Cavalieri, Buonaventura - Geometria indivisibilibvs continvorvm : noua quadam ratione promota

407387LIBER V. fe vt, FD, ad hyperbolã, CBD, quod patet nam, CBD, eſt ſigura
qualem poſtulat Prop. 29. Lib. 3. eſt enim, BE, communis axis,
vel diameter, FD, parallelogrammi, & hyperbolæ, CBD, vnde
patet propoſitum.

THEOREMA XV. PROPOS. XVI.

IN eadem anteced. Prepoſ. figura, ſi producatur, CD,
vtcunq; in, M, & compleatur parallelogrammum, HC,
regula, CM: Omnia quadrata, FM. demptis omnibus qua-
dratis, GM, ad omnia quadrata figuræ, HBCM, dem-
ptis omnibus quadratis figuræ, HBDM, erunt vt, FD, ad
hyperbolam, CBD.

Patet hoc Theor. nam, CBD, eſt ſigura, qualem poſtulat Prop.
30. Lib. 3. quia, BE, eſt communis ax@s, vel diameter, parallelo-
grammi, FD, & hyperbolæ, CBD, vnde, & c.

COROLLARIVM.

_H_Inc babetur omnia quadrata, FD ad omnia quad ſigura, GBCD,
demptis omnibus quadratis trilmet, BGD, eſſe vt omnia qua-
drata FM, demptis omnibus quadratis, GM, ad omnia quadrata figu-
ræ, HBCM, demptis omnibus quadratis ſig. HBDM, quia vtraq; ſunt,
vt, FD, ad byperbolam, CBD.

THEOREMA XVI. PROPOS. XVII.

IN eadem Prop. 15. figura ſi intelligamus ductam vt-
cunq; axi, vel diametro, BE, parallelam, RS, fiat au-
tẽ, vt oia quad FE, ad oia q uad. ſemihyperb BCE, regula,
CD, . i. vt, AE, ad compoſitam ex. AB, & BE, ita quadra-
tum, CE, ad quadratum, EI, & vt FE, ad ſemihyperbolã,
BCE, ita eſſe ſupponatur, CE, ad, EV, vbicunq; cadatpũ-
ctum, V. Dico omnia quadrata, FS, ad omnia quadrata
figuræ, RBCS, regula, CD, eſſe vt quadratum, CD, ad
quadratum, SE, quadratum, EI, & rectangulum bis ſub,
VE, ES.

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