEOREMA XXI.
Si corpora duo Viribus quibuſvis ſe mutuo trahunt, & interea re­
volvuntur circa gravitatis centrum commune: dico quod Fi­
guris, quas corpora ſic mota deſcribunt circum ſe mutuo, potest
Figura ſimilis & æqualis, circum corpus alterutrum immotum,
Viribus iiſdem deſcribi.
Revolvantur corpora S, Pcirca commune gravitatis centrum
C,pergendo de Sad Tdeque Pad queA dato puncto sipſis
104[Figure 104]
SP, TQæquales & parallelæ ducantur ſemper sp, sq; & Curva
pqvquam punctum p,revolvendo circum punctum immotum s,

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