Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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ſed E H, G F ſunt etiam parallelæ, ergo, & </
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B quoque ipſi H F æquidiſtat, vt modò oſtendimus: </
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<
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ſunt inter ſe parallelæ. </
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rectam lineam ducere.</
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<
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& </
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A B C, _MINIMAM_ rectam lineam ducere.</
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Parabolen in axe producto, vt in prima
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figura. </
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s
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">Nam cum B D ſit axis Parabolæ, ſi ex
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B ducatur B G ordinatis æquidiſtans, ipſa
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cum F D rectos angulos efficiet, ac Para-
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mi conic.</
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bolen continget. </
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_MIMA_ omnium, quæ ex F ad
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riam A B C educi poſſunt. </
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<
s
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">Si verò datum punctum F, in ſecunda
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figura, fuerit in ipſo axe B D intra Para-
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bolen A B C, quod diſtet à vertice B, per
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interuallum non maius dimidio recti B E, idem axis ſegmentum F B erit
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_MINIMA_ recta quæſita.</
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ad nu. h.</
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gura ſit in axe B D, ſed interuallum F B
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maius ſit dimidio recti B E. </
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æqualis eidem dimidio, & </
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peripheriæ occurrens in A. </
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F A eſſe _MINIMAM_ quæſitam.</
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<
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ipſa cum axe producta conueniet in H;</
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mi conic.</
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eritque H B ęqualis B G, ſiue H G
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G B, eſtque E B dupla G F, ex conſtructio-
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ne, ergo H G ad G B eſt vt E B ad G F; </
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quo rectangulum H G F æquabitur rectan-
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gulo E B G, ſiue quadrato G A; </
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pr. 1. h.</
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angulus F A H rectus erit. </
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<
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pt. Pappi.</
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@ibilium ad Parabolæ peripheriam A B C. </
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num. 1.</
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<
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figura, vel extra, vt in quarta, inter axem B D, & </
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<
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