357337LIBER IV.
Sit ergo parabola, HBM, cuius axis, vel diameter, BG, baſis,
241[Figure 241]
HM, ducatur autem intra ipſam
eidem, BG, parallela, EF, ducta
verò tangente, AC, in termino,
B, quæ erit parallela baſi, HF, pro-
ducatur verſus, FE, illi productæ
occurrens in, C, & compleatur pa-
rallelogrammum, AF, regula ve-
rò ſit, HM. Dico ergo omnia qua-
drata, AF, ad omnia quadrata fi-
guræ, CBHF, eſſe vt quadratum, HF, ad quadratum, FG, {1/2}. qua-
dtati, GH, & rectangulum ſub ſexquitertia, HG, & ſub, GF. Hęc
autem erit conſimilis demonſtrationi ſecundæ partis Theor. 32.
ideo inde colligatur.
eidem, BG, parallela, EF, ducta
verò tangente, AC, in termino,
B, quæ erit parallela baſi, HF, pro-
ducatur verſus, FE, illi productæ
occurrens in, C, & compleatur pa-
rallelogrammum, AF, regula ve-
rò ſit, HM. Dico ergo omnia qua-
drata, AF, ad omnia quadrata fi-
guræ, CBHF, eſſe vt quadratum, HF, ad quadratum, FG, {1/2}. qua-
dtati, GH, & rectangulum ſub ſexquitertia, HG, & ſub, GF. Hęc
autem erit conſimilis demonſtrationi ſecundæ partis Theor. 32.
ideo inde colligatur.
IN eadem anteced.
Propoſit.
figura oſtendemus omnia
quadrata, AF, ad omnia quadrata figuræ, CBHF, dem-
ptis omnibus quadratis trilinei, BCE, eſſe vt parallelepi-
peduw ſub, BG, & quadrato, HF, ad reliquum parallelepi-
pedi ſub, BG, & his ſpatis . ſ. quadrato, FG, {1/2}. quadrati,
GH, & rectangulo ſub ſexquitertia, HG, & ſub, GF, ab eo-
dem dempto {1/3}. parallelepipedi ſub, CE, & quadrato, FG.
quadrata, AF, ad omnia quadrata figuræ, CBHF, dem-
ptis omnibus quadratis trilinei, BCE, eſſe vt parallelepi-
peduw ſub, BG, & quadrato, HF, ad reliquum parallelepi-
pedi ſub, BG, & his ſpatis . ſ. quadrato, FG, {1/2}. quadrati,
GH, & rectangulo ſub ſexquitertia, HG, & ſub, GF, ab eo-
dem dempto {1/3}. parallelepipedi ſub, CE, & quadrato, FG.
Nam omnia quadrata, AF, ad omnia quadrata, BF, ducta per,
1111.l. 2. E, ipſa, EI, æquidiſtans, HM, ſunt vt parallelepipedum ſub, AH,
& quadrato, HF, ad parallelepipedum ſub, BI, & quadrato, IE,
ſuut autem omnia quadrata, BE, ſexcupla ommum quadratorum
2230. huius. trilinei, BCE, ideò omnia quadrata, AF, ad omnia quadrata tri-
242[Figure 242]
linei, BCE, erunt vt parallelepi-
pedum ſub, AH, vel, BG, & ſub
quadrato, HF, ad parallelepipedi
ſub, BI, & quadrato, IE, ſextam
partem: Quia verò omnia quadra-
ta, AF, ad omnia quadrata figuræ,
3324. huius. CBHF, ſunt vt quadratum, HF,
ad hæc ſpatia . ſ. quadratum FG,
{1/2}. quadrati, HG, & rectangulum
ſub ſexquitertia, HG, & ſub, GF, . i. ſumpta, BG, communi alti-
tudine, vt parallelepipedum ſub, BG, & quadrato, HF, ad
1111.l. 2. E, ipſa, EI, æquidiſtans, HM, ſunt vt parallelepipedum ſub, AH,
& quadrato, HF, ad parallelepipedum ſub, BI, & quadrato, IE,
ſuut autem omnia quadrata, BE, ſexcupla ommum quadratorum
2230. huius. trilinei, BCE, ideò omnia quadrata, AF, ad omnia quadrata tri-
pedum ſub, AH, vel, BG, & ſub
quadrato, HF, ad parallelepipedi
ſub, BI, & quadrato, IE, ſextam
partem: Quia verò omnia quadra-
ta, AF, ad omnia quadrata figuræ,
3324. huius. CBHF, ſunt vt quadratum, HF,
ad hæc ſpatia . ſ. quadratum FG,
{1/2}. quadrati, HG, & rectangulum
ſub ſexquitertia, HG, & ſub, GF, . i. ſumpta, BG, communi alti-
tudine, vt parallelepipedum ſub, BG, & quadrato, HF, ad