LIBER V.
ne hyperbolæ, BAD, bafi rectangulo ſub, BD, FY, adparallele-
pipedum ſub eadem altitudine baſi quadrato, BD: pariter omnia
quadrata hyperbolæ, BAD, ad omnia rectangula hyperbolę, HM
Q, ſimilia rectangulo ſub, HQ, EN, habent rationem compofitã
ex ratione rectanguli ſub, VC, XP, ad rectangulum ſub, RP, GC,
& parallelepipedi ſub altitudine hyperbolæ, BAD, & ſub quadra-
to, BD, ad parallelepipedum ſub altitudine hyperbolæ, HMQ,
bafi rectangulo ſub, HQ, EN, ergo, ex æquo, omnia rectangula
hyperbolæ, BAD, ſimilia rectangulo ſub, BD, FY, regula, BD, ad
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-
lo ſub, BD, FY, ad parallelepipedum ſub eadem altitudine, & baſi
quadrato, BD, & ex ratione huius parallelepipedi ad parallelepi-
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-
co omnia quadrata hyperbolæ, BAD, ad omnia quadrata hyper-
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,
ad, MP; quia verò quadratum, BC, ad rectangulum, GCA, eſt vt
hyperbolæ, BAD, rectum latus ad tranſuerſum . I. vt rectum latus
ad tranſuerſum hyperbolæ, HMQ, quia ille ſunt ſimiles . I. vt qua-
