Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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<
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<
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xml:space
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">Si coni-ſectionem, vel circuli circumferentiam recta linea con-
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tingat conueniens cum diametro, cui à tactu ſit ordinatim applica-
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ta vſque ad ſectionem, recta linea iungens alterum terminum ap-
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plicatæ, & </
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<
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xml:space
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">occurſum tangentis cum diametro, erit eidem ſectioni
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ad alteram diametri partem contingens.</
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<
s
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xml:space
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">SIt coni-ſectio quæcunque, vel circuli circumferentia ABC, cuius diame-
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ter ſit DE, & </
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<
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">ſit quæpiam AD ſectionem contingens in A, diametro oc-
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currens in D, & </
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<
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xml:space
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">ex contactu A ducta ſit in ſectione diametro DE ordinatim
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applicata AC, dico iunctam DC ſectionem quoque contingere.</
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<
s
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">Si enim poſſibile eſt, quæ ex C ducitur
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contingens, non ſit CD, ſed alia CF, quæ
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cum tangente AD conueniet, ſed in alio puncto quàm D, vt in F.</
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<
s
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">Iam cum FA, FC ſectionem contingant,
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& </
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<
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">per contactus ducta ſit AC, quæ bifariam
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ſecta eſt à diametro D E in E, ſi iungatur
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cundi co-
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nic.</
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FEG ipſa erit ſectionis diameter, hoc eſt bifariam ſecabit quamlibet aliã HI ipſi AC
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æquidiſtanter ductam, vt in G, ſed D E L
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quoque bifariam ſecat eandem HI in L, cum
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DEL ſit diameter, per hypoteſim; </
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<
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dem recta HI in duobus diuerſis punctis G,
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& </
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<
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gens linea quàm CD. </
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<
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<
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<
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<
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<
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">Pappi, in hac noſtra tractatione fre-
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quens ſit vſus, liceat hac eas transferre, vtranque ſimul ſequenti Theo-
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remate demonſtrare.</
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<
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<
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">Rectangulorum ſub partibus datæ rectę terminatæ MAXIMVM
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eſt id, quod ab æqualibus ſegmentis producitur; </
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<
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id, quod fit à partibus minus inæqualibus, maius eſt eo, quod ab
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inæqualioribus continetur.</
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</
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<
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">SIt data recta linea AB terminata bifariam ſecta in C, & </
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<
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vtcunque in D, E, &</
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<
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">Cum enim recta AB ſecta ſit bifariam in C, & </
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<
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">non bifariam in D, erit
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quadratum AC, ſiue rectangulum ACB, æquale rectangulo ADB, </
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