Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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<
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xml:space
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">Iam cum portio V M T æqualis ſit portioni I X H, erit baſis V T ad
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">45. h.</
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I H reciprocè vt altitudo X Z ad altitudinem M K, ſed eſt V T maior I H,
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cum ipſa V T ſit contingentium _MAXIMA_, ergo, & </
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facta igitur X Y æquali ipſi M K, applicataque S Y R, erunt portiones V M
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T, R X S æqualium altitudinum, ſed eſt portio R X S minor portione I X H,
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pars ſuo toto, ergo ipſa R X S minor quoque erit portione V M T, & </
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<
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per, &</
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<
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">Quare portio V M T eſt _MAXIMA_ portionum eiuſdem Ellipſis, & </
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æqualium altitudinum. </
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facilè ſimul, tanquam Conſectaria demonſtrabuntur, ſi tamen hæ tres
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concluſiones notatu dignæ præmittantur, à quibus ipſa ortum ducant. </
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">INter diametros æqualium portionum eiuſdem anguli, vel Hyperbolæ, aut
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Ellipſis, _MINIMA_ eſt ea illius portionis, cuius diameter ſimul ſit ſegmentũ
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axis dati anguli, vel Hyperbolæ: </
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axis, & </
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hibente, in portionibus A B C, H O I,
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quæ ſunt æquales, (eò quod
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baſes contingant eandem ſimilem con-
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cẽtricam Hyperbolen interiorem) dia-
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meter B D, quæ eſt axis dati anguli,
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minor eſt diametro O F, cum ſit B D
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ſemi-tranſuerſorum _MINIMA_. </
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ſecunda, Hyperbolen repræſentante,
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in portionibus item A B C, H O I, quę
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ob eandem rationem æquales ſunt, dia-
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meter B D, quæ eſt ſegmentum axis
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Hyperbolæ, minor eſt diametro O F,
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cum ſit B D ad O F, vt ſemi - axis per-
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tingens ad B ex centro exterioris Hy-
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perbole, A B C, ad ſemi-tranſuerſum
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pertingens ad O ex eodem centro, vt
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ſatis conſtat ex 44. </
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<
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minor eſt ſemi-tranſuerſo, quare pa-
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tet, &</
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bus T L V, H O I, A B C interſe pariter æqualibus, diameter L K portionis
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T L V, quæ eſt ex minori axe datæ Ellipſis, minor eſt diametro O F portionis
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H O I, atque minor diametro B D portionis A B C, & </
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E K ad K L eſt vt E F ad F O, & </
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">vt E D ad D B, eſtque antecedens E K minor
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qualibet alia antecedentium, cum ea ſit ſemi-tranſuerſorum _MINIMA_, & </
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D maior eſt ipſarum antecedentiũ, cum ſit ſemi-trãſuerſorum _MAXIMA_, qua-
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re & </
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<
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portionibus ſemi-Ellipſi maioribus. </
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tionum eiuſdem Parabolæ non datur _MAXIMA_, cum omnes æquales ſint.</
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