Full text: Cavalieri, Bonaventura: Geometria indivisibilibvs continvorvm

GEOMETRIÆ diuidendo minor ea, quam habet,
AC, ad, CE, eandem ergo, quam
habet, HL, ad, LR, habebit, AC, ad
maiorem, CE, ſit illa, CO, & per,
O, ducatur, SV, parallela ipſi regu-
læ, FG, iunganturque, SE, EV: Om-
nia ergo quadrata hyperbolæ, SEV,
ad omnia quadrata trianguli, SEV,
ſunt vt, AO, ad, OC, quia verò, AC,
ad, CO, eſt vt, HL, ad, LR, compo-
nendo, AO, ad, OC, erit vt, HR, ad,
RL, ergo omnia quadrata hyperbo-
læ, SEV, ad omnia quadrata triangu-
li, SEV, erunt vt, HR, ad, RL, . i. in
ratione data, quod facere opus erat.

539.1.

0394-01

540. THEOREMA VI. PROPOS. VII.

SI circa datam hyperbolam deſcribantur aſymptoti,
eiuſdem autem baſis vſq; ad aſymptotos producatur,
quæ ſumatur pro regula: O nnia quadrata hyperbolæ ad
omnia quadrata trianguli aſymptotis, & baſi comprchen-
ſi, habebunt rationem compoſitam ex ea, quam habet
quadratum baſis hyperbolæ ad quadratum baſis trianguli,
& ex ea, quam habet rectangulum ſub compoſita ex ſex-
quialtera tranſuerſi lateris, & axi, vel diametro datæ hy-
perbolæ, ſub eodem axi, vel diametro, ad rectangulum
ſub compoſita ex tranſuerſo latere, & axi, vel diametro
eiuſdem hyperbolæ; & ſub compoſita ex {1/2}. tranſuerſi late-
ris, & eodem axi, vel diametro.

Sit igitar data hyperbola, cuius baſis, SX, circa axim, vel dia-
metrum, OV, cuius tranſuerſum latus ſit, BO, bifariam in C, di-
uiſum, ſit autem illi in directum adiuncta, AB, æqualis, BC, de-
inde ducta per, O, tangente hyperbolam, quæ ſit, ED, cui erit
parallela baſis, SX, abicindantur, EO, OD, ita vt quadratum, E
O, & quadratum, OD, ſeorſim ſint æqualia quartæ parti rectan-
guli ſub, BO, latere tranſuerſo, & ſub eiuſdem recto latere, ſi ergo
iunctis, CE, CD, ipsæ producantur indefinitè verſus baſim, SX,
cui productæ occurant in punctis, H, R, erunt, CH, CR, afym-

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