Full text: Cavalieri, Bonaventura: Geometria indivisibilibvs continvorvm

LIBER III. M,B, E, G. Dico igitur omnia quadrata parallelogrammi, HF,
ſimul cum rectangulis bis ſub, HF, & parallelogrammo, FC, ad
omnia quadrata circuli, vel ellipſis, MBEG, ſimul cum rectangu-
lis bis ſub eodem circulo, vel ellipſi, MBEG, & ſub quadrilineo, M
GEOC, eſſe vt parallelogrammum, HF, ad circulum, vel ellipſim,
MBEG : Omnia . n. quadrata parallelogrammi, HO, ad omnia
quadrata parallelogrammi, MO, ſunt vt quadratum, DO, ad qua-
dratum, OE, omnia item quadrata parallelogrammi, MO, ad re-
ctangula ſub parallelogrammo, MO, & portione, MGE, ſunt vt,
MO, ad portionem, MGE, fiat vt, MF, ad portionem, MGE,
ita, FE, ad, EI, erit ergo vt, MO, ad portionem, MGE, ita, O
E, ad, EI, ergo omnia quadrata, MO, ad rectangula ſub, MO, & portione, MGE, erunt vt, OE, ad, EI, . i. vt quadratum, OE,
ad rectangulum ſub, OE, EI, erant autem omnia quadrata, HO,
ad omnia quadrata, OM, vt quadratum, DO, ad quadratum, O
E, ergo ex æquali omnia quadrata, HO, ad rectangula ſub, MO,
& ſub portione, MGE, erunt vt quadratum, DO, ad rectangu-
lum ſub, OE, EI, ad eadem verò quater ſumpta, vt quadratum, D
O, ad rectangulum ſub, OE, & quadrupla, EI; rectangula autem
ſub, MO, & por-
tione, MGE, æ-
quantur rectangulis
ſub quadrilineo, M
GEOC, & por
tione, MGE, vna
cum omnibus qua
dratis portionis, M
GE, ilia ig tur qua-
ter ſumpta reddunt
quater rectangula ſub portione, MGE, & quadrilineo, MGEO
C, vna cum omnibus quadratis portionis, MGE, quater ſumptis,
quia verò omnia quadrata circuli, vel ellipſis, MBEG, æquantur
omnibus quadratis portionis, MBE, & portionis, MGE, vna cum
rectangulis bis ſub vtriſq; portionibus . i. vna cum omnibus quadratis
portionis, MGE, bis ſumptis, & omnia quadrata portionis, MBE,
æquantur omnibus quadratis portionis, MGE, ideò omnia quadra-
ta portionis, MGE, quater ſumpta æquantur omnib. quadratis cir-
culi, vel ellipſis, MBEG, item rectangula ſub portione, MGE, & quadrilineo, MGEOC, quater æquantur rectangulis ſub toto circu-
lo, vel ellipſi, MBEG, & ſub quadrilineo, MGEOC, bis ſumptis, itaut
hucuſq; probauerimus rectangula ſub portione, MGE, & paralle-
logrammo, MO, quater ſumpta æquari omnibus quadratis circuli,

Note to user

Dear user,

In response to current developments in the web technology used by the Goobi viewer, the software no longer supports your browser.

Please use one of the following browsers to display this page correctly.

Thank you.

powered by Goobi viewer