1aream ILTut OQad OC.Dein perpendiculo MNabſcindatur
area Hyperbolica PINMquæ ſit ad aream Hyperbolicam PIEQ
ut arcus CZad arcum BCdeſcenſu deſcriptum. Et ſi perpendicu
lo RGabſcindatur area Hyperbolica PIGR,quæ ſit ad aream
PIEQut arcus quilibet CDad arcum BCdeſcenſu toto de
ſcriptum: erit reſiſtentia in loco Dad vim gravitatis, ut area
(OR/OQ)IEF-IGHad aream PIENM.
area Hyperbolica PINMquæ ſit ad aream Hyperbolicam PIEQ
ut arcus CZad arcum BCdeſcenſu deſcriptum. Et ſi perpendicu
lo RGabſcindatur area Hyperbolica PIGR,quæ ſit ad aream
PIEQut arcus quilibet CDad arcum BCdeſcenſu toto de
ſcriptum: erit reſiſtentia in loco Dad vim gravitatis, ut area
(OR/OQ)IEF-IGHad aream PIENM.
DE MOTU
CORPORUM
CORPORUM
Nam cum vires a gravitate oriundæ quibus corpus in locis Z, B, D,
aurgetur, ſint ut arcus CZ, CB, CD, Ca,& arcus illi ſint ut areæ
PINM, PIEQ, PIGR, PITC; exponantur tum arcus tum vi
res per has areas reſpective. Sit inſuper Ddſpatium quam minimum
a corpore deſcendente deſcriptum, & exponatur idem per aream
quam minimam RGgrparallelis RG, rgcomprehenſam; & pro
178[Figure 178]
ducatur rgad h,ut ſint GHhg,& RGgrcontemporanea arearum
IGH, PIGRdecrementa. Et areæ (OR/OQ)IEF-IGHincremen
tum GHhg-(Rr/OQ)IEF,ſeu RrXHG-(Rr/OQ)IEF,erit ad areæ
PIGRdecrementum RGgrſeu RrXRG,ut HG-(IEF/OQ)
ad RG; adeoque ut ORXHG-(OR/OQ)IEFad ORXGRſeu
OPXPI,hoc eſt (ob æqualia ORXHG, ORXHR-ORXGR,
ORHK-OPIK, PIHR& FIGR+IGH) ut PIGR+
IGH-(OR/OQ)IEFad OPIK.Igitur ſi area (OR/OQ)IEF-IGH
aurgetur, ſint ut arcus CZ, CB, CD, Ca,& arcus illi ſint ut areæ
PINM, PIEQ, PIGR, PITC; exponantur tum arcus tum vi
res per has areas reſpective. Sit inſuper Ddſpatium quam minimum
a corpore deſcendente deſcriptum, & exponatur idem per aream
quam minimam RGgrparallelis RG, rgcomprehenſam; & pro
178[Figure 178]ducatur rgad h,ut ſint GHhg,& RGgrcontemporanea arearum
IGH, PIGRdecrementa. Et areæ (OR/OQ)IEF-IGHincremen
tum GHhg-(Rr/OQ)IEF,ſeu RrXHG-(Rr/OQ)IEF,erit ad areæ
PIGRdecrementum RGgrſeu RrXRG,ut HG-(IEF/OQ)
ad RG; adeoque ut ORXHG-(OR/OQ)IEFad ORXGRſeu
OPXPI,hoc eſt (ob æqualia ORXHG, ORXHR-ORXGR,
ORHK-OPIK, PIHR& FIGR+IGH) ut PIGR+
IGH-(OR/OQ)IEFad OPIK.Igitur ſi area (OR/OQ)IEF-IGH