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

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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,

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