Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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maior erit ipſa CE. </
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0089-01
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terceptæ PO magis remouentur à
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vertice B, eò ſunt maiores: </
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huiuſmodi ſectiones inter ſe ſunt
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ſemper recedentes. </
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dò, &</
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<
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xml:space
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">Præterea ſit BY ſectionem con-
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tingens in B, & </
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uerſis lateribus, nempe GB in V,
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& </
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">cum ſit tranſuerſum
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GB maius BH, erit dimidium BV
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maius dimidio BX: </
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<
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">iam ex centro
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V ducatur VY aſymptotos inſcri-
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ptæ Hyperbolæ DBE, & </
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<
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tro X agatur XZ aſymptotos cir-
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cumſcriptæ ABC, quæ aſymptoti
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contingentem BI ſecent in Y, Z, & </
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per X agatur X & </
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">parallela ad BY contingentem ſecans in &</
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<
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">Itaque quadratum BY ad BZ eſt, vt rectangulum GBF ad rectangulum
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HBF (vtrumque enim quadratorum eſt quarta pars ſuæ figuræ) vel vt
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GB ad BH, vel ſumptis ſubduplis, vt VB ad BX, vel ob parallelas, vt YB ad
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B&</
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">, quare BZ eſt media proportionalis inter BY, & </
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<
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rallelas VY, Z& </
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">in X, ipſa produ-
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cta ad partes Z ſecabit quoque alteram parallelam VY infra BY: </
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<
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rum ſectionum aſymptoti infra contingentem ex vertice inter ſe conueniunt.</
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<
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">Amplius cum aſymptotos VY inſcriptæ occurrat diametro BG vltra cen-
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trum X circumſcriptæ Hyperbolę ABC in puncto V, ipſaque aſymptotos
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VY conueniat cum XZ aſymptoto circumſcriptæ ABC, vt modò oſtendi-
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mus, ſi producatur, ſecabit quoque Hyperbolen ABC. </
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inſcriptæ ſecat Hyperbolen circumſcriptam.</
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<
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">Tandem cum harum ſectionum aſymptoti infra contingentem BY ſe mu-
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tuò ſecent, & </
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">XZ aſymptotos circũſcriptæ BCP, cadat totas extra ipsã BCP,
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harum aſymptoton occurſus erit extra eandem BCP, vt in 2: </
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aſymptotos inſcriptæ, ſecet Hyperbolen BCP circumſcriptam, eſto earum
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communis ſectio in 3, & </
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">recta 2 3, producatur ad inferiores partes 4, atque
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ex 3 ducatur recta 3 5 parallela ad X 2 aſymptoton circumſcriptæ BC 3, quę
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recta 3 5 nunquam conueniet cum ſectione 3 7 ad inferiores partes,
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etiam recta 3 4 nunquã conuenit cum ſectione BE 6 ad eaſdem partes (nam
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eſt eius aſymptotos) & </
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">duæ rectæ 3 5, 3 4 ſunt ſemper ſimul recedentes,
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& </
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">ad interuallum perueniunt maius quolibet dato interuallo; </
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gis interuallum ſectionum BC7, BE6, datum quodcunque interuallum ex-
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cedet. </
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adſcriptarum, & </
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