Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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latere non excedent rectum Hyperbolæ, quæ ſimilis ſit, & </
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trica datæ per datum punctum adſcriptæ, MAXIMAM Hyperbo-
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len inſcribere: </
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<
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recto latere MINIMAM Hyperbolen circumſcribere.</
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<
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">Oportet autem datum punctum, vel eſſe in angulo aſymptotali,
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vel in eo, qui eſt ad verticem, dummodo in primò caſu datum re-
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ctum latus non ſit minus recto eius Hyperbolæ, quæ ſimilis ſit, & </
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concentrica datæ per datum punctum adſcriptæ, in ſecundò verò
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ſit cuiuslibet magnitudinis.</
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<
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ſit E: </
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len inſcribere.</
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ABC in B, & </
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concipiatur
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bi Hyperbole EN ſi-
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milis, & </
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datę ABC, cuius re-
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ctum ſit EG, quod ex
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more, ordinatim ap-
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plicetur diametro E
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B, & </
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EF, quod non ſit ma-
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ius E G, adſcribatur
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ipſi ABC ſimilis Hy,
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perbole HEK, cuius centrum ſit I; </
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<
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">erunt ergo Hyperbolæ EH, EN inter ſe
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ſimiles, quare vt rectum EF, ad rectum EG, ita ſemi-tranſuerſum EI ad ſe-
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mi-tranſuerſum ED, & </
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ED, ſiue punctum I centrum ſectionis EH, vel cadet in ipſo D, vel infra D
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centrum ABC, quapropter ipſa EH datæ ABC erit inſcripta.</
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<
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per E adſcripta, cum eodem recto EF, ſed cum ſemi-tranſuerſo, quod ma-
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ius ſit ipſo EI, eſt minor ſectione EH, quæ verò cum eodem recto EF,
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roll. 19. h.</
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cum ſemi-tranſuerſo EO, quod minus ſit EI, qualis ponatur eſſe ſectio EN,
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eſt quidem maior eadem EH, ſed omnino ſecat datam ABC: </
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<
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ctis DL, IM aſymptotis ſectionum ABC, EH, ipſæ erunt inter ſe parallelæ:</
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ductaque OP aſymptoto ſectionis EN, ipſa OP ſecabit IM infra
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36. huius.</
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tem, ex communi ſectionum vertice E, & </
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