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.
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, &
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.
EXpoſita denuò figura circuli Th.
21.
oſtendendum eſt
omnia quadrata portionis minoris, RFV, vtcunque
ſumptæ regula diametro. ſ. FM, ad omnia quadrata eiuſ-
dem regula baſi. ſ. RV, eſſe vt rectangulum ſub, M, & ſub
baſi, RV, ad tria quadrata lineæ, RM, cum quad. MF.
omnia quadrata portionis minoris, RFV, vtcunque
ſumptæ regula diametro. ſ. FM, ad omnia quadrata eiuſ-
dem regula baſi. ſ. RV, eſſe vt rectangulum ſub, M, & ſub
baſi, RV, ad tria quadrata lineæ, RM, cum quad. MF.
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,
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,