Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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ſimul quadrata C H, H A, ſiue vnicum
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quadratum A C, maius eſt duobus ſi-
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mul quadratis G I, I D, ſiue vnico qua-
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drato D G, hoc eſt linea A C maior
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D G.</
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<
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A H excedens ſemper D I, non tamen
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ſit C H, vel æqualis, vel maior G I, ſed
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omnino minor (eſt enim L H ad H C,
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itemque L I, ad I G, vt
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roll. 90. h.</
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ad rectum, ideoque L H ad H C, eſt vt
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L I ad I G, ſed permutando L H maior
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eſt L I, ergo, & </
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<
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">H C maior I G) opor-
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ruit hic aliam demonſtrationem inqui-
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rere, quæ, tum Hyperbolæ, tum Elli-
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pſi circa maiorem axim ſimul inſeruiet,
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ſi concipiatur tertia figura vtriuſque
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ſectionis ſpeciem exhibere.</
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">Itaque, vel ordinata AH, quæ ex re-
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motiori contactu à vertice B applicatur,
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occurrit axi in puncto G, vel infra, vel
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ſupra. </
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">Si primum, vel ſecundum, patet
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punctum C eò magis cadere infra G. </
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tertium, hoc idem tamen demonſtrabi-
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tur, videlicet punctum C cadere omnino
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infra G. </
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">Cum ſit enim G I maior G H
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habebit L G ad G I minorem rationem
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quàm L G ad GH, & </
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">componendo L I ad
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I G minorem item rationem quàm LH ad
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HG, ſed vt L I ad I G, ita LH ad HC, vt
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ſuperiùs oſtendimus, quare LH ad HC,
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minorem habebit rationem quàm eadem
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LH ad HG, vnde HC maior eſt HG, ſiue
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punctum C cadit infra G; </
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tercepta perpendicularis AC, ex A re-
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motiori contactu à vertice B, occurrit axi
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infra occurſum G interceptæ perpendi-
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cularis DG, ex propiori contactu D.</
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">DG conueniunt ſimul ad partem axis BC, vt hic ad nume-
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rum 1. </
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<
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">eſt punctum C infra G, quare ſi ex G ducatur GN,
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parallela ad C A ipſa ſectionis peripheriam ſecabit inter A, & </
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">Si igitur concipiantur puncta A, N, iungi recta linea, ipſa cadet tota intra
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ſectionem, & </
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in quo A C erit maior NG: </
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">itaque ſi cum centro G, interuallo GD deſcriba-
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tur circulus DO, cum ſit ſectioni ſemper inſcriptus, ipſæ ſecabit
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GN, vt in O, eritque NG maior GO, ſiue maior GD, quare eò magis A C
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maior erit DG. </
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