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

Q, ſimilia rectangulo ſub, HQ, EN, habent rationem compofitã
ex ratione rectanguli ſub, VC, XP, ad rectangulum ſub, RP, GC,
to, BD, ad parallelepipedum ſub altitudine hyperbolæ, HMQ,
bafi rectangulo ſub, HQ, EN, ergo, ex æquo, omnia rectangula
omnia rectangula hyperbolæ, HMQ, ſimilia rectangulo ſub, HQ,
EN, regula, HQ, habebunt rationem compoſitam ex ratione re-
ctanguli, ſub, VC, XP, ad rectangulum ſub, RP, GC, & ex ratio-
ne parallelepipedi ſub altitudine hyperbolæ, BAD, baſi rectangu-
pedum ſub altitudine hyperbolę, HMQ, baſi rectangulo ſub, HQ,
EN; . i. compoſitã ex ratione parallelepipedi ſub altitudine hy-
perbolę, ABD, baſi rectangulo ſub, BD, FY, ad parallelepipedum
ſub altitudine hyperbolę, HMQ, baſi rectangulo ſub, HQ, EN,
quę erant oſtend.

## 546.THEOREMA XII. PROPOS. XIII.

SImilium hyperbolarum omnia quadrata, regulis ea-
rum baſibus, ſunt in tripla ratione axium, vel diame-
trorum earundem.

Sint ſimiles hyperbolæ, BAD, HMQ, earum latera tranſuerſa,
GA, XM, quorum ſint ſexquialteræ, AV, MR, in directum axi-
bus, vel diametris, AC, MP, baſes, & regulæ ſint, BD, HQ. Di-
bolæ, HMQ, eſſe in tripla ratione eius, quam habet, AC, ad, M
P, iungantur, BA, AD, HM, MQ. Quoniam ergo hyperbolæ
ſunt ſimiles baſis, BD, ad, CA, erit vt baſis, HQ, ad, PM, & ſunt
anguli in clinationis, AC, ad, BD, & MP, ad, HQ, inter ſe æqua-
les, ergo triangula, BAD, HMQ, ſunt ſimilia, & ideo omnia qua. drata eorundem, regulis ijſdem, erunt inter ſe in triplaratione la-
terum homologorum . i. eius, quam habet, BD, ad, HQ, vel, AC,