Full text: Angeli, Stefano: Miscellaneum Hyperbolicum et Parabolicum

erit 24; IS, erit 1; & B S, 15. Et qualium B D,
erit 48, talium I S, erit 2, & BS, 30. Sed qualium
IS, erat 2, talium S T, erat 3. Ergo qualium B D,
erit 48, talium B T, erit 33, & T D, 15. Ergo
centrum grauitatis ſemifuſi parabolici quadratici ſic
diuidit B D, in T, vt B T, ſit ad T D, vt 33, ad
15; & ſubtriplando terminos, vt 11, ad 5.

68.1.

0136-01

Sed non ſolum ſupradicta methodo reperiemus
centrum grauitatis ſemifuſi parabolici, ſed etiam ex-
ceſſus cylindri ipſi circumſcripti ſupra ipſum; nem-
pe centrum grauitatis ſolidi ex trilineo E B A, in pri-
ma figura, reuoluto circa baſim ſemiparabolæ B D. Cum autem tale centrum facilius inuen@atur [?] alio mo-
do, ideo hunc experiemur in parabola quadratica in
numeris. Supponamus ergo BD, ſectam bifariam
in S, & in T, ſic vt BT, ſit ad T D, vt 11, ad 5. adeo vt T, ſit centrum grauitatis ſemifuſi A B C. Er-
go quarum BD, erit 16, talium ST, erit 3, & B S, 8. Ergo qualium B D, erit 37, cum tertia par-
te, talium ST, erit 7, & BS, 18, cum duobus ter-
tijs. Cum autem ex ſchol. prim. propoſit. 14. lib. 2. ſit exceſſus cylindri circumſcripti ſemifuſo ad ipſum
vt 7, ad 8, & ſi fiat vt talis exceſſus ad ſemifuſum,
ſic reriprocè T S, ad S I, ſit 1, centrum grauitatis
prædicti exceſlus; erit SI, 8, qualium BS, eſt 18,
cum duobus tertijs. Ergo talium reliqua BI, erit
10, cum duobus tertijs. Qualium ergo BD, eſt
37, cum tertia parte, erit BI, 10, cum duabus
tertijs partibus, & reliqua DI, 26, cum duo bus ter-

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