Cavalieri, Buonaventura
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Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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GEOMETRI Æ
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">Sit conus, cuius vertex, A, baſis circulus, CEFD, ſecetur autem
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prius plano per axem, quod in eo producat triangulum, ACF, ſe-
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cetur deinde altero plano baſim ſecante ſecundum rectam, ED, per-
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pendicularem ipfi, CF, cuius in cono concepta ſit figura, BED,
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erit ergo hæc figura circa axem, vel diametrum, BV, quę ſit paral-
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lela ipſi, AF, cuius vertex reſpectu ipſius, ED, erit, B; </
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<
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puncto, M, qui non ſit punctus, B, ſed vtcumque ſumptus in linea,
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EBD, extra baſim, ED, ipſi, ED, recta ęquidiſtans, MO, pro-
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ducta vſq; </
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<
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">ad ambientem ſuperficiem, cui occurrat in, O, igitur hęc
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erit vna ex ordinatim applicatis ad axim, vel diametrum, BV, ęqui-
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diſtans ipſi, ED, quę bifariam diuidetur ab ipſa, BV, in puncto, N,
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ducatur per, N, ipſi, CF, parallela, HR, eſt verò etiam, MO, ipſi,
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ED, parallela, ergo planum tranſiens per, HR, MO, æquidiſta-
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cim. El.</
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bit baſi, CEFD, & </
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<
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periphæria, cuius diameter, HR, quem
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ſecat, MO, perpendiculariter, nam an-
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gulus, HNM, æquatur angulo, CVE,
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Elem.</
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quirectus eſt, ergo quadratum, MN, æ-
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quatur rectangulo, HNR, & </
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tum, EV, rectangulo, CVF, eſt autem
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rectangulum, CVF, ad rectangulum, H
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NR, (quia eorum altitudines, VF, NR,
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ſunt æ quales, cum ſint parallelogrammi,
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NF, oppoſita latera) vt baſis, CV, ad,
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HN, ex prima Sexti Elem. </
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libro ſequentis independénter ab hac de-
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monſtrata, & </
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ipſi, CV, trianguli, BHN, BCV, ſunt æquianguli, ideò, vt, C
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Elem.</
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V, ad, HN, ita, VB, ad, BN, ergo rectangulum, CVF, ad re-
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ctangulum, HNR, ideſt quadratum, EV, ad quadratum, MN,
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erit vt, VB, ad, BN, eſt autem quadratum, ED, quadruplum
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quadrati, EV, nam eſt æquale quadratis, EV, VD, & </
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<
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Elem.</
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fub, EVD, bis, ideſt duobus quadratis, EV, quæ cum prædictis
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conficiunt quatuor quadrata, EV, & </
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<
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O, eſt quadruplum quadrati, MN, ergo quadratum, ED, ad qua-
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dratum, MO, erit vt, BV, ad, BN, quæſunt abſciſſæ ab ipſa axi,
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vel diametro, BV, verſus verticem, B, per ipſas, ED, MO, ordi-
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natim adipſam, BV, applicatas, quod oſtendere opus erat; </
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<
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tem vocatur ab Apolonio Parabola.</
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