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

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10383LIBERI.

THEOREMA XXXVI. PROPOS. XXXIX.

IIſdem poſitis, præterquamquod, BV, ſit parallela ipſi, A
F, ſed poſito, quod concurrat cum eodem latere, FA, ver-
ſus verticem producto, vt in, Z. Dico quadratum, ED, ad
quadratum, MO, eſſe vt rectangulum, ZVB, ad rectangu-
lum, ZNB.

Quia enim quadratum, EV, eſt æquale rectangulo, CVF, &
quadratum, MN, rectangulo, HNR, ideò quadratum, EV, ad
1114. Secun.
Elem.

57[Figure 57] quadratum, MN, erit vt rectangulum, CV
F, HNR, rectangulum verò, CVF, ad,
HNR, habet rationem compoſitam ex ea,
quam habet, CV, ad, HN, (vt infra inde-
pendenter ab hac Propoſit. probatur) . i. VB,
22Ex Sexta
lib. 2. ſeq.
vel ex 23.
Sexti El. ad, BN, quia trianguli, CVB, HNB, ſunt
æquianguli, & ex ea, quam habet, VF, ad,
NR, ideſt, VZ, ad, ZN, quia trianguli, V
FZ, NRZ, ſunt æquianguli, duę verò ra-
tiones, VB, ad, BN, & , VZ, ad, ZN,
33Ex Sexta
lib. 2. ſeq.
velex 23.
Sexti El. componunt rationem rectanguli, ZVB, ad
rectangulum, ZNB, ergo rectangulum, C
VF, ad rectangulum, HNR, . i. quadratum,
EV, ad quadratum, MN, vel quadratum, ED, ad quadratum, M
O, erit vt rectangulum, ZVB, ad rectangulum, ZNB, quod oſten-
dere opus erat; hæc autem ab Apollonio vocatur Hyperbola.

THEOREMA XXXVII. PROPOS. XL.

TAndem eiſdem poſitis, preterquam dicto concurſu, po-
ſito, inquam, BV, concurrere cum vtroq; latere trian-
guli per axem, & productum, etiam cum baſi trianguli per
axem conuenire, vt in, 2. Dico quadratum, RD, ad qua-
dratum, MO, eſſe vt rectangulum, VSB, ad rectangulum,
VNB.

Sit ergo talis hic appoſitum ſchema, in quo planum figuræ B ℟
VD, (cuius axis, vel diameter ſecat vtraque latera, AC, AF, &
producta incidit in baſim, CF, productam in, 2,) extenſum

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