263243LIBER III.
F M, ad omnia quadrata eiuſdem parallelogrammi;
Δ V, regula,
1129. Lib. 2. R V, ſunt vt, FM, ad, RV, ergo ex æquali omnia quadrata por-
tionis, RFV, regula, FM, ad omnia quadrata, Δ V, regula, R
V, erunt vt, {2/3}, ω M, ad, RV, vel vt, {1/3}, ω M, ad, RM, . i. ſum-
pta, RM, communi altitudine, vt rectangulum ſub, {1/3}, ω M, &
ſub, RM, ad quadratum, RM, vel ad rectangulum, FMH;
omnia vero quadrata, Δ V, regula, RV, ad omnia quadrata por-
22Vlt. 2. El. tionis, RFV, regula eadem, runt vt, HM, ad compoſitam ex,
331. Huius. {1/2}, HM, & , {1/6}, MF, . i. ſumpta, MF, communi altitudine, vt re-
445. Lib. @ ctangulum, FMH, ad rectangulum ſub, FM, & ſub compoſita ex,
{1/2}, HM, & , {1/6}, MF, erant autem omnia quadrata portionis, RFV,
regula, FM, ad omnia quadrata, Δ V, regula, RV, vt rectangulum
ſub, {1/3}, M ω, & ſub, RM, ad rectangulum, FMH, ergo ex æquali
omnia quadrata portionis, RFV, regula, FM, ad omnia quadrata
eiuſdem, regula, RV, erunt vt rectangulum ſub, {1/3}, M ω, & ſub, R
M, ad rectangulum ſub, FM, & ſub compoſita ex, {1/2}, HM, & , {1/6},
M F, . i. vt rectangulum ſub tota, M ω, & ſub, RM, ad rectangu-
lum ſub, FM, & ſub compoſita ex, {1/2}, FM, & ſexquialtera, MH,
. i. & ſub compoſita ex, {1/2}, FM, & ſexquialtera, MI, & ſexquial-
tera, IH, porrò ſexquialtera, IH, cum, {1/2}, FM, efficit duas, FM,
I H, quibus ſi iunxeris, MI, detractam de ſexquialtera ipſius, MI,
fiet tota, FH, cum, MN, æqualis dimidio, FM, & ſexquialteræ,
M H: Omnia ergo quadrata portionis, RFV, regula, FM, ad om-
nia quadrata eiuſdem portionis, regula, RV, erunt vt rectangulum
ſub, M ω, & ſub, RM, ad rectangulum ſub, FM, & ſub compoſi-
ta ex, FH, MN, . i. ad rectangulum ſub, FM, & ſub, MN, ſub,
55Ex vlt. 2.
Elem. F M, & ſub, MH, & ad quadratum, FM: quia verò rectangulum,
F MH, æquatur quadrato, RM, erunt omnia illa quadrata, vt re-
ctangulum ſub, ω M, & ſub, RM, ad quadratum, RM, quadra-
tum, MF, & rectangulum ſub, FM, MN, vel vt iſtorum dupla. ſ.
vt rectangulum ſub, ω M, & ſub, RV, ad quadratum, RM, qua-
dratum, MV, duo quadrata, FM, & duo rectangula ſub, FM, M
N, . i. vnum ſub, FM, MI, cui ſi iunxeris vnum de duobus quadra-
6612. Elem. tis ipſius, FM, componetur rectangulum, FMH, quod eſt æqua-
le quadrato, RM. Sunt ergo omnia quadrata portionis, RFV, re-
77Vlt. 2. El. gula, FM, ad omnia quadrata eiuſdem portionis, regula, RV, vt
rectangulum ſub, ω M, & ſub, RV, ad tria quadrata, R, M cum
vno quadrato, FM, quod oſtendere oportebat.
1129. Lib. 2. R V, ſunt vt, FM, ad, RV, ergo ex æquali omnia quadrata por-
tionis, RFV, regula, FM, ad omnia quadrata, Δ V, regula, R
V, erunt vt, {2/3}, ω M, ad, RV, vel vt, {1/3}, ω M, ad, RM, . i. ſum-
pta, RM, communi altitudine, vt rectangulum ſub, {1/3}, ω M, &
ſub, RM, ad quadratum, RM, vel ad rectangulum, FMH;
omnia vero quadrata, Δ V, regula, RV, ad omnia quadrata por-
22Vlt. 2. El. tionis, RFV, regula eadem, runt vt, HM, ad compoſitam ex,
331. Huius. {1/2}, HM, & , {1/6}, MF, . i. ſumpta, MF, communi altitudine, vt re-
445. Lib. @ ctangulum, FMH, ad rectangulum ſub, FM, & ſub compoſita ex,
{1/2}, HM, & , {1/6}, MF, erant autem omnia quadrata portionis, RFV,
regula, FM, ad omnia quadrata, Δ V, regula, RV, vt rectangulum
ſub, {1/3}, M ω, & ſub, RM, ad rectangulum, FMH, ergo ex æquali
omnia quadrata portionis, RFV, regula, FM, ad omnia quadrata
eiuſdem, regula, RV, erunt vt rectangulum ſub, {1/3}, M ω, & ſub, R
M, ad rectangulum ſub, FM, & ſub compoſita ex, {1/2}, HM, & , {1/6},
M F, . i. vt rectangulum ſub tota, M ω, & ſub, RM, ad rectangu-
lum ſub, FM, & ſub compoſita ex, {1/2}, FM, & ſexquialtera, MH,
. i. & ſub compoſita ex, {1/2}, FM, & ſexquialtera, MI, & ſexquial-
tera, IH, porrò ſexquialtera, IH, cum, {1/2}, FM, efficit duas, FM,
I H, quibus ſi iunxeris, MI, detractam de ſexquialtera ipſius, MI,
fiet tota, FH, cum, MN, æqualis dimidio, FM, & ſexquialteræ,
M H: Omnia ergo quadrata portionis, RFV, regula, FM, ad om-
nia quadrata eiuſdem portionis, regula, RV, erunt vt rectangulum
ſub, M ω, & ſub, RM, ad rectangulum ſub, FM, & ſub compoſi-
ta ex, FH, MN, . i. ad rectangulum ſub, FM, & ſub, MN, ſub,
55Ex vlt. 2.
Elem. F M, & ſub, MH, & ad quadratum, FM: quia verò rectangulum,
F MH, æquatur quadrato, RM, erunt omnia illa quadrata, vt re-
ctangulum ſub, ω M, & ſub, RM, ad quadratum, RM, quadra-
tum, MF, & rectangulum ſub, FM, MN, vel vt iſtorum dupla. ſ.
vt rectangulum ſub, ω M, & ſub, RV, ad quadratum, RM, qua-
dratum, MV, duo quadrata, FM, & duo rectangula ſub, FM, M
N, . i. vnum ſub, FM, MI, cui ſi iunxeris vnum de duobus quadra-
6612. Elem. tis ipſius, FM, componetur rectangulum, FMH, quod eſt æqua-
le quadrato, RM. Sunt ergo omnia quadrata portionis, RFV, re-
77Vlt. 2. El. gula, FM, ad omnia quadrata eiuſdem portionis, regula, RV, vt
rectangulum ſub, ω M, & ſub, RV, ad tria quadrata, R, M cum
vno quadrato, FM, quod oſtendere oportebat.