Full text: Cavalieri, Bonaventura: Geometria indivisibilibvs continvorvm

GEOMETRI Æ pro alis in hac propoſitione ſit pariter regula, extendaturq; hinc
indevt ſecet EC, vt in, N, HV, vt in, R, & PV, vt in, Q, ergo, CG,
ad, MO, erit vt quadratum, GH,
ad rectangulum ſub compoſita
ex, HG, GO, & ſub, OH, (hoc. n. deducitur ex prop. 3. lib. 4. quæ
non dependet à prop. 1. neq; indi-
get, quod denuò demonſtretur)
ideſt vt quadratum, GV, ad qua-
dratum, OR, ſed vt, CG, ad MO,
ita eſt quadratum, CG, ad rectan-
gulum ſub, CG, ſeu, NO, & OM, ergo quadratum, CG, ad rectan-
gulum, NOM, erit vt quadratum, GV, ad quadratum, OR, & per-
mutando quadratum, CG, ad quadratum, GV, erit vt rectan-
gulum, NOM, ad quadratum, OR, ſic ductis alijs parallelis
euenire oſtendemus; ergo ſolidum rectangulum ſub, EG, paral-
lelogrammo, & ſemiparabola, CHG, erit proportionaliter ana-
logum quadrato ſolido quadrantis, HVG, ſecundum regulam,
C V, ſecundum eandem autem oſtendemus etiam quadratum
ſolidum, EG, eſſe proportionaliter analogum quadrato ſolido, H
V, etenim quadratum, CG, ad quadratum, GV, eſt vt quadratum,
NO, ad quadratum, OQ, vnde vt quadratum, CG, ad quadratum,
GV, ſic erit quadratum ſolidum, EG, ad quadratum ſolidum, G
P, & ſic etiam rectangulum ſolidum ſub, EG, HCG, ad quadratum
ſolidum, HGV, ergo quadratum ſolidum, EG, ad quadratum ſoli-
dum, HV, erit vt rectangulum ſolidum ſub, EG, HCG, ad quadra-
tum ſolidum, HGV, ergo permutando quadratum ſolidum, EG, ad
rectangulum ſolidum ſub, EG, HCG, erit vt quadratum ſolidum,
HV, ad quadratum ſolidum, HGV, ſed quadratum ſolidum, HV,
ſequialterum eſt quadrati ſolidi, HGV, cum, VG, tranſeat per cen-
trum, G, ergo quadratum ſolidum, EG, ſexquialterum erit rectan-
guli ſolidi ſub, EG, HCG, ſed vt quadratum ſolidum, EG, ad rectan-
gulum ſolidum ſub, EG, HCG, ita baſis, EG, ad baſim, HCG, ergo,
EG, erit ſexquialtera, HCG, & conſequenter, viſa figura prop. 1. lib. 4. erit parallelogrammum, AH, ſequialterum parabolæ, FCH,
quod oſtendendum erat.

749.1.

0558-01
Elicitur
ex 20. hu-
ius.
Cor. 1. 13.
huius.

750. ANNOTATIO.

PEr hanc autem ſuppletur prop. 1. lib. 4. etenim illius poſterior
pars deducetur, vt ibi, hac vero demonſtrata reliqua nunc

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