Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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GEOMETRIÆ
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diuidendo minor ea, quam habet,
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AC, ad, CE, eandem ergo, quam
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habet, HL, ad, LR, habebit, AC, ad
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maiorem, CE, ſit illa, CO, & </
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O, ducatur, SV, parallela ipſi regu-
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læ, FG, iunganturque, SE, EV: </
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<
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nia ergo quadrata hyperbolæ, SEV,
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ad omnia quadrata trianguli, SEV,
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ſunt vt, AO, ad, OC, quia verò, AC,
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ad, CO, eſt vt, HL, ad, LR, compo-
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nendo, AO, ad, OC, erit vt, HR, ad,
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RL, ergo omnia quadrata hyperbo-
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læ, SEV, ad omnia quadrata triangu-
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li, SEV, erunt vt, HR, ad, RL, .</
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<
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ratione data, quod facere opus erat.</
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">THEOREMA VI. PROPOS. VII.</
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">SI circa datam hyperbolam deſcribantur aſymptoti,
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eiuſdem autem baſis vſq; </
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<
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">ad aſymptotos producatur,
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quæ ſumatur pro regula: </
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<
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">O nnia quadrata hyperbolæ ad
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omnia quadrata trianguli aſymptotis, & </
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">baſi comprchen-
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ſi, habebunt rationem compoſitam ex ea, quam habet
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quadratum baſis hyperbolæ ad quadratum baſis trianguli,
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& </
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<
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">ex ea, quam habet rectangulum ſub compoſita ex ſex-
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quialtera tranſuerſi lateris, & </
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<
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">axi, vel diametro datæ hy-
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perbolæ, ſub eodem axi, vel diametro, ad rectangulum
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ſub compoſita ex tranſuerſo latere, & </
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<
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">axi, vel diametro
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eiuſdem hyperbolæ; </
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">& </
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ris, & </
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<
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">Sit igitar data hyperbola, cuius baſis, SX, circa axim, vel dia-
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metrum, OV, cuius tranſuerſum latus ſit, BO, bifariam in C, di-
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uiſum, ſit autem illi in directum adiuncta, AB, æqualis, BC, de-
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inde ducta per, O, tangente hyperbolam, quæ ſit, ED, cui erit
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parallela baſis, SX, abicindantur, EO, OD, ita vt quadratum, E
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O, & </
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<
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">quadratum, OD, ſeorſim ſint æqualia quartæ parti rectan-
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guli ſub, BO, latere tranſuerſo, & </
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">ſub eiuſdem recto latere, ſi ergo
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iunctis, CE, CD, ipsæ producantur indefinitè verſus baſim, SX,
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<
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cui productæ occurant in punctis, H, R, erunt, CH, CR, </
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