Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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<
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xml:space
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">Nam intelligatur magnitudo E F æ-
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qualis primæ A, FG verò æqualis ſecun-
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dę B; </
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<
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">atque ipſis in directum magnitu-
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do F H æqualis tertiæ C, & </
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tæ D. </
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<
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ſupra F G, hoc est E G, maios exceſſu
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quantitatis H F ſupra F I, ſiue maios-
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ipſo H I, ex ſuppoſitione, quibus addi-
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ta communi quantitate G I, proueniet
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E I maior G H, ſiue aggregatum ex EF,
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& </
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<
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maius aggregato ex G F, & </
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">MINIMA linearum in Parabola ducibilium ad eius peri-
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pheriam à puncto axis intra ſectionem ſumpto, quod diſtet à
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vertice per interuallum non maius dimidio recti lateris, eſt ip-
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ſum axis ſegmentum inter punctum, & </
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<
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">verticem interceptum.
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</
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<
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">Aliarum verò ea, quæ cum MINIMA minorem conſtituit an-
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gulum, minor eſt.</
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<
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xml:space
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">ESto Parabole AB, cuius ſegmentum axis B D non excedat dimidium
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recti lateris B C datæ Parabolæ. </
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cibilium ex eodem puncto D ad Parabolæ peripheriam A B, &</
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<
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">Applicetur axi ex D, recta D A, Erit
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quadratum A D æquale
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ſub D B, & </
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primę pri
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mi huius.</
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D B C maius eſt quadrato D B (cum
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latus rectum B C poſitum ſit, vel du-
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plum, vel magis quàm duplum ipſius
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B D) igitur quadratum A D maius erit
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quadrato D B, ſiue linea D A maior
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D B.</
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<
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cunque alia D E ad peripheriam, & </
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A recta A F parallela ad B D, quæ to-
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ta ad partes F cadet intra Parabolen;</
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mi conic.</
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nec ei ad alium punctum occurret quàm
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ad A; </
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<
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ſed eſt D F maior D A (cum in triangulo D A F angulus ad A ſit rectus,
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ſiue maior acuto ad F) & </
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">D A maior ipſa D B, vt ſupra oſtendimus, qua-
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re D E multò maior erit ipſa D B.</
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<
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">Ampliùs ſit quæcunque D G ducta ex D ſupra D A, & </
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tur G H. </
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<
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">Cumque latus rectum B C ſit maios aggregato B D cum D H
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(poſitum enim fuit B C non maius quàm duplum ſegmenti BD, </
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