Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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xml:space
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">EX hucuſque demonſtratis liceat animaduertere quamcumque
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aſymptoton quodam-modo eſſe primam ex centro ducibilium,
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ſed Hyperbolæ non occurrentium; </
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<
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xml:space
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">itemque eſſe primam ſibi ipſi
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æquidiſtantium, ſed Hyperbolen non ſecantium.</
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<
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">QVæcunque enim educta ex C diuidens angulum DCE ſecat Hyperbo-
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len, quæcunque verò ex C ducta extra CD, Hyperbolæ quidem non
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occurrit, cum neque ipſa CD interior, cum ſectione conueniat.
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</
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<
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">Quare angulus DCE dici poterit MINIMVS ex centro C Hyperbolen com-
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prehendentium, rectis lineis nunquam ei occurrentibus.</
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<
s
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">Item quælibet SX aſymptoto CD æquidiſtanter ducta intra angulũ DCE,
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Hyperbolen ſecat, quælibet verò extra angulum ducta eidem CD parallela,
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nunquam conuenit cum CD, & </
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<
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">eò minus cum ſectione: </
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<
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">ex quo aſymptoton
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<
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Hyperbolæ appellari quodammodo poſſet vltima tangentium Hyperbolen,
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ad infinitum tamen interuallum. </
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<
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">Nam, quæcumque contingens Hyperbo-
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len ad finitam diſtantiam, ſecat ſemper diametrum CB infra C, & </
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<
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">quò pun-
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ctum contactus remotius fuerit à vertice eò magis occurſus contingẽtis cum
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diametro, centro C fiet propior; </
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<
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">donec, cum punctum contactus per infini-
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tum interuallum abierit à centro, prædictus occurſus cum ipſo centro con-
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ueniat.</
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<
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">Sed ne ſuſcipiendam materiam interpellare nobis ſit opus, cum in ipſius
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progreſſu Parabolæ quadratura indigeamus, inter alias, quas habemus,
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apponemus hic̀ tantùm eam, quæ, licet expeditior non ſit, nonnulla tamen
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Lemmata, ac Theoremata præmittit, quorum prima ad aliquas de MA-
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XIMIS, & </
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tres AD, DB, DC eſſe in continua eademque ratione geometrica.</
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cum ſit in prima figura, AB ad BC, vt BC ad BE,
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erit componendo AB cum BC ad BC, vt BC cum BE ad
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BE, & </
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BE, ſiue ad CE, vt BC ad BE, vel vt AB ad BC, ex con-
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ſtructione: </
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<
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<
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">Et cum ſit, ex ſuppoſitione, linea AD ad DC vt qua-
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dratum AB ad BC, & </
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ad BE, ex conſtructione, erit AD ad DC, vt AB ad BE,
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& </
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per conuerſionem rationis AD ad DB, vt AC ad </
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