Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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LIBERI.
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E, ad, BD, ita, CA, ad, AB, ergo vt, CM, ad, MB, ita erit, C
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A, ad, AB, diuidendo, CB, ad, BM, erit vt, CB, ad, BA, er-
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go, MB, erit æqualis ipſi, BA, totum parti, quod eſt abiurdum,
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non igitur, ED, producta tranſit ſupra, A, eodem modo oſtende-
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mus non tranfire infra, A, ergo tranſibit per, A, ergo tria puncta,
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A, D, E, erunt in recta linea, AE, quod erat oſtendendum.</
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">SI duarum quarumlibet ſimilium figurarum habeamus
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homologas cum duabus quibuſdam regulis, habebi-
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mus etiam homologas earundem cum duabus quibuſuis a-
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lijs, cum prædictis angulos æquales ad eandem partem fa-
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cientibus.</
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<
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">figuræ planę ſimiles, ſi ſint
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æquales, & </
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">ſimiliter poſitæ, poſſunt eſſe cuiuſdam cylindrici oppo-
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ſitæ baſes, ſi ſint inæquales, oppoſitæ bales fruſti conici, in his au-
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tem contingit, ſi habeamus homologas cum duabus quibuſdam re-
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& 11. hus
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ius.</
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gulis, nos eaſdem habere cum alijs duabus quibuſcumque cum præ-
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dictis angulos æquales ad eandem partem conſtituentibus, ergo hoc
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in quibuſcumque planis ſimilibus figuris verificatur, quod eſt pro-
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poſitum.</
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gulos ad eandem partem efficiunt æquales, ideò & </
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erunt homologarum earundem ſimilium figurarum regulæ, & </
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in quibuſdam regulis homologarum poterunt ſumi earum incidentes.</
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">SI in duarum ſimilium figurarum oppoſitas tangentes, quę
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earundem homologarum ſint regulæ, incidant duæ re-
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ctæ lineæ ad eundem angulum ex eadem parte eaſdem ſe-
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cantes, ductis verò quibuſdam duabus, prædictis tangenti-
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bus parallelis, in dictis figuris, quæ ſecantes diuidant ſimi-
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liter ad eandem partem, vel aſſumptis ipſis oppoſitis tangen-
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tibus, reperiamus harum portiones inter incidentes, & </
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