Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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LIBERI.
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ad verticem, A, duci poſſunt, iacent autem omnes illæ in plano
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trianguli, cuius baſis eſt linea contactus vertex reſpectu eius, pun-
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ctus, A, igitur, contactus plani per, AB, DF, ductifit vel in vna,
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vel pluribus rectis lineis, vel in plano, quod eſt triangulum, ſiue
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plura triangula, non ſecabit autem alicubi tale planum ipſum coni-
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cum, tunc enim aliquis punctus talis plani per, AB, DF, tranſeun-
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tis eſſet intra ſuperficiem conicularem, ſit is punctus, I, iuncta igi-
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tur, AI, & </
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<
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">producta verſus baſim incidet intra baſim, vt facilè o-
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ſtendi poteſt, & </
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<
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">quia eſt, AX, in plano per, AB, DF, ducto, & </
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punctus, X, eſt etiam in plano baſis, erit in communi fectione, ideſt
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in linea, DF, igitur aliquis punctus rectæ, DF, erit intra baſim,
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igitur illam ſecabit, quod eſt abſurdum, ergo falſum eſt planum per,
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A, DF, ductum ſecare alicubi ipſum conicum, igitur illum tanget
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in his, quæ dicta ſunt, quod oſtendere oportebat.</
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">_E_X hoc habetur, ſi conicus ſecetur plano baſi æquidiſtante, commu-
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nem ſectionem huius, & </
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">tangentem baſim
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ducti, tangere figuram à plano æquidiſtante baſi in conico productam, ſi
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enim eam ſecaret, etiam tangens planum ſecaret conicum, quod eſt ab-
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ſurdum.</
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eo figura erit ſimilis baſi, & </
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">eidem ſimiliter poſita.</
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">Sit conicus, cuius vertex, A, baſis, TDF, ſecetur autem plano
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baſi æquidiſtante, quod in eo producat figura, VBO. </
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eſſe ſimilem baſi, & </
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ſis duæ vtcumque oppoſitæ tangentes, quæ ſint, TH, SP, indefi-
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huius.</
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nitè productæ, deinde per verticem, & </
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tium extendatur planum, erunt ergo hęc plana tangentia conicum,
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ADF, ſecent autem figuræ, VBO, productum planum in rectis,
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VK, XN, quæ erunt ipſius figuræ, VBO, oppoſitæ tangentes,
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teced.</
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ſumatur deinde in altera ipſarum, TH, SP, vtin, TH, vtcumq;
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">punctum, vt, H, à quo verſus reliquam tangentem eiuſdem figurę,
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TDF, in eiuſdem plano ducatur vtcumque, HP, in, SP, termi-
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nata, deinde intelligatur extenſum planum per, A, &</
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ſiens ita, vtſecet plana conicum tangentia in rectis, AH, AP, &</
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