Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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datur planum, quod baſimiſecet in recta, DV, figuram planam, M
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cimi Ele.</
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BOF, in recta, OM, & </
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">iungantur, MN, puncta, quia ergo plana
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parallela, BF, CE, ſecantur plano quodam, communes eorum ſe-
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ctiones, nempè, OM, DV, erunt inuicem parallelæ, ſed etiam, O
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D, MV, ſunt parallelæ, ergo, OV, erit parallelogrammum, &</
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<
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D, æqualis ipſi, MV, eſt autem, MV, æqualis ipſi, ND, quia am-
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bo ſunt latera eiuſdem cylindrici, ergo, DO, æqualis erit ipſi, DN,
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pars toti, quod eſt abſurdum, non igitur aliquod punctum circuitus
<
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deſcripti a puncto, M, eſt extra planum æquidiſtans baſi, CE, igi-
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tur omnia ſunt in tali plano, iuncta igitur, NM, ipſa erit in eodem
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cum illis plano, in quo pariter iacebunt duo quæuis puncta iungen-
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tes eiuſdem circuitus, & </
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<
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">ideò figura tali ambitu contenta eſt ſuper-
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ficies plana ipſi baſi, CE, æquidiſtans, quod erat oſtendendum: </
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autem vocantur cylindrici oppoſitæ baſes.</
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baſi æquidictantem, & </
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dimus, OV, eſſe parallelogrammum, ideò cum ſciamus, MANH,
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eſſe ſuperficiem planam baſi, CE, æquidiſtantem, ducto per latera vtcum-
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que plano cylindricum ſecante, oſtendemus eodem pacto, ducti plani ſe-
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cantis in cylindrico conceptam figuram eſſe parallelogrammum, cum ſci-
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licet planum ducitur tantum per duo latera, vel parallelogramma, cum
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per plura duobus, ipſum in eorum aliquo non tangens.</
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eiuſdem latera ductis, quę non fint inter ſe parallela, ſint
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autem illa producta donec ſibi occurrant, communis eorum
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ſectio erit eiuſdem cylindrici lateribus parallela.</
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na non parallela, quæ ita ſint producta, donec ſibi occurrant, ſint
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autem illa plana, AM, DN, quorum, & </
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lyndrici, FG, communes ſectiones, AC, HM, DE, SN, erunt
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teced.</
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igitur, AM, DN, parallelogramma, intelligantur oppoſitarum
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baſium, FL, GK, indefinitè productarum plana ſecarià planis di-
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ctorum parallelogrammorum pariter indefinitè productis, in rectis,
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AR, DR, HO, SO, & </
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">eadem ſe inuicem ſecare in recta, RO.</
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