Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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vt incidentes) ynde etiam figuræ eſſent æquales, & </
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<
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ipſa figura, TDF, eſſet minor figura, BVO, contra ſuppoſitum,
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eſtigitur, DC, maior ipſa, BR, eſt autem, vt, DC, ad, BR, ita,
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PH, ad, NK, nam vt, DG, ad, BM, itaeſt, PH, ad, NK, & </
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10.</
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etiamita, CG, ad, RM, ergo reliqua, DC, ad reliquam, BR,
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erit vt, PH, ad, NK, ſic etiam eſſe oſtendemus, EF, ad, IO, vt,
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PH, ad, NK, & </
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<
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">quia, DC, eſt maior ipſa, BR, vel, EF, ipſa,
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IO, ideò, HP, erit maior, KN, ſi igitur iunxerimus puncta, PN,
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HK, ipſæ, PN, HK, ſi producantur ad partes ipſius, NK, con-
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current, vt in, A. </
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<
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">Dico, A, eſſe verticem conici, cuius eſt baſis ipſa,
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TDF, & </
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<
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TDF, ęquidiſtanter du-
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cto eſt in ipſo concepta
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figura, VBO. </
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<
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Elem.</
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go, NK, eſt parallela
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ipſi, PH, erunt triangu-
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la, ANK, APH, ęqui-
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angula, & </
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<
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">circa æquales
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angulos latera propor-
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tionalia, igitur, HP, ad,
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PA, erit vt, KN, ad, N
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A, &</
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<
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P, ad, NK, erit vt, PA,
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ad, AN, vt autem, PH,
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ad, NK, ita eſt, PG, ad, NM, nam ipſa, HP, KN, ſimiliter
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ſunt diuiſæ in punctis, G, M, ergo, PA, ad, AN, erit vt, PG,
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ad, NM, & </
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<
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">ſunt parallelæ ipſæ, PG, NM, ergo puncta, G, M,
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A, erunt in vna recta linea, ſit illa, AG, igitur, vt, PG, ad, NM,
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mate leq.</
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vel, PH, ad, NK, ita erit, GA, ad, AM, eſt autem, PH, ad,
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NK, vt, FG, ad, OM, & </
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<
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G, ad, BM, ergo, vt, GA, ad, AM, ita erit, FG, ad, OM; </
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G, ad, IM; </
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">&</
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<
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">, DG, ad, BM, ergo, cum ſint
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parallelæ, erunt tum puncta, AOF, tum, AIE, ARC, tum etiam,
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ABD, in vna recta linea, extendantur ergo dictæ rectæ lineæ, quę
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mate leq.</
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erunt, AF, AE, AD, AC. </
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">Eodem modo, ſi per duas quaslibet
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homologas figurarum, VBO, TDF, planum extendamus, fiet in
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cæteris demonſtratio; </
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<
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">igitur ſi ſumantur in ambitu figurę, TDF,
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quęcumq; </
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tes tranſibunt per circuitum figuræ, VBO, ergo figurę, TDF, &</
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VBO, erunt fruſti conici oppoſitę baſes, quod à conico, ATDF,
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abſcinditur per figuram, VBO, quod erat demonſtrandum.</
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