Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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GEOMETRIÆ
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poſitas, ex quibus ſumantur quotcunque partes æquales, AI, IH,
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nempè æquales ipſi, CA, &</
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<
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tur parallelogramma, AM, IK, BQ; </
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<
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">ſunt igitur parallelogramma,
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CF, AM, IK, in æqualibus altitudinibus, ac baſibus, & </
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<
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gulorum omnia quadrata regulis eiſdem baſibus, erunt æqualia, & </
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pari ratione omnia quadrata parallelogrammorum, BQ, CQ, e-
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runt ęqualia, regula, CD, altitudines autem parallelogrammorum,
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CF, AM, IK, ſunt æquales ipſi, AO, & </
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<
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">altitudines parallelogram-
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morum, CE, BQ, ſunt æquales, nempè ipſi, CN, habemus ergo
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æquèmultiplices primę, & </
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">compoſitum ex altitudinibus pa-
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rallelogrammorum, CF, AM, IK, quod tam multiplex eſt altitu-
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0142-01
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dinis, AO, quam compoſitum ex omnibus qua-
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dratis, CF, AM, IK, multiplex eſt omnium
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quadratorum parallelogrammi, CF, & </
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<
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">ſic com-
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poſitum ex altitudinibus parallelogrammorum,
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CE, BQ, tam multiplex eſt altitudinis, CN,
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ac compoſitum ex omnibus quadratis parallelo.
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</
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<
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">grammorum, BQ, CE, multiplex eſt omnium
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quadratorum, CE; </
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<
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">ideſt quam multiplicia ſunt
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omnia quadrata parallelogrammi, HD, omnium quadratorum pa-
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rallelogrammi, AD, tam altitudo parallelogrammi, HD, multi-
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plex eſt altitudinis parallelogrammi, AD, ſiue tam ipſa, CH, mul-
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tiplex eſt ipfius, CA, dum ſunt æquiangula, & </
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<
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">quam omnia qua-
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drata parallelogrammi, PD, multiplicia ſunt omnium quadratorum
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parallelogrammi, BD, tam altitudo parallelogrammi, PD, mul-
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tiplex eſt altitudinis, CN, vel tam, PC, multiplex eſt ipſius, CB: </
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Si autem multiplex primæ fuerit æquale multiplici ſecundæ, etiam
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multiplex tertiæ erit æquale multiplici quartæ, ſi maius maius, & </
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minus minus, nam ſi altitudo parallelogrammi, HD, fuerit æqua-
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lis altitudini parallelogrammi, DP, omnia quadrata, HD, erunt
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æqualia omnibus quadratis, DP, nam parallelogramma, HD, D
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P, ſunt in eadem baſi, CD, ſi illa maior, & </
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<
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<
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nor minora, ergo prima ad ſecundam erit, vt tertia ad quartam,
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<
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">5. Quinti
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nempè vt altitudo parallelogrammi, AD, ad altitudinem paralle-
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logrammi, DB, .</
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<
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">AO, ad, CN, vel, AC, ad, CB, dum ſunt
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æquiangula, ita erunt omnia quadrata, AD, ad omnia quadrata,
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DB, ſunt ergo, vt altitudines ipſorum parallelogrammorum, vel
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vt latera ęqualiter baſi inclinata, cum nempè parallelogramma ſunt
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æquiangula: </
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<
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">hæc autem etiam verificarentur ſi parallelogramma
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eſſent in æqualibus baſibus, quod oſtendere opus erat.</
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