Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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<
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">Siverò CB fuerit maior BA, erit quoque ED maior DA, & </
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cta IDH ſupra ſubiectum planum dematur DH, quæ minor ſit ipſa DA, & </
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iungatur AH, & </
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">erit rectangulum HDI æ-
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quale quadrato DF, ſiue rectangulo EDB, ſed rectangulum EDB maius eſt
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rectangulo ADB, cum ſit ED maior DA, quare rectangulum HDI maius
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erit rectangulo ADB. </
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">Iam ex I ducatur IR parallela ad AH, ſecans produ-
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ctam AD in R; </
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<
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ergo & </
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">ID erit minor DR, vnde rectangulum ſub maioribus AD, DR, maius
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erit rectangulo ſub minoribus HD, DI; </
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<
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tum eſt maius rectangulo ADB, ergo rectangulum ADR eò amplius maius
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erit rectangulo ADB: </
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<
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">vnde recta BR maior erit recta DB, hoc eſt punctum
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B cadet inter D, & </
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">quare iuncta I B, & </
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ducta conueniet cum producta AH ad partes B, H, veluti in L.</
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">cum factum ſit vt ID ad DF, vel
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ad DG, ita DG ad DH, ſi circa diametrum IH in plano ſecante deſcribatur
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circulus ipſe tranſibit per puncta F, G: </
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">ſi ergo intelligatur deſcriptus conus,
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cuius vertex L, baſis circulus IFHG; </
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">& </
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">in infinitum productus infra baſim,
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communis ſectio eius conicæ ſuperficiei cum ſubiecto plano ſit linea AMF
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BGNA. </
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">Eſt enim conus ILH ſectus plano per axem, triangulum facient LIH, & </
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ſecatur altero plano FBGA, (nempe ſubiecto plano) quod baſi non æquidi-
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ſtat (cum ſe mutuò ſecent ſecundum rectam FG) & </
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coni I H, & </
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">ſecantis plani BA eſt recta linea FG, quæ ad IH baſim trianguli
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per axem eſt ducta perpendicularis, erit, per primam huius, ſectio AMFBGN
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Ellipſis, cuius vertex B, diameter BA, cui ordinatim ductæ, qualis eſt FG,
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ad datum angulum P applicantur ex conſtructione. </
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<
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">Cumque factum ſit vt
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ED ad DF, ita DF ad DB, erit rectangulum EDB ęquale quadrato DF, ſiue
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rectangulo IDH, vnde rectangulum ADB, ad rectangulum EDB, erit vt
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idem rectangulum ADB, ad rectangulum IDH; </
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<
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EDB, eſt vt AD ad DE, vel vt AB ad BC, ergo rectangulum ADB, ad re-
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ctangulum IDH, erit vt AB ad BC: </
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">vnde AB eſt latus tranſuerſum, BC ve-
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rò rectum deſcriptæ Ellipſis BFAG, vt ex prima huius. </
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dum.</
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">CVm ad MAXIMARV M, MINIMARV Mque coni-ſe-
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ctionum inſcriptibilium, ac circumſcriptibilium inuentionem
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nobis ſit opus admir andam illam affectionem propagare circa
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lineas ſemper magis, ac magis inter ſe accedentes, nunquam
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verò ſimul coeuntes, ab ipſo Apollonio præcipuè animaduerſam inter curuam
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Hyperbolæ, rectamque lineam, quàm ipſe Aſymptoton appellauit, neceſsè
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quidem videretur, ad hoc vt integram huius argumenti doctrinam hic ſi-
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mul habeatur, addere nunc, primam, ſecundam, decimam tertiam, ac de-
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cimam quartam ſecundi conicorum ad prædictam Aſymptoton ſpectantes; </
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