Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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ſed omnino, vel Ellipſim ſecat, velintra eam cadit, cum punctum I ſit quo-
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que intra. </
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<
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">Quare circulus GBH _MINIMV S_ eſt circumſcriptibilium per ver-
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ticem B maioris axis datæ Ellipſis ABC. </
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Ellipſi inſcriptis, & </
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<
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">_MINIMV M_ circulum per verticem minoris axis AC Ellipſi circumſcri-
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ptum, cuius diameter eſt rectum latus AB.</
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roll. 20. h.</
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">_MINIMV M_ circulum per verticem maioris axis DE circumſcriptũ, cuius
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diameter eſt ipſe maior axis DE.</
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">_MAXIMV M_ circulum per verticem minoris axis AC inſcriptum, cuius
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diameter eſt ipſe minor axis AC.</
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">Et _MAXIMV M_ circulũ per ver-
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ticem maioris axis DE inſcriptum,
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cuius diameter eſt rectum
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roll. 20. h.</
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DF, eſſe quatuor circulos in conti-
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nua eademque ratione geometri-
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ca; </
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DE, AC, DF ſunt quatuor lineæ
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continuè proportionales.</
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">ELicitur quoque, Ellipſim quamcunque, mediam eſſe proportionalem
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inter extremos prædictos circulos, mediamque inter medios. </
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enim quatuor lineæ AB, DE, AC, DF ſint continuè proportionales, erit
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rectangulum ſub extremis AB, DF æquale rectangulo ſub medijs DE, AC,
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nempè quadrato G, quæ ſit media proportionalis inter DE, AC; </
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AB ad G, ita erit G ad DF; </
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">quare circulus ex diametro AB, ad circulum ex
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diametro G, erit vt circulus G, ad circulum ex DF. </
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">Item cum ſit DE ad G,
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ita G ad AC, erit circulus ex DE ad circulum ex G, vt circulus G ad circu-
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de Co-
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noid. &
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Sphęroid.</
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lum ex AC, ſed circulus ex G æquatur Ellipſi; </
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<
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inter medios DE, AC.</
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