Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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vt eadem M D ad D N, erit G M ad E N, vt M F ad N B, & </
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tando G M ad M F, vt E N ad N B.</
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<
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">Cum ergo, in figuris prima, ſecunda, quarta, quinta, ſeptima, octaua,
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decima, ac decimaprima ſit G M ad M F, vt E N ad N B, erit quoq; </
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dratum G M ad M F, vt quadratum E N ad N B, vel vt rectangulum
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conic.</
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M I ad rectangulum C M A, & </
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gulum H M I, vt quadratum F M ad rectangulum C M A, & </
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in prima, quarta, ſeptima, & </
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">decima figura (in quibus applicatæ H I, C A
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ſecant ſe mutuò intra ſectionem in puncto M) rectangulum H M I ad qua-
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dratum G M, vtrectangulum C M A ad quadratum F M, & </
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<
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">componendo
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rectangulum H M I cum quadrato G M, ſiue vnicum quadratum H G, (nam
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eſt A C bifariam ſecta in G, & </
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">non bifariam in M) ad quadratum G M, vt
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rectangulum C M A cum quadrato F M, ſiue vt vnicum quadratum C F
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(cum A C quoque ſecta ſit bifariam in F, & </
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">non bifariam in M) ad quadra-
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tum F M. </
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">vndecima, in quibus
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applicatæ H I, C A ſe mutuò ſecant extra ſectionem in puncto M, cum ſit
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G M quadratum ad rectangulum H M I, vt quadratum F M ad rectangu-
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lum C M A, erit per conuerſionem rationis quadratum M G ad quadratum
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G H (eſt enim rectangulum H M I cum quadrato G H æquale quadrato G
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M, cum ſit H I bifariam ſecta in G, & </
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">ei adiecta ſit I M) vt quadratum M
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F ad quadratum F C, ob eandem rationem, (nam C A quoq; </
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eſt in C, eiq; </
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G M quadratum, erit vt quadratum C F ad F M. </
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figuris, déptis tertia, ſexta, nona, & </
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dratum H G ad G M eſſe vt quadratum C F ad F M, erit quoque linea H G
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G M, vt linea C F ad F M. </
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ma, in quibus applicatę H I, C A conueniunt ſimul cum ipſa ſectione in pun-
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cto M, patet quoque eſſe H G ad G M, vt C F ad F M, cum ipſæ H I, C
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A, vel H M, C M bifariam ſecentur in G, F ab earum diametris E G, B F.
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">Eſt igitur in qualibet datarum figurarum huius ſchematiſmi, H G ad G M, vt
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C F ad F M, quare iuncta H C æquidiſtabit iunctæ G F; </
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lis H G, & </
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">A F æqualis C F, ergo etiam I G ad G M erit vt A F ad F M,
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ideoque iuncta A I æquidiſtabit eidem G F, ſed E B quoque ipſi G F ęqui-
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diſtat (vt iam ſupra oſtendimus in Parabolis, & </
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ſit D E ad E G, vt D B ad B F ex hypoteſi) ergo quatuor iunctæ rectæ lineæ
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E B, A I, G F, H C ſunt inter ſe parallelæ; </
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">ſed N M, quàm ſuperiùs oſten-
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dimus eſſe ſectionis diametrum, tranſit per N occurſum contingentium E
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N, B N, ergo recta E B puncta contactuum iungens, ab eadem diametro N
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M D bifariam ſecabitur, vt in O, ac ideò omnes aliæ in ſectione
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di conic.</
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ipſi E B ęquidiſtantes, nempe A I, G F, H C, ab eadem D N M bifariam
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ſecabuntur, vt H C in P.</
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ius oppoſita latera H C, E B ſunt parallela, & </
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qua ſumptum eſt punctum M, & </
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nempe ad H, C ductę ſunt rectæ M H, M C, ac in triangulo H M C eſt G F
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ipſi H C parallela, quare iunctę E G, B F auferent triangula E G H, B F C
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inter ſe æqualia; </
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