Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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LIBER I.
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E, ED, erunt æquales, eodem pacto oſtendemus quaſcumque du-
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ctas à puncto, E, ad lineam ambientem, MBND, eſſe æquales
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cuilibet ipſarum, BE, EN, ED, EM, ergo figura, MBND, erit
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circulus, cuius centrum, E, in axe reperitur, quod erat oſtendendum.</
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">_C_olligimus autem ipſas, BD, MN, communes ſectiones figurã-
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rum per axem ductarum, & </
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<
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">circulorum, qui per ſectionem dicti
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ſolidi per plana ad axem recta in eo produsuntur, eſſe eorum diametros,
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cum per centrum tranſeant.</
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<
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xml:space
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">conus ſecetur plano baſi æquidiſtante conce-
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pta in cono figura erit circulus centrum in axe habens.</
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<
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xml:space
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">Si conus ſit rectus patet hoc ex antecedenti Propoſ. </
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xml:space
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ſcalenus, qualis ſit conus, ACFD, qui ſecetur plano baſi, CFD,
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æquidiſtante, quod in eo producat figuram, BRE. </
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<
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">Dico ipſam eſſe
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circulum, centrum in axe habentem. </
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quod in eo producat triangulum, ACD, cuius & </
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<
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communis ſectio ſit, CD, quę erit diameter dicti circuli; </
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<
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& </
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">figuræ, BRE, communis ſectio, BE; </
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l, ACN, ſimiles, quia, BI, ęquidiſtat ipſi, C
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N, ergo, CN, ad, NA, erit vt, BI, ad, IA,
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eodem modo oſtendemus, AN, ad, ND, eſſe
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vt, BI, ad, IE, ergo, ex æquo, CN, ad, N
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D, erit vt, BI, ad, IE, ſed, CN, eſt ęqualis,
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ND, ergo &</
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<
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">, BI, ipſi, IE. </
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<
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">Ducatur nunc
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aliud planum per axem, quod producat trian-
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gulum, ANF, quodq; </
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<
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">ſecet figuram, BRE,
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in, IR, fient ergo trianguli, AIR, ANF, æ-
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quianguli, ergo, FN, NA, NC, erunt lineæ
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in eadem proportione cum ipſis, RI, IA, IB,
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ergo, ex ęquo, FN, ad, NC, erit vt, RI, ad,
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IB, ſed, FN, eſt æqualis ipſi, NC, ergo, R
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I, erit æqualis ipſi, IB, eodem modo oſtende
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mus quaſcunque ductas à puncto, I, ad lineam ambientem, BRE,
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eſſe æquales ipſi, BI, ergo figura, BRE, erit circulus, cuius, cen-
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trum, I, quod oſtendere oportebat.</
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