Newton, Isaac - Philosophia naturalis principia mathematica

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1in caſu hujus Corollarii, ſit DS+DHad DHut 4 DSad L,&
diviſim DSad DHut 4 DS-Lad L.

DE MOTU
CORPORUM

Corol.2. Unde ſi datur corporis velocitas in vertice principali D,
invenietur Orbita expedite, capiendo ſcilicet latus rectum ejus, ad
duplam diſtantiam DS,in duplicata ratione velocitatis hujus datæ
ad velocitatem corporis in Circulo, ad diſtantiam DS,gyrantis (per
Corol. 3. Prop. XVI.) dein DHad DSut latus rectum ad differen
tiam inter latus rectum & 4 DS.

Corol.3. Hinc etiam ſi corpus moveatur in Sectione quacunque
Conica, & ex Orbe ſuo impulſu quocunque exturbetur; cognoſci
poteſt Orbis in quo poſtea curſum ſuum peraget. Nam componen
do proprium corporis motum cum motu illo quem impulſus ſolus
generaret, habebitur motus quocum corpus de dato impulſus loco,
ſecundum rectam poſitione datam, exibit.

Corol.4. Et ſi corpus illud vi aliqua extrinſecus impreſſa conti
nuo perturbetur, innoteſcet curſus quam proxime, colligendo mu
tationes quas vis illa in punctis quibuſdam inducit, & ex ſeriei ana
logia mutationes continuas in locis intermediis æſtimando.

Scholium.

Si corpus Pvi centripeta ad

27[Figure 27]
punctum quodcunQ.E.D.tum R
tendente moveatur in perimetro
datæ cujuſcunque Sectionis co
nicæ cujus centrum ſit C,& re
quiratur Lex vis centripetæ: du
catur CGradio RPparalle
la, & Orbis tangenti PGoc
currens in G; & vis illa (per
Corol. 1 & Schol. Prop. X, & Corol. 3 Prop. VII.) erit ut
(CG cub./RP quad.)

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