253233LIBER III.
ſub, MX, &
, MYT, in omnia quadrata, MYT, &
in rectangula
ſub, MYT, & ſub, MTXC, omnia ergo quadrata, MX, ad om-
nia quadrata, MYT, cum rectangulis ſub, MYT, & ſub quadri-
lineo, MTXC, erunt vt, MX, ad, MYT, . i. vt, XY, ad, YZ,
. i. vt quadratum, XY, ad rectangulum ſub, XY, & , YZ, eadem
verò ad hæc quater ſumpta erunt, vt quadratum, XY, adrectangu-
lum ſub, XY, & quadrupla, YZ, ſunt autem omnia quadrata ſe-
miportionis, MYT, quater ſumpta æqualia omnibus quadratis por-
11D.23. hu-
ius. tionis, MST, & rectangula ſub, MYT, & quadrilineo, MTXC,
quater ſumpta æqualia rectangulis ſub eodem quadrilineo, & ſub
portione, SMT, bis ſumptis, nam portio, SMT, bis continet ſe-
miportionem, MYT, ergo conuertendo, omnia quadrata portio.
nis, SMT, cum rectangulis bis ſub eadem, & quadrilineo, MTX
C, ad omnia quadrata, MX, erunt vt rectangulum ſub quadrupla,
YZ, & ſub, YX, ad quadratum, YX, omnia autem quadrata, M
X, ad omnia quadrata, HV, cum rectangulis bis ſub parallelogram-
158[Figure 158]
mis, HV, VC, ſunt
vt vnum ad vnum.
vt quadratum, YX,
ad quadratum, RV,
cum rectangulis bis
ſub, RV, VX, ergo
exęquali omnia qua-
drata portionis, SM
T, cum rectangulis
bis ſub eadem, & ſub
quadrilineo, MTX, adomnia quadrata, HV, cum rectangulis bis
ſub parallelogrammis, HV, VC, erunt vt rectangulum ſub, XY, &
quadrupla, YZ, ad quadratum, RV, cum rectangulis bis ſub, RV
X, vel vt eorum dim dia . ſ. vt rectangulum ſub, XY, & dupla, YZ,
ad dimidium quadrati, RV, ſeil cet ad rectangulum ſub, RV, VY,
cum rectangulo ſub, RV, VX, vel adhuc, vt horum dimidia (com-
pone autem rectangulum ſub, RV, VY, cumrectangulo ſub, RV,
VX, ex quibus fit rectangulum ſub, RV, YX,). ſ. vtrectangulum
ſub, ZY, YX, ad rectangulum ſub, RY, YX, . ſ. vt, ZY, ad, YR,
. ſ. vt ſemiportio, MYT, ad, MV, vel vt portio, SMT, ad, HV.
ſub, MYT, & ſub, MTXC, omnia ergo quadrata, MX, ad om-
nia quadrata, MYT, cum rectangulis ſub, MYT, & ſub quadri-
lineo, MTXC, erunt vt, MX, ad, MYT, . i. vt, XY, ad, YZ,
. i. vt quadratum, XY, ad rectangulum ſub, XY, & , YZ, eadem
verò ad hæc quater ſumpta erunt, vt quadratum, XY, adrectangu-
lum ſub, XY, & quadrupla, YZ, ſunt autem omnia quadrata ſe-
miportionis, MYT, quater ſumpta æqualia omnibus quadratis por-
11D.23. hu-
ius. tionis, MST, & rectangula ſub, MYT, & quadrilineo, MTXC,
quater ſumpta æqualia rectangulis ſub eodem quadrilineo, & ſub
portione, SMT, bis ſumptis, nam portio, SMT, bis continet ſe-
miportionem, MYT, ergo conuertendo, omnia quadrata portio.
nis, SMT, cum rectangulis bis ſub eadem, & quadrilineo, MTX
C, ad omnia quadrata, MX, erunt vt rectangulum ſub quadrupla,
YZ, & ſub, YX, ad quadratum, YX, omnia autem quadrata, M
X, ad omnia quadrata, HV, cum rectangulis bis ſub parallelogram-
vt vnum ad vnum.
vt quadratum, YX,
ad quadratum, RV,
cum rectangulis bis
ſub, RV, VX, ergo
exęquali omnia qua-
drata portionis, SM
T, cum rectangulis
bis ſub eadem, & ſub
quadrilineo, MTX, adomnia quadrata, HV, cum rectangulis bis
ſub parallelogrammis, HV, VC, erunt vt rectangulum ſub, XY, &
quadrupla, YZ, ad quadratum, RV, cum rectangulis bis ſub, RV
X, vel vt eorum dim dia . ſ. vt rectangulum ſub, XY, & dupla, YZ,
ad dimidium quadrati, RV, ſeil cet ad rectangulum ſub, RV, VY,
cum rectangulo ſub, RV, VX, vel adhuc, vt horum dimidia (com-
pone autem rectangulum ſub, RV, VY, cumrectangulo ſub, RV,
VX, ex quibus fit rectangulum ſub, RV, YX,). ſ. vtrectangulum
ſub, ZY, YX, ad rectangulum ſub, RY, YX, . ſ. vt, ZY, ad, YR,
. ſ. vt ſemiportio, MYT, ad, MV, vel vt portio, SMT, ad, HV.
Inſuper omnia quadrata, HV, cum rectangulis bis ſub parallelo-
grammis, HV, VC, ad omnia quadrata, RF, cum rectangulis bis
ſub parallelogrammis, RF, FX, funt vt, HR, ad, RD, & tan-
dem modo ſuperiori oſtendemus omnia quadrata, RF, cum rectan-
gulis bis ſub parallelogrammis, RF, FX, ad omnia quadrata
portionis, SET, cum rectangulis bis ſub eadem, & ſub
grammis, HV, VC, ad omnia quadrata, RF, cum rectangulis bis
ſub parallelogrammis, RF, FX, funt vt, HR, ad, RD, & tan-
dem modo ſuperiori oſtendemus omnia quadrata, RF, cum rectan-
gulis bis ſub parallelogrammis, RF, FX, ad omnia quadrata
portionis, SET, cum rectangulis bis ſub eadem, & ſub
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