352332GEOMETRIÆ
ctangulo ſub ſexquitertia, ME, &
ſub, ED, quia baſes eorum
ſunt altitudinibus reciprocę, & eadem ratione rectangulum ſub ſex-
quitertia, EF, & ſub, FM, æquatur rectãgulo ſub EF, & ſexquitertia,
FM, ideò ſupradicta ratio erit eadem ei, quam habet rectangulũ ſub,
DE, vel, EF, & ſub ſexquitertia, EM, cum {1/2}. quadrati, DE, ideſt
cum rectangulo ſub, EF, & {1/2}. EF, ad rectangulum ſub, EF, & ſub
ſexquitertia, FM, cum {5/6}. quadrati, EF, ideſt cum rectangulo ſub,
EF, & {5/6}. EF, duo autem rectangula ſub, EF, & ſub ſexquitertia,
EM, & ſub, EF, & {1/2}. EF, conficiunt rectangulum ſub, EF, & ſub
compoſita ex {1/2}. EF, & ſexquitertia, EM; pariter alia duo rectan-
gula ſub, EF, & {5/6}. EF, & ſub, EF, & ſexquitertia, FM, conficiunt
rectangulum ſub, EF, & compoſita ex {5/6}. EF, & ſexquitertia, FM,
ergo omnia quadrata figuræ, BDMH, demptis omnibus quadra-
tis, BM, ad omnia quadrata, BM, demptis omnibus quadratis figu-
111.2,elem. ræ, BFMH; erunt vt rectangulum ſub, EF, & compoſita ex {1/2}. E
F, & ſexquitertia, EM, ad rectangulum ſub eadem altitudine, EF,
& ſub compoſita ex {5/6}. EF, & ſexquitertia, FM, . i. vt compoſita
ex {1/2}. EF, vel {1/2}. ED, & ſexquitertia, EM, ad compoſitam ex {5/6}. E
F, & ſexquitertia, FM, ideſt vt, EM, cum {1/3}. ME, & {1/2}. ED, ad, M
F, cum {1/2}. MF, & {5/6}. FE, quod oſtendere oportebat.
ſunt altitudinibus reciprocę, & eadem ratione rectangulum ſub ſex-
quitertia, EF, & ſub, FM, æquatur rectãgulo ſub EF, & ſexquitertia,
FM, ideò ſupradicta ratio erit eadem ei, quam habet rectangulũ ſub,
DE, vel, EF, & ſub ſexquitertia, EM, cum {1/2}. quadrati, DE, ideſt
cum rectangulo ſub, EF, & {1/2}. EF, ad rectangulum ſub, EF, & ſub
ſexquitertia, FM, cum {5/6}. quadrati, EF, ideſt cum rectangulo ſub,
EF, & {5/6}. EF, duo autem rectangula ſub, EF, & ſub ſexquitertia,
EM, & ſub, EF, & {1/2}. EF, conficiunt rectangulum ſub, EF, & ſub
compoſita ex {1/2}. EF, & ſexquitertia, EM; pariter alia duo rectan-
gula ſub, EF, & {5/6}. EF, & ſub, EF, & ſexquitertia, FM, conficiunt
rectangulum ſub, EF, & compoſita ex {5/6}. EF, & ſexquitertia, FM,
ergo omnia quadrata figuræ, BDMH, demptis omnibus quadra-
tis, BM, ad omnia quadrata, BM, demptis omnibus quadratis figu-
111.2,elem. ræ, BFMH; erunt vt rectangulum ſub, EF, & compoſita ex {1/2}. E
F, & ſexquitertia, EM, ad rectangulum ſub eadem altitudine, EF,
& ſub compoſita ex {5/6}. EF, & ſexquitertia, FM, . i. vt compoſita
ex {1/2}. EF, vel {1/2}. ED, & ſexquitertia, EM, ad compoſitam ex {5/6}. E
F, & ſexquitertia, FM, ideſt vt, EM, cum {1/3}. ME, & {1/2}. ED, ad, M
F, cum {1/2}. MF, & {5/6}. FE, quod oſtendere oportebat.
THEOREMA XXXV. PROPOS. XXXVII.
IN figura Prop.
32.
oſtendemus, regula, DF, omnia qua-
drata ſemiparabolæ, DBE, ad omnia quadrata ſiguræ,
CBDF, demptis omnibus quadratis trilinei, BCF, eſſe vt
octaua pars, DF, ad duas tertias eiuſdem, DF, . i. vt 3. ad 16.
drata ſemiparabolæ, DBE, ad omnia quadrata ſiguræ,
CBDF, demptis omnibus quadratis trilinei, BCF, eſſe vt
octaua pars, DF, ad duas tertias eiuſdem, DF, . i. vt 3. ad 16.
Nam omnia quadrata ſemiparabolæ, BDE, ſunt dimidium om.
238[Figure 238]
nium quadratorum, AE, ideſt
ſunt ad illa, vt {1/2}. quadrati, D
2220. huius. E, ad quadratum, DE, item
omnia quadrata, AE, ad om-
nia quadrata, AF, ſunt vt qua-
dratum, DE, ad quadratum,
DF; tandem omnia quadrata,
DF, ad omnia quadrata figurę,
33Corol. 32.
huius. CBDF, demptis omnibus
quadratis trilinei, BCF, ſunt ſexquialtera, ideſt ſunt vt quadratũ,
DF, ad rectangulum ſub, DF, & {2/3}. DF, ergo, exæquali,
ſunt ad illa, vt {1/2}. quadrati, D
2220. huius. E, ad quadratum, DE, item
omnia quadrata, AE, ad om-
nia quadrata, AF, ſunt vt qua-
dratum, DE, ad quadratum,
DF; tandem omnia quadrata,
DF, ad omnia quadrata figurę,
33Corol. 32.
huius. CBDF, demptis omnibus
quadratis trilinei, BCF, ſunt ſexquialtera, ideſt ſunt vt quadratũ,
DF, ad rectangulum ſub, DF, & {2/3}. DF, ergo, exæquali,