Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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interceptæ applicatarum portiones à contingente AE magis remouentur eò
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ſunt minores, vnde tales ſectiones ad ſe propiùs accedunt. </
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<
s
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xml:space
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">Sed quod de
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congruentibus, ſiue æqualibus parabolis hactenus expoſuimus, & </
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<
s
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xml:space
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">iam olim
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demonſtrauimus (dum Aſymptoton doctrina promoueri poſſe animaduer-
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timus) maximos poſtea Geometras, Torricellium nempe, ac Gregorium à
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S. </
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<
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">Vincentio aliter quoque oſtendiſſe reperimus, quorum edita opera ad
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vberiorem de hac re eruditionem conſulere ſuademus.</
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<
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<
s
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xml:space
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">Dico tandem has con-
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0098-01
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0098-01
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gruentes Parabolas ad in-
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teruallum ſimul peruenire
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minus quocunque dato in-
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teruallo 1 2. </
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<
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xml:space
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">Fiat enim vt
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1 2 ad AE, ita AE ad 2 3
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quæ ipſi 1 2 indirectum po-
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natur, & </
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ſecetur in 4, & </
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<
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cetur BK ęqualis 1 4; </
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<
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turque KI parallela ad BX,
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& </
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">per I recta IDS contingẽti
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BK æquidiſtans, erit ergo
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IX æqualis KB, ſiue 4 1;
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</
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4 1 dimidium 1 3; </
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IS, 1 3 ſunt æquales; </
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factum eſt rectangulum 1 2 3 æquale quadrato AE, & </
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<
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">rectangulum IDS
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oſtenſum eſt æquale eidem quadrato AE, ergo rectangula IDS, 1 2 3 in-
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ter ſe ſunt æqualia; </
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<
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">ſed rectæ IS, 1 3, ſunt æquales, quare ſegmentum ID
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æquatur dato interuallo 1 2; </
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intercepta ID, quapropter huiuſmodi congruentes Parabolę ad interuallum
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perueniunt minus dato interuallo 1 2. </
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">EXhac patet, in congruentibus Parabolis per diuerſos vertices ſimul ad-
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ſcriptis, omnes, inter eas, interceptas lineas communi diametro ęqui-
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diſtanter ductas, eſſe inter ſe æquales, quales ſunt EB, DN, &</
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<
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plicatarum vtranque Parabolen ſecantium omnia inter ſe æqualia eſſe,
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qualia ſunt rectangula LMY, IDS, &</
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