Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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GEOMETRIÆ
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">SI in circulo, vel ellipſiad axim, vel diametrum eiuſdem
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ordinatim applicetur vtcumque recta linea, quæ ſuma-
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tur pro regula; </
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<
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">Omnia quadrata eiuſdem ad omnia quadra-
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ta alterutrius portionis peream conſtitutæ, erunt vt paralle-
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lepipedum ſub quadrato totius axis, vel diametri, altitudi-
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ne eiuſdem dimidia, ad parallele pipedum ſub quadrato aſ-
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ſumptæ portionis, altitudine autem linea compoſita ex reli-
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quæ portionis axi, vel diametro, & </
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<
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runt, vt cubus totius axis, vel diametri ad parallelepipe-
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dum ſub quadrato aſſumptæ portionis axis, vel diametri, & </
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ſub altitudine linea compoſita ex tripla axis, vel diametri
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reliquæ portionis, cum cubo axis, vel diametri reliquæ por-
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tionis.</
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<
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">Sit circulus, vel ellipſis, ABCD, cuius axis, vel diameter, AC,
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centrum, O, & </
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<
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">ordinatim vtcunq; </
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<
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">ad ipſam applicata, BD, con-
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ſtituens duas portiones, BAD, BCD, quæ quoque ſit regula.
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">Dico ergo omnia quadrata circuli, vel ellipſis, ABCD, ad omnia
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quadrata portionis, BAD, ex duabus portionibus, BAD, BC
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D, ad libitum ſumptæ, eſſe, vt parallelepipedum ſub baſi quadra-
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0226-01
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0226-01
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to, AC, altitudine, CO, vel, CX, quæ ſit
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æqualis, CO, & </
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<
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">illi in directum conſtituta, ad
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parallelepipedum ſub baſi quadrato, AE, al-
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titudine, EX, vel vt cubus, AC, ad parallele-
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pipedum ſub baſi quadrato, AE, altitudine tri-
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pla. </
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<
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">EC, cum cubo, AE; </
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<
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">iungantur, BA, A
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D, BC, CD: </
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<
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">Omnia ergo quadrata portio-
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nis, BCD, ad omnia quadrata portion@s, BA
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lib. 1.</
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D, habent rationem compoſitam ex ea, quam
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habent omnia quadrata portionis, BCD, ad
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omnia quadrata trianguli, BCD, & </
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<
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">ex ea,
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quam habent hæc ad omnia quadrata trianguli, BAD, & </
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<
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">ex ratio-
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ne iſtorum ad omnia quadrata portionis, BAD: </
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<
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xml:space
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">1. huius.</
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drata portionis, BCD, ad omnia quadrata trianguli, BCD, ſunt
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rollar. 22.
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lib. 2.</
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vt compoſita ex, OA, AE, ad, AE: </
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<
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">Omnia item quadrata trian-
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guli, BCD, ad omnia quadrata trianguli, BAD, (quia triangula
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ſunt in eadem baſi, BD,) ſunt vt, CE, ad, EA: </
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