Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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ipſa HM producta omnino ſecabit ſectionem CBA, vel ſupra contingentem
<
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CEA, vt in N, vel in ipſo occurſu A, vel infra ad partes AL; </
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<
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xml:space
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A, patet interiorem ſectionem totam cadere infra applicatas ex N, vel ex A,
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& </
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<
s
xml:id
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xml:space
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">nunquam infra N, vel A ſectioni BNA occurrere, ne priùs ſecet propriam
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aſymptoton HM.</
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</
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<
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<
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xml:space
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">Si verò HM ſecet exteriorẽ
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0110-01
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BA infra contingentem CAE,
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vt in hac ipſa figura; </
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<
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xml:space
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tet ſectiones BA, ED infra LD
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nunquam ſimul conuenire, ſin
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aliter propriam aſymptoton
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ſecaret.</
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<
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<
s
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xml:space
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">Præterea indirectũ produ-
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cta communi diametro EBG,
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ſumptiſque in ea punctis V, T,
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quæ ſint extrema tranſuerſo-
<
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rum laterum datarum ſectio-
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num, ductiſque regulis TX,
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VZ; </
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<
s
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xml:space
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">ipſę vti ſuperiùs oſtenſum
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fuit, inter ſe æquidiſtabunt.
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</
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<
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">Ampliùs ſumpto in portione
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ED quolibet puncto K, per ip-
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ſum applicetur KY vtranque Hyperbolen ſecans in P, K; </
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<
s
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xml:space
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">regulas verò in
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Z, X.</
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</
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<
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<
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">Iam, vel recta VZ eſt regula interioris ſectionis DEF, & </
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</
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<
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xml:space
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">vel ipſæ ſimul congruunt, ſi tamen puncta V, T, in vnum conueniant; </
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<
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xml:space
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contra VZ eſt regula exterioris, TX verò interioris. </
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<
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xml:space
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">Si primum, cum in ſe-
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ctione ABC quadratum applicatæ PY æquale ſit rectangulo BYX, & </
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">Coroll.
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1. huius.</
note
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Hyperbola DEF quadratum KY ſit æquale rectangulo EYZ, ſitque rectan-
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gulum BYX maius EYZ, cum ſub maioribus lateribus contineatur, erit quo-
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que quadratum PY, maius quadrato KY: </
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<
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nem ABC. </
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">Si ſecundum nempe ſit VZ vtriuſque ſectionis communis regu-
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la, erit quadratum PY æquale rectangulo BYZ, & </
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<
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xml:space
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">quadratum KY æquale
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rectangulo EYZ, ſed rectangulum BYZ maius eſt EYZ, cum altitudo BY
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maior ſit altitudine EY, quare quadratum PY maius eſt quadrato KY, ſiue
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punctum K eſt intra ſectionem ABC. </
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<
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xml:space
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">Si denique interior recta VZ fuerit re-
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gula exterioris ſectionis ABC, & </
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<
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">exterior TX, regula interioris DEF, erit
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HE ipſi HT æqualis, ſed eſt ablata HB minor ablata GV (cum ponatur GB,
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quæ maior eſt HB, æqualis GV) ergo reliqua BE maior erit reſiduis ſegmen-
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tis GH, VT, & </
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">eò maior vnico ſegmento VT, ſed eſt EY minor VY, quare
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BE ad EY maiorem habebit rationẽ quàm TV ad VY, vel quàm XZ ad ZY,
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& </
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<
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">componendo BY ad YE maiorem habebit rationem quàm XY ad YZ, vn-
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de rectangulum BYZ ſiue quadratum PY maius erit rectangulo EYX
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">ibidem.</
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Pappi.</
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quadrato KY, hoc eſt punctum K incidet intra ſectionem ABC, & </
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1. huius.</
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quolibet alio puncto portionis DEF; </
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neque infra applicatam LF, neque inter lineas LF, AC ſimul conueniunt,
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vnde ſunt in totum nunquam coeuntes. </
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<
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