265245LIBER III.
culo, tum in ellipſi) eſt vt quadratum, CN, ad quadratum, NF, vel
vt quadratum, CE, ad quadratum, FH, ideò ſex rectangula, RMV,
ad rectangulum, FMH, erunt vt ſex quadrata, CE, ad vnum qua-
dra um, FH, . i. erunt vt omnia quadrata, RZ, ad rectangula ſub
portione, RFV, & quadrilineo, RTHY V, vt autem ſunt ſex re-
ctangula, RMV, ad rectangulum, FMH, ita quatuor rectangu-
la, RMV, ad, {2/3}, rectanguli, FMH, . i. ad rectangulum ſub, FM,
& , {2/3}, MH, ergo omnia quadrata, RZ, ad rectangula ſub portio-
ne, RFV, & quadrilineo, RTHY V, erunt vt quatuor rectangu-
la, RMV, ad rectangulum ſub, FM, & , {2/3}, MH, erant autem om-
nia quadrata, Δ V, ad omnia quadrata, RZ, vt quadratum, FM,
ad quatuor rectangula ſub, RMV, ergo ex æquali omnia quadra-
ta, Δ V, ad rectangula ſub portione, RFV, & quadrilineo, RTH
YV, erunt vt quadratum, FM, ad rectangulum ſub, FM, & ſub, {2/3}, MH,
eadem verò omnia quadrata, Δ V, ad rectangula ſub portione, R
F V, & ſub, VT, oſtenſa ſunt eſſe, vt quadratum, FM, ad rectan-
gulum, ΓΜΙ, (ex quibus habemus rectangulum ſub, ΓΜΙ, mi-
nus eſſe rectangulo ſub, FM, & ſub, {2/3}, MH, nam rectangula ſub
portione, RFV, & ſub, VT, minora ſunt rectangulis ſub eadem
portione, RFV, & quadrilineo, RTHY V,) ergo omnia quadra-
ta, Δ V, ad reſiduum omnium rectangulorum ſub portione, RFV,
& quadrilineo, RTHY V, demptis rectangulis ſub portione, RF
V, & ſub, VT, . i. ad rectangula ſub vtriſq; portionibus, RFV, THY,
. i. ad omnia quadrata portionis, RFV, erunt vt quadratum, FM,
ad reſiduum ſpatium, dempto rectangulo, ΓΜΙ, a rectangulo ſub,
F M, & ſub, {2/3}, MH, (hoc autem vocetur reſiduum rectangulum
huius Theor.) quod oſtendere opus erat.
vt quadratum, CE, ad quadratum, FH, ideò ſex rectangula, RMV,
ad rectangulum, FMH, erunt vt ſex quadrata, CE, ad vnum qua-
dra um, FH, . i. erunt vt omnia quadrata, RZ, ad rectangula ſub
portione, RFV, & quadrilineo, RTHY V, vt autem ſunt ſex re-
ctangula, RMV, ad rectangulum, FMH, ita quatuor rectangu-
la, RMV, ad, {2/3}, rectanguli, FMH, . i. ad rectangulum ſub, FM,
& , {2/3}, MH, ergo omnia quadrata, RZ, ad rectangula ſub portio-
ne, RFV, & quadrilineo, RTHY V, erunt vt quatuor rectangu-
la, RMV, ad rectangulum ſub, FM, & , {2/3}, MH, erant autem om-
nia quadrata, Δ V, ad omnia quadrata, RZ, vt quadratum, FM,
ad quatuor rectangula ſub, RMV, ergo ex æquali omnia quadra-
ta, Δ V, ad rectangula ſub portione, RFV, & quadrilineo, RTH
YV, erunt vt quadratum, FM, ad rectangulum ſub, FM, & ſub, {2/3}, MH,
eadem verò omnia quadrata, Δ V, ad rectangula ſub portione, R
F V, & ſub, VT, oſtenſa ſunt eſſe, vt quadratum, FM, ad rectan-
gulum, ΓΜΙ, (ex quibus habemus rectangulum ſub, ΓΜΙ, mi-
nus eſſe rectangulo ſub, FM, & ſub, {2/3}, MH, nam rectangula ſub
portione, RFV, & ſub, VT, minora ſunt rectangulis ſub eadem
portione, RFV, & quadrilineo, RTHY V,) ergo omnia quadra-
ta, Δ V, ad reſiduum omnium rectangulorum ſub portione, RFV,
& quadrilineo, RTHY V, demptis rectangulis ſub portione, RF
V, & ſub, VT, . i. ad rectangula ſub vtriſq; portionibus, RFV, THY,
. i. ad omnia quadrata portionis, RFV, erunt vt quadratum, FM,
ad reſiduum ſpatium, dempto rectangulo, ΓΜΙ, a rectangulo ſub,
F M, & ſub, {2/3}, MH, (hoc autem vocetur reſiduum rectangulum
huius Theor.) quod oſtendere opus erat.
THEOREMA XXV. PROPOS. XXVI.
EXpoſita adhuc figura Theor.
antecedentis, oſtendemus
omnia quadrata portionis, RFV, regula, FM, ad om-
nia quadrata eiuſdem portionis, regula baſi, eſſe vt paralle-
lepipedum ſub b ſireſiduo rectangulo antecedentis Theor-
altitudine tripla, MH, ad parallelepipedum ſub baſi rectan-
gulo ipſius, FM, ductæ in, RV, altitudine linea compoſita
ex, MH, HN.
omnia quadrata portionis, RFV, regula, FM, ad om-
nia quadrata eiuſdem portionis, regula baſi, eſſe vt paralle-
lepipedum ſub b ſireſiduo rectangulo antecedentis Theor-
altitudine tripla, MH, ad parallelepipedum ſub baſi rectan-
gulo ipſius, FM, ductæ in, RV, altitudine linea compoſita
ex, MH, HN.
Omnia .
n.
quadrata portionis, RFV, regula, FM, ad omnia
quacrata eluidem, regula, RV, habent rationem compoſitam ex
11Defin. 12.
lib. 1. ea, quam habent omnia quadrata, RFV, ad omnia quadrata,
quacrata eluidem, regula, RV, habent rationem compoſitam ex
11Defin. 12.
lib. 1. ea, quam habent omnia quadrata, RFV, ad omnia quadrata,