Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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LIBER II.
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quiangula, etenim, CO, ad, CO, habet rationem compoſitam ex
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lib. 1.</
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ea, quam habet, CO, ad, RZ, & </
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CD, ex ea, quam habet, CD, ad, RX, &</
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">, RX, ad, CD, quia
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verò omnia quadrata, HX, ſunt æqualia omnibus quadratis, AD,
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ideò ſunt ad illa, vt, CO, ad, CO, vel vt, CD, ad, CD, .</
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<
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">i. </
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tione compoſita ex ratione, CO, ad, RZ, &</
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<
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xml:space
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">, RZ, ad, CO, vel,
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CD, ad, RX, &</
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<
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xml:space
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">, RX, ad, CD, ſunt autem omnia quadrata, H
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X, ad omnia quadrata, AD, in ratione compoſita ex ea, quam ha-
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bet quadratum, VX, ad quadratum, BD, &</
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<
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">, RZ, ad, CO, ſiue,
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RX, ad, CD, cum ſunt æquiangula, ideò duæ rationes, CO, ad,
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RZ, &</
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<
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xml:space
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">, RZ, ad, CO, ſiue aliæ duę rationes, CD, ad, RX, &</
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RX, ad, CD, componunt eandem rationem, quam iſtę duę .</
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tio quadrati, VX, ad quadratum, BD, &</
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<
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">, RZ, ad, CO, vel, R
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X, ad, CD, eſt autem communis ratio, RZ, ad, CO, vel, RX,
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ad, CD, ergo reliqua ratio, quam habet quadratum, VX, ad qua-
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dratum, BD, erit eadem reliquę, quam nempè habet, CO, ad,
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RZ, vel, CD, ad, RX, cum ſunt æquiangula, quod erat oſten-
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dendum.</
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grammorum, HX, AD, regulis ijſdem, VX, BD, oſtendi poſſe ex
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ſuperiori methodo colligitur.</
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">SImilium parallelogrammorum omnia quadrata, regulis
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homologis lateribus, ſunt in tripla ratione laterum ho-
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mologorum.</
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">Sint ſimilia parallelogramma, AC, EG, quorum latera homo-
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Sex. El.</
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loga, BC, FG, ſint ſumpta pro regula. </
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C, ad omnia quadr. </
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tione eius, quam habet, BC, ad, FG. </
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Sex. El.</
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niam enim parallelogramma, AC, EG,
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ſunt ſimilia, ideò ſunt æquiangula, & </
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æquales angulos latera habent proportio-
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nalia, &</
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<
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ra ad inuicem æqualiter inclinata, quorum,
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BC, FG, ſunt regulę, ideò omnia quadrata, AC, regula, BC, </
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