Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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151 - 160
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201 - 210
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<
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xml:space
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xml:space
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">Hyperbola interceptam axis portionem in-
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ter verticem, & </
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<
s
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xml:space
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">contingenti perpendicularem ſemper item eſſe pluſ-
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quam dimidium recti lateris propriæ ſectionis. </
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<
s
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xml:space
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">Quoniam cum demonſtra-
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tum ſit DB maiorem eſſe DA, & </
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<
s
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xml:space
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">DA in præcedenti Corollario ſit maior
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">88. h.</
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midio rectilateris, eò magis DB erit maior prædicto dimidio.</
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<
head
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xml:space
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">COROLL. III.</
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<
s
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">MAnifeſtum eſt etiam in Hyperbola, & </
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<
s
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xml:space
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">Ellipſi ſemper eam axis portio-
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nem, quæ eſt inter centrum ſectionis, & </
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>
<
s
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="
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xml:space
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">ordinatim ductam ex con-
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tactu, ad portionem eiuſdem axis inter ipſam ordinatam, & </
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<
s
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xml:space
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">contingenti
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perpendicularem, eſſe vt ſemi-tranſuerſum ſectionis ad ſemi-rectum, vel vt
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tranſuerſum ad rectum. </
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>
<
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">Demonſtratum eſt enim in ſecunda, tertia, & </
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<
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">quar-
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ta figura rectam GF ad FD eſſe vt tranſuerſum latus ad rectum.</
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</
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</
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<
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<
s
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xml:space
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">Si Ellipſim quædam recta linea contingat inter axium extrema,
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cui à tactu ducta ſit perpendicularis cum vtroque axe conueniens,
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ſemper ipſius portio inter contactum, & </
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<
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xml:space
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">minorem axim intercepta,
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eſt maior ſemi-axe maiori; </
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<
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xml:space
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">portio verò inter contactum, & </
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<
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">maio-
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rem axim, maior eſt ſemi-recto latere maioris axis; </
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<
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xml:space
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">& </
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<
s
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">eadem por-
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tio eſt minor ſemi-axe minori; </
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<
s
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xml:space
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">ac demum portio inter contactum,
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& </
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<
s
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xml:space
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">minorem axim minor eſt ſemi-recto latere minoris axis.</
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<
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</
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<
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<
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xml:space
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">SIt Ellipſis ABC, cuius maior axis BC, minor IL, centrum G, & </
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<
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contingens MAE inter axium extrema, quæ ipſis occurret in E, M; </
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">&</
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<
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<
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mi conic.</
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ex A ducta ſit ADH contingenti perpendicularis, quæ vtrique axi occurret,
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ſed priùs cum maiori in D, cum minori verò in H.</
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</
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<
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<
s
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">Dico primùm interceptam AH ſemper maiorem eſſe maiori ſemi-axe
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G B.</
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</
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<
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<
s
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">Agatur HP æquidiſtans ad GE, & </
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<
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">AFO ad NH. </
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<
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xml:space
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">Et quoniam eſt HP ma-
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ior GE, & </
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<
s
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">HO æqualis GF, erit rectangulum PHO, ſiue quadratum HA (in
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triangulo rectangulo PAH) maius rectangulo EGF, ſiue quadrato
<
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mi conic.</
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hoc eſt linea AH maior ipſa GB. </
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</
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<
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<
s
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">Ampliùs, dico AD eſſe pluſquam dimidium recti lateris axis BC.</
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<
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<
s
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">Quoniam cum ſit GB minor AH, vt modò oſtendimus, habebit GD ad
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AD minorem rationem quàm AH ad AD, vel quàm FG ad FD, vel quàm
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eadem GB ſemi-tranſuerſum, ad ſemi-rectum; </
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<
s
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roll. 90. h.</
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ſemi-rectum latus maioris axis. </
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<
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<
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</
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<
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<
s
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xml:space
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minoris axis.</
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