Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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GEOMETRIÆ
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communem ſectionem borum duorum planorum fore intra figuram in,
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conico productan à plano omnibus eiuſdem lateribus coincidente, vt
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patet in conico, ACD qui ſecatur plano, ACD, & </
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quorum com nunis ſectio ſit, BE. </
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<
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MDV, etiam, BE, fore intra figuram, BNEO, nam, ACVD, e§t
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conicus, & </
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<
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">quia latera non vniuntur, niſi in puncto, A, ideo, BOE,
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eſt aliqua figura, vt etiam, BNE, & </
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<
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BNEO.</
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">rectam tangentem eius baſim
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extendatur planum, hoc tanget ipſum conicum in vna,
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vel pluribus rectis lineis, quę erunt latera conici, velin pla-
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no tranſeunte per eiuſdem latera, quod erit triangulum, ſiue
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in plurib us triangulis.</
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">Sit conicus, cuius vertex, A, baſis, BCE, quam tangat recta,
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DF, in puncto, vel punctis, ſiue in linea. </
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">Dico planum, ADF,
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tangere dictum conicum in recta linea, ſiue in pluribus rectis lineis,
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ſiue in plano, quod erit triangulum per eiuſdem latera tranſiens.
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Tangat igitur, DF, figuram, BCE,
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in puncto, B, & </
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">, DF, dictum ſit extenſum pla-
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num, ergo, AB, erit latus conici, A
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CE, nam latus, quod reuoluitur tran-
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ſiens per, B, congruit rectę, AB, alio-
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quin duæ rectæ lineæ clauderent ſuper-
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ficiem, eſt ergo, AB, in ſuperficie co-
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niculari, eſt etiam in plano per, A, &</
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DF, tranſeunte, ergo, AB, eſt com-
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munis tum ſuperſiciei coniculari, tum
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plano per, A, &</
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<
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">, DF, ducto, nullus
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autem punctus rectę, AB, eſt intra ſu-
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perſiciem cylindraceam, ergo planum
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per, AB, DF, ductum tangit conicum
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in recta, AB: </
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">Eodem pacto oſtendemus idem tangere conicum in
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quibuſuis alijs lateribus, quæ ducuntur à punctis contactus rectæ li-
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neæ, DF, qui fi ſint plures, fit etiam contactus in omnibus lineis,
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fi vero contactus rectæ, DF, fiat in recta linea tunc contactus plani
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per, AB, DF, fit in ſingulis rectis lineis, quæ à recta talis </
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