Cavalieri, Buonaventura - Geometria indivisibilibvs continvorvm : noua quadam ratione promota

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145125LIBER II. quiangula, etenim, CO, ad, CO, habet rationem compoſitam ex
11Defin. 13.
lib. 1. ea, quam habet, CO, ad, RZ, & RZ, ad, CO, & ſic, CD, ad,
CD, ex ea, quam habet, CD, ad, RX, & , RX, ad, CD, quia
verò omnia quadrata, HX, ſunt æqualia omnibus quadratis, AD,
ideò ſunt ad illa, vt, CO, ad, CO, vel vt, CD, ad, CD, . i. in ra-
tione compoſita ex ratione, CO, ad, RZ, & , RZ, ad, CO, vel,
CD, ad, RX, & , RX, ad, CD, ſunt autem omnia quadrata, H
X, ad omnia quadrata, AD, in ratione compoſita ex ea, quam ha-
22Exantec. bet quadratum, VX, ad quadratum, BD, & , RZ, ad, CO, ſiue,
RX, ad, CD, cum ſunt æquiangula, ideò duæ rationes, CO, ad,
RZ, & , RZ, ad, CO, ſiue aliæ duę rationes, CD, ad, RX, & ,
RX, ad, CD, componunt eandem rationem, quam iſtę duę . ſ. ra-
tio quadrati, VX, ad quadratum, BD, & , RZ, ad, CO, vel, R
X, ad, CD, eſt autem communis ratio, RZ, ad, CO, vel, RX,
ad, CD, ergo reliqua ratio, quam habet quadratum, VX, ad qua-
dratum, BD, erit eadem reliquę, quam nempè habet, CO, ad,
RZ, vel, CD, ad, RX, cum ſunt æquiangula, quod erat oſten-
dendum.

COROLLARIVM.

_I_Dem eodem modo de omnibus figuris ſimilibus quibuſuis parallelo-
grammorum, HX, AD, regulis ĳſdem, VX, BD, oſtendi poſſe ex
ſuperiori methodo colligitur.

THEOREMA XIII. PROPOS. XIII.

SImilium parallelogrammorum omnia quadrata, regulis
homologis lateribus, ſunt in tripla ratione laterum ho-
mologorum.

Sint ſimilia parallelogramma, AC, EG, quorum latera homo-
33Tux. diff. 1.
Sex. El. loga, BC, FG, ſint ſumpta pro regula. Dico omnia quadrata, A

85[Figure 85] C, ad omnia quadr. EG, eſſe in tripla ra-
tione eius, quam habet, BC, ad, FG. Quo-
44Ex def. 1.
Sex. El. niam enim parallelogramma, AC, EG,
ſunt ſimilia, ideò ſunt æquiangula, & circa
æquales angulos latera habent proportio-
nalia, & , BC, CD; FG, GH, ſunt late-
ra ad inuicem æqualiter inclinata, quorum,
BC, FG, ſunt regulę, ideò omnia quadrata, AC, regula, BC,

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