358338GEOMETRIÆ
lelepipedum ſub, BG, &
dicti, ſpatijs, ideò omnia quadrata, AF,
ad omnia quadrata figuræ, CBHF, demptis omnibus quadratis
trilinei, BGE, erunt vt parallelepipedum ſub, BG, & quadrato, H
F, ad reſiduum, dempta ſexta parte parallelepipedi ſub, BI, vel, C
E, exceſſu, BG, ſuper, EF, & ſub quadrato, IE, à parallelepipedo
ſub, BG, & dictis ſpatijs . ſ. quadrato, FG, {1/2}. quadrati, GH, & re-
ctangulo ſub ſexquitertia, HG, & ſub, GF.
ad omnia quadrata figuræ, CBHF, demptis omnibus quadratis
trilinei, BGE, erunt vt parallelepipedum ſub, BG, & quadrato, H
F, ad reſiduum, dempta ſexta parte parallelepipedi ſub, BI, vel, C
E, exceſſu, BG, ſuper, EF, & ſub quadrato, IE, à parallelepipedo
ſub, BG, & dictis ſpatijs . ſ. quadrato, FG, {1/2}. quadrati, GH, & re-
ctangulo ſub ſexquitertia, HG, & ſub, GF.
THEOREMA XLII. PROPOS. XLIV.
INeadem figura Prop.
42.
ducta intra fruſtum parabolæ,
EBHF, recta, VR, parallela baſi, HM, oſtendemus
omnia quadrata figuræ, CBHF, ad omnia quadrata figu-
ræ, CBRV, eſſe vt parallelepipedum ſub, BG, & his ſpa-
tijs . ſ. quadrato, FG, {1/2}. quadrati, GH, & rectangulo ſub
ſexquitertia, HG, & ſub, GF, ad parallelepipedum ſub, B
S, & ſub his ſpatijs, ſcilicet quadrato, VS, 1. quadrati, SR,
& rectangulo ſub ſexquitertia, RS, & ſub, SV.
EBHF, recta, VR, parallela baſi, HM, oſtendemus
omnia quadrata figuræ, CBHF, ad omnia quadrata figu-
ræ, CBRV, eſſe vt parallelepipedum ſub, BG, & his ſpa-
tijs . ſ. quadrato, FG, {1/2}. quadrati, GH, & rectangulo ſub
ſexquitertia, HG, & ſub, GF, ad parallelepipedum ſub, B
S, & ſub his ſpatijs, ſcilicet quadrato, VS, 1. quadrati, SR,
& rectangulo ſub ſexquitertia, RS, & ſub, SV.
Huius demonſtratio non eſt alia à demonſtratione Propoſ.
41.
ideò ibi in ſecunda eiuſdem parte recolatur.
ideò ibi in ſecunda eiuſdem parte recolatur.
THEOREMA XLIII. PROP. XLV.
INeodem Propoſ.
42.
Schemate oſtendemus omnia qua-
drata figuræ, CBHF, demptis omnibus qua dratis trili-
nei, BCE, ad omnia quadrata ſemiparabolæ, BHG, eſſe
vt reliquum parallelepipedi ſub, BG, & his ſpatijs . ſ. qua-
drato, FG, {1/2}. quadrati, GH, & rectangulo ſub, FG, & ſex-
quitertia, GH, ab eodem dempta ſexta parte parallelepi-
pediſub, CE, & quadrato, FG, ad dimidium parallelepi-
pediſub, BG, & quadrato, GH.
drata figuræ, CBHF, demptis omnibus qua dratis trili-
nei, BCE, ad omnia quadrata ſemiparabolæ, BHG, eſſe
vt reliquum parallelepipedi ſub, BG, & his ſpatijs . ſ. qua-
drato, FG, {1/2}. quadrati, GH, & rectangulo ſub, FG, & ſex-
quitertia, GH, ab eodem dempta ſexta parte parallelepi-
pediſub, CE, & quadrato, FG, ad dimidium parallelepi-
pediſub, BG, & quadrato, GH.
Etenim omnia quadrata figuræ, CBHF, demptis omnibus
quadratis trilinei, BCE, ad omnia quadrata, AF, conuertendo,
ſunt vt parallelepipedum ſub, BG, & his ſpatijs, ſcilicet quadrato.
FG, {1/2}. quadrati, GH, & rectangulo ſub, FG, & ſexquitertia, G
H, ab eodem dempto {1/6}. parallelepipedi ſub, CE, & quadrato,
quadratis trilinei, BCE, ad omnia quadrata, AF, conuertendo,
ſunt vt parallelepipedum ſub, BG, & his ſpatijs, ſcilicet quadrato.
FG, {1/2}. quadrati, GH, & rectangulo ſub, FG, & ſexquitertia, G
H, ab eodem dempto {1/6}. parallelepipedi ſub, CE, & quadrato,