Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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& </
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">diameter B G erit æquo maior: </
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">ſi igitur ipſa ad æquum reducatur in N,
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ita vt, vel B N ſit æqualis ipſi E H, (dum ſolidum ſuerit Conoides Parabo-
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licum,) vel ita vt B N, & </
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<
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">E H ad proprias ſemi- diametros ſint in eadem ra-
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tione,) dum ſolidum ſuerit Hyperbolicum, vel Sphæra, aut Sphæroides;) </
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<
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">vel
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ita vt eędem pertingant ad eandẽ ſimilem concentricam ſectionem inſcriptã;
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</
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<
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">erit B N omnino minor B G, & </
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">ſi per N agatur ipſi A C ęquidiſtans O N P,
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quę ad eandem diametrum B G erit ordinatim ducta, atq; </
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<
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">minor ipſa A C,
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ſiet portio, ſeu Canon O B P æqualis portioni, ſiue Canoni D E F, & </
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">40. h. &
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ex 45. h.</
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O P ſecabit B L in R, eritque B R altitudo Canonis O B P, cum ob paral-
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lelas ſit angulus B R N rectus: </
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">& </
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<
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">ſi per rectam O P ducatur planum O Q P,
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quod baſi A I C ſit parallelum, ſiue rectum ad Canonem A B C, id abſcin-
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det ex dato ſolido portionem
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O B P, cuius altitudo erit B
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R eadem atque Canonis O B
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P. </
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æqualis ſit Canoni D E F,
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erit ſolida portio O B P
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">78. h.</
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qualis ſolidæ portioni D E F,
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ac ideo vt baſis O Q P ad ba-
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ſim D K F, ita reciprocè
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ma parte
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huius.</
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titudo E M ad altitudinem B
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R, eſtque baſis D K F ad ba-
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ſim A I C, ex hypotheſi, vt
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altitudo B L ad altitudinem
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E M, quare, ex æquali in ratione perturbata, erit baſis O Q P ad baſim A
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I C, vt altitudo B L ad altitudinem B R, ſed eſt B L maior B R, ergo & </
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baſis O Q P maior erit baſi A I C, quod eſt falſum, cum ſit minor, eò quod
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O P diameter Ellipſis, aut circuli O Q P minor ſit homologa diametro A C
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ſimilis Ellipſis, vel circuli A I C. </
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<
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">Non erit ergo Canonum A B C, D
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15. Arch.
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de Co-
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noid. &c.</
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F alter altero maior, quare inter ſe æquales eſſe neceſſe eſt: </
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portiones ſolidæ A B C, D E F ęquales erunt. </
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propoſitum ſuit.</
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">Æquales portiones ſolidæ de eodem quocunque Conoide, aut
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Sphæra, aut Sphæroide ad ſibi inſcriptam Coni portionem, vel ad
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circumſcriptum Cylindricum, vnam, eandemque ſimul habent
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rationem.</
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">ETenim huiuſmodi portiones habent baſes altitudinibus reciprocè pro-
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portionales, vt in præcedenti, primo loco demonſtratum eſt, ſed ba-
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ſes, & </
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rum Coniportionum, quare, & </
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bus erunt reciprocè proportionales, ſed eædem portiones Conorum </
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