## Full text: Cavalieri, Bonaventura: Geometria indivisibilibvs continvorvm

GEOMETRIÆ quoties, BD, ſecta eſſe ſupponitur, exceptis tamen extremis, vt ex. gr. ipſa, CI, in qua parte, CI, quæin recta, CI, feparari debuiſ-
ſent per lineas, AEC, AFI, in puncta, C, I, partibus, BE, FD,
reſpondentia degenerauerunt. Dico quæcunque demonſtrantur in
linea, BD, circa quadrata, vel rectangula, illi, vel illius partibus ap-
partium eiuſdem figuræ per dictas lineas conſtitutarum, ſiue de re-
ctangulis ſub eiuſdem partibus. Vtex gr. quia in 3. Propoſ. lib. 2. Elem. oſtenditur rectangulum ſub, BD, DF, æquari rectangulo
ſub, BFD, cum quadrato, FD, ſic dico verum eſſe rectangula ſub
figura, ABCD, & figura, ADI, æquari re-
ctangulis ſub figuris, ABIF, ADIF, cum om-
vtcunque duxerimus regulæ, BD, parallelam,
vt, HO, ſecantem lineas, AC, in, M, & , A
I, in, N, verum eſſe comperiemus rectangulum,
HON, æquari rectangulo, HNO, cum qua-
drato, NO, & idem in cęteris regulę, BD, pa-
rallelis in figura, ABCD, ductis reperiemus,
ergo verum erit rectangula illa ſimul collecta, ideſt rectangula ſub fi-
gura, ABID, & figura, ADI, æquari rectangulis ſub figuris, AB

### 234.1.

Vide D.
Defin. 8.
huius.
Coroll. 4.
huius.

Similiter ſi ſupponamus, BF, bifariam ſecari in, E, cui adiunga-
tur, FD, ſuppoſuerimus etiam lineam, AC, bifariam ſecare quam-
libet omnium linearum figuræ, ABI, regula, BD, ſupradictarum,
luti Propoſ. 6. oſtenditur rectangulum, BDF, cum quadrato, FE,
guræ, ACI, æquari omnibus quadratis figuræ, ACD, quod re-
ſpondet Prop. 6. eiuſdem lib. Conſimiliter reliqua demonſtrabimus,
vnde iuxta I. Propoſ. Secundi Elem. colligemus.

## 235.A. COROLLARII SECTIO I.

_R_Ectangula ſub figura indiuiſa, ABID, & ſub diuiſa, ACD, per
lineam, AI, æquari rectangulis ſub indiuiſa, ABID, & ſub
partibus diuiſæ, quæ ſunt, ACI, AID.

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