Full text: Cavalieri, Bonaventura: Geometria indivisibilibvs continvorvm

GEOMETRIÆ P, in eadem altitudine ſumpta iuxta baſes, TP, OP, & ideò eſſent,
vt ipſæ baſes, TP, OP, ideſt vt latera, TP, OP, æqualiter baſi,
NP, inclinata, hæc autem pariter verificabuntur etiamſi baſis, NP,
non ſit communis, ſint tamen duæ baſes æquales, quæ oſtendere o-
pus erat.

181.1.

Ex prima
parte hu-
ius Prop.
Ex prima
par. huius
Propoſ.

182. THEOREMA VI. PROPOS. VI.

PArallelogramma habent rationem compoſitam ex ra-
tione baſium, & altitudinum iuxta eaſdem baſes ſum-
ptarum, ſiue laterum æqualiter baſibus inclinatorum, cum
ſcilicetilla ſunt æquiangula.

Sint parallelogramma vtcunque, AD, FM. Dico eadem habe. re inter ſe rationem compoſitam ex rationibus baſium, quæ ſint, C
D, GM, & altitudinum, quę ſint, BV, ON, ſumptæ iuxta baſes,
CD, GM, illiſque productis, ſi opus ſit, in punctis, V, N, occur-
rentes, ſiue ex ratione laterum, BD, OM, ſi ſint æquiangula: Ab-
ſcindatur à, BV, verſus, V, ipſa,
XV, æqualis ipſi, ON, & per, X,
ducatur, XP, parallela, CD, ſe-
cans, BD, in, R, vt fiat paralle-
logrammum, PD, in eadem altitu-
dine cum parallelogrammo, FM,
& in eadẽ baſi cum parallelogram-
mo, AD. Parallelogrammum er-
go, AD, ad parallelogrammum,
FM, ſumpto medio de foris parallelogrammo, PD, habet ratio-
nem compoſitam ex ratione parallelogrammi, AD, ad parallelo-
grammum, PD, ideſt ex ratione, quam habet, BV, ad, VX, vel,
ON, ſiue, BD, ad, DR, quoniam, AD, PD, ſunt æquiangu-
la, ideſt ex ratione, BD, ad, OM, & hoc quotieſcunque, PD, F
M, ſint pariter æquiangula, & inſuper eſt compoſita ex ea, quam
habet parallelogrammum, PD, ad parallelogrammum, FM, ideſt
ex ea, quam habet, CD, ad, GM, ergo parallelogrammum, AD,
ad parallelogrammum, FM, habet rationem compoſitam ex ea,
quam habet, BV, ad, ON, quæ ſunt altitudines, vel etiam ex ea,
quam habet, BD, ad, OM, ſi, AD, FM, ſint æquiangula; & ex
ea, quam habet, CD, ad, GM, quod oſtendere opus erat.

182.1.

Defin. 12.
lib. 1.
0138-01
Defin. 12.
lib. 1.
Exſecun.
par. ant.
Ex prima
parte an-
teced.
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