Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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LIBER II.
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trìangulorum in eadem baſi, & </
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">altitudine cum parallelogrammis conſti-
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tutorum ſunt omnium quadratorum dictorum parallelogrammorum ſub-
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tripla, ſumpto communi latere pro regula, vt probatum eſt.</
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bus oppoſitis parallela, & </
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<
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xml:space
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grammorum vnius ducatur diameter: </
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parallelogrammis ad rectangula ſub trapezio, & </
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toto parallelogrammo per dictam diametrum conſtitutis, re-
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gula baſi, habebunt eandem rationem, quam baſis paralle-
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logrammi, in quo non ducitur diameter ad compoſitam ex,
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{1/2}, eiuſdem, &</
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parallelogrammo, & </
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ctangula ſub dicto trapezio, & </
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zijportio, erunt vt baſis totius parallelogrammi ad compoſi-
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tam ex, {1/2}, baſis parallelogrammi, in quo non ducitur diame-
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ter, & </
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<
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</
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<
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">Sit ergo parallelogrammum, AF, in baſi, DF, quæ ſit regula,
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intra quam ſumptum ſit punctum, E, & </
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acta parallela, BE, ducatur autem in alterutro parallelogrammo-
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rum, AE, EC, vtin, EC, diameter, EC. </
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ſub, AE, EC, ad rectangula ſub tra-
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pezio, ADEC, & </
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eſſe vt, DE, ad compoſitam ex, {1/2}, D
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E, &</
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Coroll.
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@3. huius.</
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trapezio, ADEC, diuiſo per lineam,
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BE, & </
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ſo, æquantur rectangulis ſub, AE, & </
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triangulo, CEF, vel triangulo, BE
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C, & </
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C, & </
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<
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rectangula ſub, AE, EC, ad rectan-
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26. huius.</
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gula ſub, AE, & </
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EC, .</
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rectangulum, DEF, ad quadratum, EF, .</
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<
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nia verò quadrata, BF, ſunt ſexcupla rectangulorum ſub </
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