Full text: Cavalieri, Bonaventura: Geometria indivisibilibvs continvorvm

GEOMETRIÆ ſunt vt quadratum, VR, ad quadratum, CR, . ſ. vt rectangulum,
AOD, vel quadratum, AO, ad rectangulum, DRA, omnia au-
tem quadrata parallelogrammi, BR, ad omnia quadrata ſemipor-
tionis, ICRM, ſunt vt rectangulum, D
RA, ad rectangulum ſub, DR, & ſub
compoſita ex, {1/2}, RM, & ex, MA, vna
cum rectangulo ſub, RM, & ſub com-
poſita ex, {1/6}, RM, & , {1/2}, MA, ergo ex
æquali omnia quadrata parallelogram-
mi, GR, ad omnia quadrata ſemiportio-
nis, ICRM, vel omnia quadrata paral-
lelogrammi, GX, ad omnia quadrata
portionis, ICFS, erunt vt quadratum,
AO, ad rectangulum ſub, DR, & ſub compoſita ex, {1/2}, RM, & ex, MA, vna cum rectangulo ſub, RM, & ſub compoſita ex, {1/6}, R
M, & , {1/2}, MA; quod etiam pater, ſi parallelogrammum, GX, non
ſit circa axim, vel diametrum, MR, quod erat oſtendendum.

304.1.

0223-01
9. Lib. 2.
Ex 40. l. 1.
& eiuidẽ
Scholio.
0224-01
Ex anter.
Ex 9. & B.
Cor. 22.
lib. 2.

305. THEOREMA V. PROPOS. V.

SI in circulo, vel ellipſi ducantur coniugati axes, vel dia-
metri, in altera autem eorundem ſit tamquam in baſi pa-
rallelogrammum circa eundem axim, vel diametrum cum cir-
culo, vel ellipſi, circa quæm ſit etiam triangulus, ſed in baſi
oppoſita baſi parallelogrammi, ſumatur autem in dicta axi,
vel diametro vtcunq; punctum, per quod baſibus dictis aga-
tur parallela; quadratum eiuſdem parallelæ trianguli lateri-
bus interceptæ æquabitur reliquo quadrati eius, quæ inter-
cipitur lateribus parallelogrammi, dempto quadrato eius,
quæ intra circulum, vel ellipſim concludetur.

Sit circulus, vel ellipſis, BDHF, eius coniugati axes, vel diame-
tri, BH, DF, in altera autem earum, vtin, DF, tanquam in baſi,
& circa axim, vel diametrum, BE, ſit parallelogrammum, AF, cir-
ca eundem verſo4; , ſed in baſi, AC, ſit triangulum, AEC, ſumatur
autem in, BE, vtcunque punctum, M, per quodipſi, DF, agatur
parallela, VR, ſecans curuam, DBF, in, T, I, & latera trianguli,
AEC, in, S, N. Dico ergo quadratum, SN, æquari reliquo qua-
drati, VR, dempto quadrato, TI. Nam rectangulum, HEB, ad
rectangulum, HMB, eſt vt quadratum, FE, vel quadratum, RM,

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