Gravesande, Willem Jacob 's - Physices elementa mathematica, experimentis confirmata sive introductio ad philosophiam Newtonianam; Tom. 1

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12063MATHEMATICA. LIB. I. CAP XVIII. tur, ſi eodem tempore cadere incipiant, ſunt ſemper in ea-
dem ratione quam in principio caſus ; ergo ſpatia 11251. 263. tempore percurrunt, quæ ſunt in ratione longitudinis plani
ad illius altitudinem.
22237.

In plano AB ſpatium a corpore percurſum, dum aliud li-
33266. bere cadit per altitudinem plani AC, determinatur, du-
44TAB. X.
fig. 9. cendo ad AB perpendicularem CG: tunc enim longitudo
plani AB eſt ad illius altitudinem AC, ut AC ad AG. 558 El. VI. circulus deſcribatur diametro AC, punctum G erit in pe-
ripheria circuli; quia angulus in ſemicirculo, ut AGC,
ſemper eſt rectus ; & ideo punctum ut G, pro plano 6631 El. III. cunque inclinato, ſemper eſt in eadem illa peripheria: un-
de ſequitur, chordas omnes, ut AG eſſe inter ſe ut vires,
quibus corpora ſuper his deſcendere conantur; & has per-
curri a corporibus devolventibus, in tempore in quo cor-
pus, libere cadendo, poteſt percurrere diametrum AC;
& ita tempora devolutionum per illas chordasſunt æqualia.

Per punctum C nulla poteſt duci chorda ut HC, quin de-
tur per A chorda ut AG ei parallela, id eſt, æqualiter in-
clinata, & æqualis; igitur in ſemicirculo, ut AHC, Vires
77267. quibus corpora juxta chordas, in puncto infimo terminatas
deſcendere conantur, ſunt inter ſe ut hæ chordæ & quando
88268. corpus ſibi permittitur eodem tempore, ad punctum infimum
ſemicirculi perveniet, ſive libere cadat juxta diametrum,
ſive deſcendat ſuper chorda HC quacunque.

Tempus devolutionis per totum planum AB poteſt confer-
99269. ri cum tempore deſcenſus per plani altitudinem AC; nam
hocce tempus eſt æquale tempori devolutionis per AG; &
quadrata temporum ſunt inter ſe ut AB ad AG ; 1010264 255.AB eſt ad AC ut AC ad AG: quadrata igitur linearum AB &
AC ſunt inter ſe, ut AB ad AG; & ideo iſtæ lineæ AB
& AC ſunt inter ſe, ut tempora deſcenſus per AB, &
AG, aut AC, id eſt, tempora, in eo caſu, ſunt ut ſpa-
tia percurſa.

In eodem caſu velocitates in fine deſcenſus ſunt æquales;
1111270. nam poſt tempora æqualia, quando corpora ſunt in G &

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Scan	Original
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121	64
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Scan	Original
111
112
113
114	57
115	58
116	59
117	60
118	61
119	62
120	63
121	64
122
123
124
125	65
126	66
127	67
128	68
129	69
130	70
131	71
132	72
133
134
135
136	73
137	74
138	75
139	76
140	77