Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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diametro vltra centrum 2 in D, quare ſi eadem D 5 producatur, neceſſa-
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riò ſecabit Hyperbolen SPEQ, ſed ipſa D 5 tota cadit extra
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ABC, cum ſit eius aſymptotos, quapropter occurſus rectæ D 5 cum Hyper-
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bola SPEQ ſiet extra ABC, ideoque ſectio EP ſecabit priùs Hyperbolen
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ABC, & </
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">ſic Hyperbole IEL erit _MAXIMA_ inſcripta quæſita. </
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dum, ac demonſtrandum erat.</
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">PRoducatur contingens HE vſque ad circumſcriptã ſectionem ABC in K.
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">Cum Hyperbolę ABC, IEL ſimiles ſint per diuerſos vertices, & </
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dem regulam ſimul adſcriptæ erunt infra EK ad ſe propiùs accedentes,
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mirum ſectio KAT recedet ab EI per interuallum minus ipſo EK; </
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cum Hyperbolę PEQ, IEL ſint concentricæ, & </
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">per eundem verticem ſimul
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adſcriptæ, erunt ſemper magis recedentes, & </
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quocunq; </
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">dato interuallo, videlicet ſectio EPS recedet ab eadem EI per
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teruallũ omnino maius eodẽ EK: </
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ſe mutuò ſecabunt: </
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Hyperbolen circumſcribere, quarum eadem ſit regula.</
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">Oportet autem datum punctum, vel eſſe in angulo aſymptotis
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contento, vel in eo, quod
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eſt ad verticem, dummodo in hoc caſu,
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ipſius diſtantia à centro datæ ſectionis, minor ſit eius ſemi-tranſ-
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uerſo latere per datum punctum tranſeunte.</
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tum extra ipſam punctum ſit E, quod tamen ſit in angulo aſymptotali
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FDG, vt in prima figura; </
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">vel in eò qui ipſi eſt ad verticem, vt in ſecunda,
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dummodo coniuncta ED, & </
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