Full text: Cavalieri, Bonaventura: Geometria indivisibilibvs continvorvm

Omnia . n. quadrata figuræ, RBCS, ſecantur per, BE, in omnia
quadrata, BS, in omnia quadrata ſemihyperbolæ, BCE, & inre-
ctangula bis ſub, BCE, & ſub, BS, ad horum ergo ſingula compa-
remus omnia quadrata, FS; hæcigitur ad omnia quadrata, BS,
ſunt vt quadratum, CS, ad quadratum, SE, pariter omnia qua-
drata, FS, ad omnia quadrata, FE, ſunt vt quadratum, SC, ad
quadratum, CE, omnia verò quadrata, FE, ad omnia quadrata,
BCE, ſunt vt quadratum, CE, ad
quadratum, EI, ergo, ex æquali, om-
nia quadrata, FS, ad omnia quadra-
ta, BCE, erunt vt quadratum, CS, ad
quadratum, EI; quodſerua. Item
omnia quadrata, FS, ad rectangula
ſub, FE, ER, ſunt vt quadratum, C
S, ad rectangulum, CES, rectangula
verò ſub, FE, ER, adrectang. ſub, BC
E, ER, ſunt vt, FE, ad, BCE, . i. vt, C
E, ad, VE, . i. ſumpta, ES, communi altitudine, vt rectangulum,
CES, ad rectangulum, VES, ergo, ex æquo, omnia quadrata, FS,
ad rectangula ſub, BCE, ER, erunt vt quadratum, CS, ad rectan-
gulum, VES, ad eadem verò bis ſumpta, vt quadratum, CS, ad
rectangulum bis ſub, VES; ergo, conſequentibus ſimul collectis,
omnia quadrata, FS, ad omnia quadrata, BS, ad omnia quadra-
ta, BCE, & ad rectangula bis ſub, BCE, ER, ideſt ad omnia qua-
dratà figuræ, RBCS, erunt vt quadratum, CS, ad quadra-
SE, quadratum, EI, & rectangulum bis ſub, VE, ES; qua me-
thodo ſimiliter oſtendemus omnia quadrata, FD, ad omnia
quadrata figurę, GBCD, eſſe vt quadratum, CD, ad quadra-
tum, DE, quadratum, EI, & rectangulum bis ſub, VE, ED; & ſimiliter omnia quadrata, FM, ad omnia quadrata figuræ, HB
CM, eſſe vt quadratum, CM, ad quadratum, ME, quadratum,
EI, & rectangulum bis ſub, VE, EM, quod oſtendere opus erat.

552.1.

D.Co.23.
l. 2.
0408-01
0408-02
14. @ 2.
Coroll 1.
26. l. 2.
D. Co 3. 2.
l. 2.

553. THE OREMA XVII. PROPOS. XVIII.

IN eadem Prop. 15. figura oſtendemus omnia quadrata
figuræ, HBCM, dempti omnibus quadratis figuræ, H
BDM regula eadem retenta, ad omnia quadrata figuræ,
GBCD, demptis omnibus quadratis trilinei, BGD, eſſe
vt compoſita ex, CM, MD, ad, DC.

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