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.
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.
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.
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.
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.
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.