Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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LIBER IV.
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">INeadem ſupradicti Theorematis figura oſtendemus tri-
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lineum, VNAI, ad trilineum, VNABX, eſſe vt pa-
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rallelepipedum ter ſub, EI, & </
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">quadrato, IA, cum cubo,
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IA, ad parallelepipedum ter ſub, CX, & </
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cum cubo, XB. </
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">Similiter trilineum, VEI, ad trilineum,
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VECX, eſſe vt parallelepipedum ter ſub, AI, & </
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to, IE, cum cubo, IE, ad parallelepipedum terſub, BX, & </
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quadrato, XC, cum cubo, XC.</
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s
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">Trilineum enim, VNAI, ad parabolam, ANE, eſt vt paral-
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lelepipedum ter ſub, EI, & </
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">quadrato, IA, cum cubo, IA, ad cu-
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bum, AE, item parabola, ANE, ad parabolam, BNC, eſt vt
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cubus, AE, ad cubum, BC, & </
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<
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">tandem parabola, BNC, ad trili-
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">2.huius.</
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neum, VABX, eſt vt cubus, CB, ad parallelepipedum ter ſub, C
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X, & </
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">quadrato, XB, cum cubo, BX, ergo, ex æquali, trilineum,
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VNAI, ad trilineum, VNBX, erit vt parallelepipedum ter ſub,
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EI, & </
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">quadrato, IA, cum cubo, IA, ad parallelepipedum ter
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ſub, CX, & </
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ſtendemus trilineum, VIE, ad trilineum, VXC, eſſe vt paralle-
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lepipedum ter ſub, AI, & </
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<
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">quadrato, IE, cum cubo, IE, ad pa-
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rallelepipedum ter ſub, BX, & </
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quod, &</
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<
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">SI duæ intra curuam parabolicam ducantur rectæ lineæ
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axem ſecantes, fuerint autem conſtitua@um ab eiſdem
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parabolarum diametri, vel axis, & </
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parabolæ erunt æquales.</
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">Sit curua parabolica, BAC, intra quam ducantur vtcunque duę,
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DF, MC, axem ſecantes, ideſt non parallelæ axi, ſint autem, A
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R, HO, diametri, vel axis, & </
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parabolam, DAF, eſſe æqualem parabolæ, MHFC; </
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