1
DE MOTU
CORPORUM
CORPORUM
Cas.2. Si Figura illa RPBHyperbola eſt, deſcribatur ad ean
dem diametrum principalem ABHyperbola rectangula BED:
& quoniam areæ CSP, CBfP, SPfBſunt ad areas CSD,
CBED, SDEB,ſingulæ ad ſingulas, in data ratione altitudi
num CP, CD; & area SPfB
81[Figure 81]
proportionalis eſt tempori quo
corpus Pmovebitur per arcum
PfB; erit etiam area SDEBei
dem tempori proportionalis.
Minuatur latus rectum Hyper
bolæ RPBin infinitum ma
nente latere tranſverſo, & coibit
arcus PBcum recta CB& um
bilicus Scum vertice B& recta
SDcum recta BD.Proinde a
rea BDEBproportionalis erit
tempori quo corpus Crecto
deſcenſu deſcribit lineam CB.
que E. I.
dem diametrum principalem ABHyperbola rectangula BED:
& quoniam areæ CSP, CBfP, SPfBſunt ad areas CSD,
CBED, SDEB,ſingulæ ad ſingulas, in data ratione altitudi
num CP, CD; & area SPfB
81[Figure 81]proportionalis eſt tempori quo
corpus Pmovebitur per arcum
PfB; erit etiam area SDEBei
dem tempori proportionalis.
Minuatur latus rectum Hyper
bolæ RPBin infinitum ma
nente latere tranſverſo, & coibit
arcus PBcum recta CB& um
bilicus Scum vertice B& recta
SDcum recta BD.Proinde a
rea BDEBproportionalis erit
tempori quo corpus Crecto
deſcenſu deſcribit lineam CB.
que E. I.
Cas.3. Et ſimili argumento ſi
Figura RPBParabola eſt, &
eodem vertice principali Bde
ſcribatur alia Parabola BED,
quæ ſemper maneat data interea
dum Parabola prior in cujus perimetro corpus Pmovetur, dimi
nuto & in nihilum redacto ejus latere recto, conveniat cum linea
CB; fiet ſegmentum Parabolicum BDEBproportionale tempori
quo corpus illud Pvel Cdeſcendet ad centrum Svel B. que E. I.
Figura RPBParabola eſt, &
eodem vertice principali Bde
ſcribatur alia Parabola BED,
quæ ſemper maneat data interea
dum Parabola prior in cujus perimetro corpus Pmovetur, dimi
nuto & in nihilum redacto ejus latere recto, conveniat cum linea
CB; fiet ſegmentum Parabolicum BDEBproportionale tempori
quo corpus illud Pvel Cdeſcendet ad centrum Svel B. que E. I.
PROPOSITIO XXXIII. THEOREMA IX.
Poſitis jam inventis, dico quod corporis cadentis Velocitas in loco quo
visC est ad velocitatem corporis centroB intervalloBC Circu
lum deſcribentis, in ſubduplicata ratione quamAC, diſtantia cor
poris a Circuli vel Hyperbolæ rect angulæ vertice ulterioreA, habet
ad Figuræ ſemidiametrum principalem1/2 AB.
visC est ad velocitatem corporis centroB intervalloBC Circu
lum deſcribentis, in ſubduplicata ratione quamAC, diſtantia cor
poris a Circuli vel Hyperbolæ rect angulæ vertice ulterioreA, habet
ad Figuræ ſemidiametrum principalem1/2 AB.
Biſecetur AB,communis utriuſque Figuræ RPB, DEBdia
meter, in O; & agatur recta PTquæ tangat Figuram RPBin P,atque
meter, in O; & agatur recta PTquæ tangat Figuram RPBin P,atque
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