Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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RVM, & </
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aſſignare.</
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<
s
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">ESto Conus ſcalenus A B C, cuius vertex B, baſis B C, centrum D.
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</
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aſſignare.</
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</
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<
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<
s
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A B C. </
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s
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">Patet alterum ipſius laterum, vt puta B A eſſe _MAXIMVM_,
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Sereni.</
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rum verò B C _MINIMVM._</
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</
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<
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<
s
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">Radius D A ad partes _MAXIMI_ lateris ſecetur bifariam in E, ita vt C
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E ſit tripla ad E A; </
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<
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">& </
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<
s
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xml:space
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">per E iuxta regulam _MAXIMI_ lateris B A concipia-
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tur ductum planum efficiens Parabolen: </
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<
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cunque cadat punctum H veſtigium verticis.</
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<
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<
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">Nam _MAXIMA_ Parabole, ducta per E iuxta latus B A, ad quamlibet
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aliam _MAXIMAM_ Parabolen iuxta aliud quodcunque latus, nempe iuxta
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B F (cum ipſæ ſint æqualium baſium) eſt homologè, vt altitudo vnius
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96. h.</
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altitudinem alterius, ſed altitudo ad altitudinem eſt vt perpendicularis
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mi h.</
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B ſuper contingentem circuli B C peripheriam ad punctum A, quæ
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roll. 98. h.</
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ipſum latus B A, ad perpendicularem ex B ſuper contingentem ad pun-
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ctum F, atque perpendicularis B A maior eſt perpendiculari ex B ſuper
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contingentem ad F, cum ipſa B A ſit earundem perpendicularium
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num. 1.</
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_MA,_ ergo, & </
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_MAXIMA_ Parabola ducta iuxta latus B F, & </
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<
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per E iuxta _MAXIMVM_ Coni latus B A, erit _MAXIMARVM MAXIMA:_
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</
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<
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ciderit, vel intra circulum B C, vel in ip-
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ſius peripheria: </
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<
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ad partem _MINIMI_ lateris B C Coni A
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B C) bifariam in G, & </
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<
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plano iuxta regulam lateris B C efficiente
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_MAXIMA_ Parabola. </
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<
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<
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ta latus B C, ad quamcumque aliam _MA_-
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_XIMAM_ iuxta quodcunque aliud latus B
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F, eſt homologè vt altitudo vnius ad
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huius.</
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titudinem alterius, cum ipſæ ſint
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96. h.</
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lium baſium; </
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eſt vt perpendicularis, ex B ſuper contingentem ad C, quæ eſt
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roll. 98. h.</
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_MINIMVM_ latus B C, ad perpendicularem ex B ſuper contingentem ad </
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