Full text: Cavalieri, Bonaventura: Geometria indivisibilibvs continvorvm

LIBER IV. guli, ad portionem parabolæ dicto parallelogrammo inſcri-
ptam ratio nota erit.

Sit parabola, cuius baſis, FG, ad axim, vel diametrum, CX, or-
dinatim applicata; ad baſim autem, FG, ſit etiam ordinatim appli-
cata, AN, vtcunq; diuidens baſim, FG, in puncto, N, ſiat autem
parallelogrammum, RN, & triangulum, AFN, ſublateribus, A
N, NF, vel ſub, AN, NG; Vel ſint duæ vtcunque ad baſim, FG,
ordinatim applicatæ, AN, CX, ſiat autem parallelogrammum, & triangulum ſub, AN, NX, vel ſub, CX, XN. Dico parallelogram-
mum, RN, veltrian-
gulum, FAN, ad
portionem, AFN,
parabole, FCG, pa-
rallelogrammo, RN,
inſcriptam, eſſe in ra-
tione nota. Similiter
parallelogrammum,
ZX, & triangulum,
NCX, ad portio-
nem, ACXN, habe-
re rationem notam. Producatur, CX, vt-
cunque in, E, & cir-
ca ſemiaxes, vel ſemi-
diametros coniuga-
tas, FX, XE, intel-
ligatur deſcriptus ſe-
micirculus, velſemi-
ellipſis, FEG, pro-
ducantur deinde, RF, ZN, indeſinitè, ſecetque, ZN, curuam ſe-
micirculi, vel ſemiellipſis, FEG, in puncto, O, & compleantur pa-
rallelogramma, VN, RX, ſumatur deindein, FN, vtcunq; pun-
ctum, S, per quodipſi, CE, parallela ducatur, YT, ſecans curnam
parabolæ in, I, curuam autem, FEG, in, M; eſt ergo, AN, ad, I
S, vt rectangulum, GNF, ad rectangulum, GSF, eſt autem etiam
quadratum, ON, ad quadratum, SM, vt rectangulum, GNF, ad
rectangulum, GSF, ergo, AN, vel, YS, ad, SI, erit vt quadra
tum, NO, vel vt quadratum, TS, ad quadratum, SM, ſunt au-
tem, RN, NV, parallelogramma in eiſdem baſibus, & altitudini-
bus cum portionibus, AFN, NFO, & punctum, S, ſumptum eſt
vtcunque, repertumque eſt, vt, YS, ad, SI, ita eſſe quadratum, T

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