Full text: Cavalieri, Bonaventura: Geometria indivisibilibvs continvorvm

LIBER V. quadratum, DC, quadratum, DC, ad quadratum, YN, & qua-
dratum, YN, ad quadratum, AV, componunt rationem quadra-
ti, AV, ad quadratum, AV, quę ſimul cum ratione ipſius, EC, ad
MN, componit rationem parallelepipedi lub, EC, & quadrato,
AV, ad parallelepipedum ſub, MN, & quadrato, AV, quæ tandẽ
eſt eadem ei, quam habet, EC, ad, MN, quia illa ſunt parallelepi-
peda in eadem baſi, & ideò omnia quadrata figuræ, FADCVE,
demptis omnibus quadratis triangulorum, KOI, POQ, ad om-
nia quadrata figuræ, TAYNVM, demptis omnibus quadratis
triangulorum, & O℟, ΩΟΠ, erum vt, EC, ad, MN, vel, XL, ad,
HG, quod demonſtrare opus erat.

566.1.

0422-01
Coroll. 1.
22. huius.
Coroll. 1.
22. huius.
Defin. 13.
lib .1.

567. THEOREMA XXV. PROPOS. XXVI.

ASumpta iterum figura Propoſ. 23. dimiſſo quouis pa-
rallelogrammorum, FC, TN, vt dimiſſo, TN, cæte-
ris ijſdem manentibus, oſtendemus omnia quadrata, FC,
demptis omnibus quadratis oppoſitarum hyperbolarum,
FAD, EVC, regula, EC, ad omnia quadrata figuræ, FAD
CVE, regula, DC, vel, AV, habere rationem compoſitam
ex ratione rectanguli, AOZ, bis cum @. quadrati, VZ, ad
rectangulum, AZO, & ex ratione rectanguli ſub, DC, vel,
RZ, & ſub EC, ad quadratum, AV, cum. quadrati, KI,
vel cum rectangulo ſub, AZ, & ſexquitertia, ZV.

Omnia namq; quadrata, FC, demptis omnibus quadratis oppo-
ſitarum hyperbolarum, FAD, EVC, regula, EC, ad omnia qua-
drata figuræ, FADCVE, regula, AV, habent rationem compoſi-
tam ex ratione omnium quadratorum, FC, demptis omnious qua-
dratis oppoſitarum hyperbolarum, FAD, EVC, ad omnia qua-
drata, FC, communiregula, EC, . f. ex ratione rectanguli, AOZ,
bis cum {2/3}. quadrati, VZ, ad rectangulum, AZO, & ex ratione
omnium quadratorum, FC, regula, EC, ad omnia quadrata, FC,
regula, CD, vel, AV, . ſ. ex ratione, EC, ad, CD, vel rectanguli
ſub, EC, CD, ad quadratum, CD, & tandem componitur ex ra-
tione omnium quadratorum, FC, regula, DC, ad omnia quadra-
ta figuræ, FADCVE, regula eadem, DC, . ſ. ex ratione quadrati,
DC, ad quadratum, AV, cum {1/3}. quadrati KI, duæ verò rationes,
ſcilicet rectanguli ſub, ED, CD, ad quadratum, CD, & quadrati,
CD, ad quadratum, AV, cum {1/3}. quadrati, KI, componunt ratio-

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