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.
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
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.
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,
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,