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.

258.1.

14. huius.
3. huius.
0192-01
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

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