Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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recti Canones erunt æquales (eo quod ijdem ſint axes ſolidarum, &</
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diametri Canonum) ac propterea ipſorum baſes altitudinibus erunt
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69. h.</
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procè proportionales, ſed in æqualibus portionibus de eodem ſolido, vt
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ſunt baſes rectorum Canonum ita ſunt baſes ſolidarum portionum, & </
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roll. 78. h.</
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titudines tùm portionum, tùm Canonum ſunt eædem, ergo in datis
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69. h.</
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tionibus, quibus inſunt prædictæ conditiones, erunt quoque baſes altitudi-
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nibus reciprocè proportionales. </
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quocunque Sphæroide, vel etiam de Cono recto, habent baſes al-
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titudinibus reciprocè proportionales: </
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">& </
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">è conuerſo.</
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procè proportionales, ipſæ portiones æquales erunt.</
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">QVando enim huiuſmodi portiones ſolidæ ſunt æquales, neceſſariò ea-
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rum axes (ſi portiones fuerint de eodem Conoide Parabolico) erunt
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æquales (ſi de eodem Hyperbolico, aut Sphæra, aut Sphæ-
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roide) erunt proprijs ſemi - diametris proportionales; </
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eædem portiones ſolidæ habent baſes altitudinibus proportionales,
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& </
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">cum portiones de eodem quocunque prædictorum ſolidorum fuerint
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æquales, ipſarum baſes altitudinibus reciprocabuntur.</
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aut obliqui, iam id oſtenſum fuit à Commandino in Comment. </
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chim. </
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">PRæterea ſint duæ ſolidæ portiones A B C, D E F de eodem ſolido,
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quodcunque ſit ex prædictis (quæ tamen in Sphæroide non excedant
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eius dimidium) quarum axes ſint B G, E H, & </
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tudines verò B L, E M, & </
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baſis A I C ad D K F reci-
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procè, vt altitudo E M ad B
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L. </
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ſe æquales eſſe.</
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darum portionum recti Ca-
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nones A B C, D E F, quo-
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rum diametri, & </
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eædem erunt atque axes, &</
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69. h.</
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altitudines ſolidarum portio-
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num.</
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nes ſunt æquales, & </
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inæquales eſſet alter ipſorum, vt puta A B C, altero D E F maior erit: </
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