Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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GEOMETRIÆ
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vel ellipſis, MBEG, vna cum rectangulis bis ſub eodem circulo, vel
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ellipſi, & </
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<
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">ſub quadrilineo, MGEOC, quoniam verò oſtenſum eſt
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omnia quadrata, HO, ad rectangula ſub portione, MGE, & </
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<
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rallelogrammo, MO, quater ſumpta eſſe, vt quadratum, DO, ad
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rectangulum ſub, OE, & </
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<
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xml:space
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">quadrupla, EI, ideò ex æquali omnia
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quadrata, HO, ad omnia quadrata circuli, vel ellipſis, MBEG,
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vna cum rectangulis bis ſub eodem circulo, vel ellipſi, & </
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<
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xml:space
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lineo, MGEOC, erunt vt quadratum, DO, ad rectangulum ſub,
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OE, & </
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<
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xml:space
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parallelogrammis, HF, FC, ad omnia quadrata, HO, ſunt, vt
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vnum, ad vnum .</
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<
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DF, FO, ad quadratum, DO, omnia quadrata verò parallelogram-
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mi, HO, ad omnia quadrata circuli, vel ellipſis, MBEG, vna cum
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rectangulis bis ſub eodem circulo, vel ellipſi, & </
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<
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GEOC, eſſe oſtenſa ſunt, vt idem quadratum, DO, ad rectangu-
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lum ſub, OE, & </
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xml:space
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rallelogrammi, HF, vna cum rectangulis bis ſub parallelogrammis,
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HF, FC, ad omnia quadrata circuli, vel ellipſis, MBEG, vna
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cum rectangulis bis
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ſub eodem circulo,
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vel ellipſi, MBE
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G, erunt vt quadra-
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tum, DF, vna cum
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rectangulo ſub, D
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F, FO, bis, ad re-
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ctangulum ſub, OE,
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& </
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vel erunt, vt eorum
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dimidia .</
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dium quadrati, DF,
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quod erit rectangulum, DFE, vna cum rectangulo ſub, DFO, ſe-
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mel (ex quibus componetur rectangulum ſub, OE, FD,) ad rectan-
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gulum ſub, OE, & </
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rectangulum ſub, OE, &</
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.</
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ergo eſt omnia quadrata, HF, vna cum rectangulis bis ſub paralle-
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logrammis, HF, FC, ad omnia quadrata circuli, vel ellipſis, MB
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EG, vna cum rectangulis bis ſub eodem, & </
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OC, eſſe, vt, DE, vel, FE, ad, EI, .</
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F, ad portionem, MGE, vel vt parallelogrammum, HF, ad cir-
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culum, vel ellipſim, MBEG, quod erat propoſitum.</
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