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

404384GEOMETRIÆ dratum, HP, ad rectangulum, MPX, ideò quadratum, BC, ad re-
1121 primi
Co 1. ctangulum, ACG, erit vt quadratum, HP, ad rectangulum, MPX;
quia autem ratio, quam habet, BC, ad, CA, & , BC, ad, CG, com-
22Iuxta def.
Cõmand.
& dicta
ad Schol.
28. l. 1. ponit rationem quadrati, BC, ad rectangulum, ACG, & item ra-
tio, quam habet, HP, ad, PM, & , HP, ad PX, componit rationem

275[Figure 275] quadrati, HP, ad rectã-
gulum, MPX, harum
autem rationum com-
ponentium ea, quam
habet, BC, ad, CA, eſt
eadem, ei, quam ha-
bet, HP, ad, PM, ideò
reliquæ componentiũ
erunt eædem . ſ. BC, ad
CG, erit vt, HP, ad, P
X, eſt autem etiam, A
C, ad, CB, conuerten.
do, vt, MP, ad PH,
ergo, ex æquali, & con-
uertendo, GC, ad CA,
erit vt, XP, ad PM, &
diuidendo, GA, ad, A
C, erit vt, XM, ad MP, & antecedentium dimidia . ſ. VG, ad AC,
erit vt, RX, ad, MP, eſt autem eadem, VG, ad, GA, vt eadem, R
X, ad, XM, ergo, VG, ad, GC, erit vt, RX, ad, XP, & componen-
do, VC, ad, CG, erit vt, RP, ad PX, eſt autem, VC, ad, CG, vt om-
nia quadrata hyperbolæ, BAD, ad omnia quadrata trianguli, B
AD, & , RP, ad PX, vt omnia quadrata hyperbolę, HMQ, ad om-
nia quadrata trianguli, HMQ, ergo omnia quadrata hyperbolę,
331. huius. BAD, ad omnia quadrata trianguli, BAD, erunt vt omnia qua-
drata hyperbolæ, HMQ, ad omnia quadrata trianguli, HMQ, &
permutando, omnia quadrata hyperbolę, BAD, ad omnia gua-
drata hyperbolę, HMQ, erunt vt omnia quadrata trianguli, BA
D, ad omnia quadrata trianguli, HMQ, . @. in tripla ratione eius,
44F Cor. 22.
l. 2. quam habet, AC, ad, MP, quod oſtendere opus erat.

THEOREMA XIII, PROPOS. XIV.

SIexponatur ſemiperbola, quæ per axem, vel diametrũ
integrę ſit abſciſſa, habens pro baſi dimidiam

401 (381)	402 (382)
403 (383)	404 (384)
405 (385)	406 (386)
407 (387)	408 (388)
409 (389)	410 (390)

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