Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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ma P Q, R S, &</
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">c, concipiantur deſcripta ſolida parallelepipeda æqualium
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altitudinum cum Cylindrico A, vel L; </
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<
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">quorum inſiſtentes lineæ ſint
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æquidiſtantes inſiſtentibus Cylindrici A, &</
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<
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<
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xml:space
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">erit ergo vnumquodque pa-
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rallelepipedorum inſcriptorum, ad parallelepipedum L, vt propria baſis
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Elem.</
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baſim, ac ideò omnia ſimul inſcripta ſuper P Q, R S, &</
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<
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<
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">ad vnicum paralle-
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lepipedum, vel Cylindricum L, erunt vt omnes baſes P Q, R S, &</
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<
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vt figura inſcripta ad baſim R T; </
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">ſed inſcripta ad K T maiorem habet ratio-
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nem quàm Cylindricus A ad L, ergo, & </
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">omnia ſimul parallelepipeda in-
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ſcripta, ad Cylindricum L maiorem habebunt rationem, quàm Cylindri-
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cus A circumſcriptus ad eundem Cylindricum L, ergo inſcripta ſimul pa-
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rallelepipeda maiora erunt Cylindrico A, pars ſuo toto, quod eſt abſurdũ:
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</
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">non eſt ergo baſis C D E maior quàm opus eſt ad hoc vt ad baſim K T ſit vt
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Cylindricus A ad L.</
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C D E ad K T hab ere mi-
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norem rationem quàm
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Cylindricus A ad L, erit
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baſis C D E minor quàm
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opus eſt ad hoc vt huiuſ-
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modi magnitudines ſint
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proportionales, inuento
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igitur defectu, &</
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baſi C D E circumſcri-
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ptione figuræ ex paralle-
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logrammis, &</
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<
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baſim K T adhuc minorẽ
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habeat rationem quàm
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Cylindricus A ad L, & </
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circumſcriptis parallele-
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pipedis vt ſupra, oſtendetur aggregatum circumſcriptorum parallelepipe-
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dorum ad Cylindricum L eſſe vt figura circumſcripta ab baſim K T, hoc eſt
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habere minorem rationem quàm Cylindricus A ad eundem Cylindricum
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L, ideoque prædictum aggregatum parallelepipedorum minùs eſſe Cylin-
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drico A, totum ſua parte, quod eſt abſurdum. </
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habet maiorem, nec minorem rationem quàm Cylindricus A ad L, ergo
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erit baſis C D E ad baſim K T, vt Cylindricus A ad L. </
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">Eadem ratione
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demonſtrabitur, baſim K T ad Acuminatum F G H, ſiue ad baſim Cylin-
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drici B, eſſe vt Cylindricus L ad Cylindricum B; </
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">quare, ex æquo, erit vt
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baſis C D E ad baſim F G H, ita Cylindricus A ad Cylindricum B. </
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erat, &</
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æquales baſes habuerint inter ſe æquales erunt.</
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