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

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144124GEOMETRIÆ poſitam ex ea, quam habet, BV, ad, ON, vel, BD, ad, OM, cum
ſunt æquiangula, & ex ea, quem habet quadratum, CD, ad qua-
dratum, GM, quod oſtendendum erat.

COROLLARIVM.

_H_Inc patet, ſi vice quadratorum ſumamus alias figuras planas ſimi-
les, quod eodem pacto oſtendemus omnes figuras ſimiles, AD, F
M, habere inter ſerationem compoſitam ex ratione quadratorum, CD,
GM, & altitudinum, BV, ON, vel laterum, BD, OM, æqualiter
baſibus inclinatorum, cum parallelogramma ſunt æquiangula.

THEOREMA XII. PROPOS. XII.

P Arallelogrammorum, quorum baſium quadrata altitu-
dinibus iuxta eaſdem baſes ſumptis reciprocantur, vel
lateribus æqualiter dictis baſibus inclinatis; omnia quadra-
ta, regulis eiſdem baſibus, ſunt æqualia: Et quorum paral-
lelogrammorum, regulis baſibus, omnia quadrata ſunt æ-
qualia, baſium quadrata altitudinibus, vellateribus æqua-
liter dictis baſibus inclinatis, reciprocantur.

Sint parallelogramma, HX, AD, quorum baſium, VX, BD,
quadrata altitudinibus iuxta ipſas baſes ſumptis, vel lateribus, RX,
CD, ſi hæc baſibus, VX, BD, æqualiter ſint inclinata, recipro-

84[Figure 84] centur. Dico omnia quadrata pa-
rallelogrammorum, HX, AD, eſſe
inter ſe æqualia. Nam omnia qua-
11Ex auce-
ced. drara, HX, ad omnia quadrata, A
D, habent rationem compoſitam ex
ea, quam habet quadratum, VX, ad
quadratum, BD, . i. ex ea, quam
habet, CO, ad, RZ, vel, CD, ad,
RX, cum ſunt æquiangula, & ex ea, quam habet, RZ, ad, CO,
vel, RX, ad, CD, quæ duæ rationes componunt rationem, CO,
ad, CO, vel, CD, ad, CD, quæ eſt ratio æqualitatis, & ideò om-
nia quadrata, HX, erunt æqualia omnibus quadratis, AD.

Sint nunc omnia quadrata, HX, æqualia omnibus quadratis, A
D, regulis eiſdem, VX, BD. Dico quadratum, VX, ad quadra-
tum, BD, eſſe vt, CO, ad, RZ, vel, CD, ad, RX, cum ſunt

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