# Full text: Cavalieri, Bonaventura: Geometria indivisibilibvs continvorvm

GEOMETRIÆ BEC, CEF, . i. ſunt ad illa, vt, EF, ad, {1/6}, eiuſdem, EF, ergo ex
æquali, rectingula ſub, AE, EC, ad rectangula ſub triangulis, BE
C, CEF, erunt vt, DE, ad, {1/6}, EF, eadem verò ad rectangula ſub,
AE, & triangulo, BEC, ſiue, CEF, oſtenſa ſunt eſſe, vt, DE,
ad, {1/2}, DE, ergo, colligendo, rectangula ſub, AE, EC, ad rectan-
gula ſub, AE, & triangulo, CEF, & ſub triangulo, BEC, & eo-
dem, CEF, . i. ad rectangula ſub trapezio, ADEC, & triangulo,
CEF, erunt vt, DE, ad compoſitam ex, {1/2}, DE, & , {1/6}, EF, quę
eſt Theorematis prima pars.

### 258.1.

14. huius.
Elicitur
ex.
24. huius.
Per A. Co
roll. 23.
huius.

Dico vlterius rectangula ſub, AF, FB, ad rectangula ſub trape-
zio, ADEC, & triangulo, BEC, eſſe vt, DF, ad compoſitam ex,
{1/6}, DE, & , {1/3}, EF; rectangula . n. ſub, AF, FB, ad rectangula ſub,
AE, EC, ſunt vt rectangulum, DFE, ad rectangulum, DEF, . i. vt, FD, ad, DE, rectangula vero ſub, AE, EC, ad rectangula ſub,
AE, & triangulo, BEC, ſunt vt, B
F, ad triangulum, BEC, . i. dupla . i. vt, DE, ad, {1/2}, ipſius, DE, ergo, ex
æquali rectangula ſub, AF, FB, ad
rectangula ſub, AE, & triangulo, B
EC, erunt vt, FD, ad, {1/2}, DE, quod
ſerua. Item rectangula ſub, AF, FB,
ad omnia quadrata, BF, ſunt vt re-
ctangulum, DFE, ad quadratum, F
E, . i. vt, DF, ad, FE: Omnia verò
quadrata, BF, ſunt tripla omnium
quadratorum trianguli, BEC, . i. ſunt vt, FE, ad, {1/3}, FE, ergo ex
æquali rectangula ſub, AF, FB, ad omnia quadrata trianguli, BE
C, ſunt vt, DF, ad, {1/3}, FE, erant autem eadem ad rectangula ſub,
AE, & triangulo, BEC, vt, DF, ad, {1/2}, DE, ergo, colligendo,
rectangula ſub, AF, FB, ad rectangula ſub, AE, & triangulo, BE
C, vna cum omnibus quadratis trianguli, BEC, . i. ad rectangula
ſub trapezio, ADEC, & triangulo, BEC, erunt vt, DF, ad com-
poſitam ex, {1/2}, DE, & , {1/3}, EF, quę eſt Theorematis ſecunda pars; hæc autem erant demonſtranda.

14. huius.
3. huius.
Coroll. 1.
26. huius.
14. huius.
3. huius.
24. huius.
Per C.
Coroll.
23. huius.

## 259.COROLLARIVM.

_C_Olligimus autem ex hoc Theoremate rectangula ſub maximis ab-
ſciſſarum propoſitæ lineæ, adiunctis eiſdem tot vni cuidam æquali-
bus, ad rectangula ſub omnibus abſciſſis eiuſdem adiunctaiam dicta li-
nea, & ſub reſiduis abſciſſarum eiuſdem, eſſe vt adiuncta ad compoſitam
ex, {1/2}, adiunctæ, & {1/2}, propoſitæ lineæ, & hoc ex prima parte huius

## 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