Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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">Si duæ menſales ABCD, EFGH fuerint ſuper eadem linea AH
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ad eaſdem partes deſcriptæ, ita vt ipſarum baſes AB, DC; </
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<
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">EF,
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HG ſint omnes inter ſe parallelæ, ſintque proportionales lateribus
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in directum poſitis; </
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<
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">nempe ſit vt AB ad EF, ita AD ad EH, & </
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ad HG. </
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<
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">reliqua latera BC, FG eſſe inter ſe parallela.</
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<
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">DVctis enim diagonalibus BD, FH, productaque BC in I. </
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">Cum ſit BA
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ad EF, vt AD ad EH, erit permutando BA ad AD, vt FE ad EH, eſtq;
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<
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">angulus BAD ęqualis angulo FEH, ob parallelas BA, FE, quare triangulum
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BAD ſimile eſt triangulo FEH; </
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<
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<
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& </
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">totus CD A, æquatur
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toto GHE, ob parallelas
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CD, GH, vnde reliquus
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CDB, æquatur reliquo
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GHF. </
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ad GH, vt DA ad HE,
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erit permutando CD ad
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DA, vt GH ad HE, eſtq;
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</
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">DA ad DB, vt HE ad HF,
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ob triangulorum ADB,
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EHF ſimilitudinem, qua-
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re ex æquali CD ad DB,
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erit vt GH ad HF, ſuntq; </
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<
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ſiue HIB, æqualis angulo HGF, ideoque rectæ BC, FG inter ſe æquidiſtant. </
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Quod erat, &</
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<
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">Sià terminis æqualium ſegmentorum ex diametris ſimilium Hy-
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perbolarum abſciſſorum rectæ ordinatim applicentur, vſque
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ad ſectionum aſymptoto
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, erit ſegmentum applicatæ in Hyperbo-
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la maiorum laterum, inter ſectionem, & </
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">aſymptoton interceptum,
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maius ſegmento applicatæ, quod in Hyperbola minorum laterum
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inter ſectionem eiuſque aſymptoton intercipitur.</
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<
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BE, aſymptotos FG, & </
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">Hyperbole minorum ſit HIL, cuius tranſuer-
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ſum MG, rectum GN, aſymptotos OP, & </
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<
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">ipſarum ſectionum diametris, dem-
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pta ſint ęqualia diametri ſegmenta BQ, IR, è quorũ terminis Q, R applicate
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ſint (ad partes æqualium inclinationum) rectæ QAG, RHP vique ad earum
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aſymptotos: </
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<
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ſegmento PH in ſectione minorum.</
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