Cavalieri, Buonaventura - Geometria indivisibilibvs continvorvm : noua quadam ratione promota

311291LIBER IV.& , ZX, ad portionem, ACXN, eſſe, vt omnia quádratà, ℟ X, ad
omnia quadrata quadrilinei, NOEX, & , AN, CX, ordinatim ad ba-
ſim, FG, applicatæ ſumptæ ſunt vtcunq; vnde patet.

THEOREMA V. PROPOS. V.

DVctis vtcunque ad baſim parabolæ ordinatim applica-
tis, parallelogramma ſub ipſis, & portionibus baſis ab
ijſdem abſciſſis ad ſibi inſcriptas portiones parabolæ infra-
ſcriptam rationem habebunt.

Sit ergo parabola, HGA, in baſi, HA, circa axim, vel diame-
trum, GO, & ſint ductæ ipſi, GO, parallelæ vtcunque, ST, EC,
compleantur autem parallelogramma, LT, BO, DC, deinde pro-
ducatur, GO, vtcunque in, M, & circa ſemiaxes, vel ſemidiame-
tros, HO, OM, intelligatur, HMA, ſemicirculus, vel ſemiellipſis,

205[Figure 205] cuius curuam, ST,
EC, productæ ſe-
cent in, VN, com-
pleàtur pariter pa-
rallelogramma, H
V, HM, HN, pro-
ducantur inſuper, Y
M, BG, vſque in,
& ℟, & , SV, EN,
vſq; ad puncta, P,
Z, Q, I, quæ ſunt
in lateribus, B ℟, Y
& . Igitur paralle-
logrammum, LT,
ad portionem, HS
T, erit vt omnia
quadrata, HV, ad
omnia quadrata ſe-
miportionis, HT
V, (regula, GM, pro hac Propoſ. ſumpta). i. vt, TA, ad compó-
ſitam ex {1/2}, TA, & , {1/6}, HT, vt patet in Libro de Circulo, & Ellipſi
Propoſitione I.

Similiter oſtendemus, BO, ſemiparabolæ, HGO, eſſe ſexqui-
alterum, eſt enim vt omnia quadrata, HM, ad omnia quadrata, H
VMO, ideſt in ratione ſexquialtera, vt patet in eadem Propoſit. I.

Pariter demonſtrabimus, DC, ad portionem, HGEC, eſſe vt,
AC, ad compoſitam ex, {1/2}, AC, & , {1/6}, CH, ſicenim ſunt

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