553533LIBER VII.
ASſumpto ex ſchemate prop.
3.
ſemicirculo, vel ſemiel-
lipſi, ASFD, circa diametrum, AD, ſimul cum appli-
catis, RF, MS, quarum altera ſit regula, & parallelogram-
mo, NR, oſtendemus in illius figura, quadratum ſolidum
FB, ad quadratum ſolidum portionis, ICFS, eſſe vt rectan-
gulum, DRA, ad rectangulom ſub, DR, & ſub compoſita
ex {1/2}. RM, & ex, MA, vna cum rectangulo ſub, RM, & ſub
compoſita ex {1/6}. RM, & {1/2}. MA.
lipſi, ASFD, circa diametrum, AD, ſimul cum appli-
catis, RF, MS, quarum altera ſit regula, & parallelogram-
mo, NR, oſtendemus in illius figura, quadratum ſolidum
FB, ad quadratum ſolidum portionis, ICFS, eſſe vt rectan-
gulum, DRA, ad rectangulom ſub, DR, & ſub compoſita
ex {1/2}. RM, & ex, MA, vna cum rectangulo ſub, RM, & ſub
compoſita ex {1/6}. RM, & {1/2}. MA.
Producantur enim indefinitè ipſæ applicatæ, SM, FR, verſus,
MR, à quibus abſcindantur, CR, HM, ſingillatim ipſi, DA, æqua-
363[Figure 363]
les, vt etiam, GQ, HK, ſin-
gillatim pariter æquales ipſi,
DR, & , YR, LM, æquales
ipſi, MA, & iungantur, HG,
kQ, LY, QL, & ſit, TX, quę
cumq; inter, RF, MS, diame-
tro, AD, ſimiliter applicata,
quæ indefinitè hincinde ex-
tendatur ſecans, NF, in, V, A
D, in, T, LY, in, I, LQ, in, O, KQ, in, Z, & , HG, in, P. Erunt
ergo, HQ, KY, LR, parallelogramma, & rectangulum, GQR, æ-
quabitur rectangulo, DRA, cum autem, GQ, ſit æqualis, DR, & ,
YR, ipſi, MA, erit, QY, æqualis, RM, hoc eſt ipſi, YL, eſt autem,
QY, ad, YL, vt, OI, ad, L, ergo, OI, æquatur, IL, ideſt, TM, & , Z
I, ipſi, RM, ergo, ZO, æquatur, RT, ergo rectangulum, POT,
MR, à quibus abſcindantur, CR, HM, ſingillatim ipſi, DA, æqua-
gillatim pariter æquales ipſi,
DR, & , YR, LM, æquales
ipſi, MA, & iungantur, HG,
kQ, LY, QL, & ſit, TX, quę
cumq; inter, RF, MS, diame-
tro, AD, ſimiliter applicata,
quæ indefinitè hincinde ex-
tendatur ſecans, NF, in, V, A
D, in, T, LY, in, I, LQ, in, O, KQ, in, Z, & , HG, in, P. Erunt
ergo, HQ, KY, LR, parallelogramma, & rectangulum, GQR, æ-
quabitur rectangulo, DRA, cum autem, GQ, ſit æqualis, DR, & ,
YR, ipſi, MA, erit, QY, æqualis, RM, hoc eſt ipſi, YL, eſt autem,
QY, ad, YL, vt, OI, ad, L, ergo, OI, æquatur, IL, ideſt, TM, & , Z
I, ipſi, RM, ergo, ZO, æquatur, RT, ergo rectangulum, POT,