Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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tionculam, ASB, .</
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xml:space
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tol.antec.</
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componunt rationem parallelepipedi ſub altitudine, BH, baſi re-
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ctangulo, HOB, vel quadrato, OH, ad parallelepipedum ſub
<
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altitudine, CE, baſi rectangulo, HCB, ergo triangulum, HNB,
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ad portionculam, ASB, eſt vt parallelepipedum ſub altitudine,
<
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BH, baſi quadrato, HO, ad parallelepipedum ſub altitudine, C
<
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E, baſi rectangulo, HCB, eſt autem, vt dicebatur, triangulum,
<
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HNB, ad triangulum, HAB, vt rectangulum, HOB, vel qua-
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dratum, HO, ad rectangulum, HCB, ideſt ſumpta, HB, com-
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munialtitudine, vt parallelepipedum ſub altitudine, HB, baſi qua-
<
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drato, HO, ad parallelepipedum ſub altitudine, HB baſi rectan-
<
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gulo, HCB, ergo, colligendo, triangulum, HNB, ad portion-
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culam, ASB, cum triangulo, ABH, ſilicet ad trilineum, HAS
<
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B, erit vt parallelepipedum ſub altitudine, HB, baſi quadrato, H
<
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O, ad parallelepipedum ſub altitudine compoſita ex, HB, CE,
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baſi rectangulo, HCB; </
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<
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">vel vt iſtorum quadrupla ſilicet vt paralle-
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lepipedum ſub eadem altitudine, HB, baſi quadruplo quadrati, H
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O, ideſt quadrato, HB, ſilicet vt cubus, HB, ad parallelepipedum
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ſub eadem altitudine compoſita ex, HB, CE, baſi quadruplo re-
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ctanguli, HCB. </
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guli, HNB, ideò erit ad ipſum, vt ſolidum ſexquitertium cubi, H
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B, ad cubum, HB, eſt autem triangulum, HNB, ad trilineum,
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HASB, vt cubus, HB, ad parallelepipedum ſub altitudine com-
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poſita ex, HB, CE, & </
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">ſub baſi quadruplo rectanguli, HCB, ergo
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ex æquali parabola, HNB,
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ad trilineum, HASB, erit vt
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ſolidum ſexquitertium cubi, H
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B, ad parallelepipedum ſub al-
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titudine compoſita ex, HB, C
<
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E, baſi quadruplo rectanguli,
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HCB; </
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<
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">vel vt iſtorum ſubſex-
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quitertia ſilicet vt cubus, HB,
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ab parallelepipedum ſub ea-
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dem altitudine compoſita ex,
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HB, CE, baſi triplo rectan-
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guli, HCB, eſt enim quadruplum rectanguli, HCB, ſexquiter-
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tium tripli eiuſdem rectanguli; </
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<
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pedum poteſt diuidi in parallelepipedum ſub altitudine, CE, baſi
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triplo rectanguli, HCB, vel baſi rectangulo ſub, BC, & </
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<
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CH, & </
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">in parallelepipedum ſub altitudine, HB, baſi etiam rectan-
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gulo ſub, BCH, ter ſumpto, quoniam verò tripla, HC, &</
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CE, ſunt deinceps proportionales, ideò parallelepipedum, </
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