Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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velvt AB ad BC, vt ſuperius oſtendimus: </
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<
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0046-01
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do, & </
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DC. </
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<
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<
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">cum ſit AB ad BC, vt BC ad BE, erit
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diuidendo, & </
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vt AB ad BC, ex conſtructione: </
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<
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<
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</
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<
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<
s
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">Et cum ſit AD ad DC vt quadratũ AB ad BC, & </
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dratum AB ad BC vt linea AB ad BE, ex conſtructione,
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erit AD ad DC vt AB ad BE, & </
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<
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nis, permutando, conuertendo, diuidendo, & </
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conuertendo AD ad DB, vt AC ad CE, vel vt AB ad
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BC, vt modò oſtenſum fuit, & </
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d
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o, per conuerſionem rationis, & </
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<
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">diuidendo AD ad DB vt BD ad DC. </
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erat in ſecunda demonſtrandum.</
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tro AD perpendicularis, iunganturque DE, AE, & </
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cta in ſecuuda figura, occurrat cum AF ipſi CE parallela in puncto F.</
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<
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ſit per hypoteſim quadratum
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AB ad BC, vt recta AD ad DC,
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vel vt quadratum AD ad DE,
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vel vt quadratum AE ad EC,
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ob triangulorum ſimilitudiné,
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erit recta AB ad BC, vt recta
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AE ad EC: </
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<
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">quare in prima fi-
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gura erit angulus AEB, æqua-
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lis angulo BEC, ſed angulus
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BAE æquatur angulo D E C,
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quare duo ſimul AEB, BAE,
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ſiue vnicus DBE, æqualis erit
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duobus ſimul BEC, DEC, ſiue vnico DEB, ergo BD eſt æqualis ipſi DE. </
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ſecunda verò, cum ſit AB ad BC, vel FA ad EC, vt AE ad EC erunt AF,
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A E interſe æquales, vnde angulus AEF, æqualis angulo AFE ſiue paralle-
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larum externo CEB, ſed eſt AEF æqualis duobus ſimul ABE, EAB, quare
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& </
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vnico angulo EAD, ergo reliquus angulus DEB reliquo DBE æqualis erit,
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hoc eſt recta DB æqualis DE. </
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DE, ſitque DE media proportionalis inter AD, DC, erit quoq; </
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inter eaſdem AD, DC. </
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<
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