Newton, Isaac - Philosophia naturalis principia mathematica

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1perimetro Figuræ revolventis uCp,eodemque tempore deſcribet
arcum ejus upquo corpus aliud Parcum ipſi ſimilem & æqualem
VPin Figura quieſcente VPKdeſcribere poteſt. Quæratur igi
tur, per Corollarium quintum propoſitionis VI, Vis centripeta qua
corpus revolvi poſſit in Curva illa linea quam punctum pdeſcribit
in plano immobili, & ſolvetur Problema. q.E.F.

DE MOTU
CORPORUM

PROPOSITIO XLIV. THEOREMA XIV.

Differentia Virium, quibus corpus in Orbe quieſcente, & corpus a
liud in eodem Orbe revolvente æqualiter moveri poſſunt, est
in triplicata ratione communis altitudinis inverſe.

Partibus Orbis quie

94[Figure 94]
ſcentis VP, PKſunto
ſimiles & æquales Or
bis revolventis partes
up, pk; & punctorum
P, Kdiſtantia intelli
gatur eſſe quam miNI
ma. A puncto kin re
ctam pCdemitte per
pendiculum kr,idem
que produc ad m,ut ſit
mrad krut angulus
VCpad angulum VCP.
Quoniam corporum al
titudines PC& pC, KC
& kCſemper æquan
tur, manifeſtum eſt quod linearum PC& pCincrementa vel
decrementa ſemper ſint æqualia, ideoque ſi corporum in locis
P& pexiſtentium diſtinguantur motus ſinguli (per Legum
Corol. 2.) in binos, quorum hi verſus centrum, ſive ſecundum
lineas PC, pCdeterminentur, & alteri prioribus tranſverſi ſint,
& ſecundum lineas ipſis PC, pCperpendiculares directionem
habeant; motus verſus centrum erunt æquales, & motus tranſ
verſus corporis perit ad motum tranſverſum corporis P,ut mo
tus angularis lineæ pC,ad motum angularem lineæ PC,id eſt,

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