Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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LIBER IV.
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guli, ad portionem parabolæ dicto parallelogrammo inſcri-
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ptam ratio nota erit.</
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<
s
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echoid-s7030
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">Sit parabola, cuius baſis, FG, ad axim, vel diametrum, CX, or-
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dinatim applicata; </
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<
s
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xml:space
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">ad baſim autem, FG, ſit etiam ordinatim appli-
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cata, AN, vtcunq; </
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<
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echoid-s7032
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xml:space
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">diuidens baſim, FG, in puncto, N, ſiat autem
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parallelogrammum, RN, & </
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<
s
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echoid-s7033
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xml:space
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">triangulum, AFN, ſublateribus, A
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N, NF, vel ſub, AN, NG; </
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">Vel ſint duæ vtcunque ad baſim, FG,
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ordinatim applicatæ, AN, CX, ſiat autem parallelogrammum, & </
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<
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<
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triangulum ſub, AN, NX, vel ſub, CX, XN. </
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<
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<
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0309-01
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0309-01
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figure
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mum, RN, veltrian-
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gulum, FAN, ad
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portionem, AFN,
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parabole, FCG, pa-
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rallelogrammo, RN,
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inſcriptam, eſſe in ra-
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tione nota. </
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<
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parallelogrammum,
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ZX, & </
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<
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">triangulum,
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NCX, ad portio-
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nem, ACXN, habe-
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re rationem notam.
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</
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cunque in, E, & </
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ca ſemiaxes, vel ſemi-
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diametros coniuga-
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tas, FX, XE, intel-
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ligatur deſcriptus ſe-
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micirculus, velſemi-
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ellipſis, FEG, pro-
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ducantur deinde, RF, ZN, indeſinitè, ſecetque, ZN, curuam ſe-
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micirculi, vel ſemiellipſis, FEG, in puncto, O, & </
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<
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xml:space
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">compleantur pa-
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rallelogramma, VN, RX, ſumatur deindein, FN, vtcunq; </
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<
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ctum, S, per quodipſi, CE, parallela ducatur, YT, ſecans curnam
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parabolæ in, I, curuam autem, FEG, in, M; </
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<
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">eſt ergo, AN, ad, I
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S, vt rectangulum, GNF, ad rectangulum, GSF, eſt autem etiam
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">40. Et
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Sch. 1. 1.</
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quadratum, ON, ad quadratum, SM, vt rectangulum, GNF, ad
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rectangulum, GSF, ergo, AN, vel, YS, ad, SI, erit vt quadra
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tum, NO, vel vt quadratum, TS, ad quadratum, SM, ſunt au-
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tem, RN, NV, parallelogramma in eiſdem baſibus, & </
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<
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">Coroll.3.
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26. lib. 2.</
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bus cum portionibus, AFN, NFO, & </
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<
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vtcunque, repertumque eſt, vt, YS, ad, SI, ita eſſe quadratum, </
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