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

262242GEOMETRIÆ vel vtrectangulum, FMN, ad, {1/6}, quadratorum, RM, MV,. .
ad, {1/3}, quadrati, RM, . i. ad rectangulum ſub; FM, & , {1/3}, MH, . i. vt,
MN, ad, {1/3}, MH, vel vt tripla, MN, ad, MH. Inſuper eadem
rectangula ſub, Δ V, VT, ad rectangula ſub portione, RFV, &

162[Figure 162] ſub, RY, ſunt vt parallelogrammum,
Δ V, ad portionem, RFV, ergo ſi
fiat, vt, Δ V, ad portionem, RFV,
11Coroll. 1.
26. l. 2. ita tripla, MN, ad, H ω; rectangula
ſub, Δ V, VT, ad reliquum, demptis
rectangulis ſub portione, RFV, &
ſub, RY; à rectangulis ſub eadem por-
tione, & ſub quadrilineo, RTHYV,
. i. ad rectangula ſub portione, RFV,
& portione, THY, . i. ad omnia qua-
drata portionis, RFV, erunt vetripla,
MN, ad, M ω, omnia autem quadra-
ta, Δ V, ad rectangula ſub, Δ V, VT,
ſunt vt quadratum, FM, ad rectangu-
lum, FMI, . i. vt, FM, ad, MI, vel
vt ſexquialtera, FM, ad ſexquialte-
ram, MI, . i. ad triplam, MN, rectan-
gula autem ſub, Δ V, VT, ad omnia
22@4. l. 2. quadrata portionis, RFV, ſunt vt
tripla, MN, ad, M ω, ergo ex æqua-
33@. l. 2. li omnia quadrata, Δ V, ad omnia
quadrata portionis, RFV, erunt vt ſexquialtera ipſius, FM, ad,
M ω, quæ eſt reſiduumipſius, MH, dempta, H ω, ad quam tri-
pla, MN, eſt vt, Δ V, ad portionem, RFV, quod oſtendere
opus erat.

THEOREMA XXIII. PROPOS. XXIV.

Omnia . n. quadrata portionis, RFV, regula, FM, ad omnia
44ex antec. quadrata, Δ V, regula eadem, ſunt vt, ω M, ad ſexquialteram, F
M, . i. vt, {2/3}, M ω, ad, FM; omnia item quadrata, Δ V,