Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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factum, tunc ex dictis binis contingentibus, quæ ad partem axis ducitur ſem-
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per altera contingente ad oppofitam axis partem minor erit, atq; </
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<
s
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xml:space
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XIMA. </
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<
s
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xml:space
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">Si verò punctum fuerit extra Ellipſim inter axes, tunc contingens
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ad partem maioris axis ducta, minor erit altera contingente ad partem mino-
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ris, pariterque hæc erit MAXIMA ad conuexam Ellipſis peripheriã. </
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<
s
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xml:space
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">Quæ
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omnia facili negotio demonſtrabuntur ſi animaduertatur, quod in quocunque
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triangulo, cuius vnum latus altero ſit maius, hoc ipſum eſſe MAXIMIAM
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linearum omnium à vertice anguli ab ipſis lateribus comprehenſi, ad puncta
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baſis prædicti trianguli ducibilium, (tale enim triangulum eſt, quod a prædi-
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ctis contingentibus tanquam lateribus, & </
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<
s
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xml:space
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">à recta puncta contactuum iungen-
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te, tanquam baſi efficitur, in quo idem maius latus, ſiue contingentium ma-
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ior eò magis erit MAXIMA ad incluſam ſectionis peripheriam.) </
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<
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xml:space
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">Si tandem
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punctum fuerit in angulo ad verticem aſymptotalis, aut in aſymptotis eum
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comprehendentibus, tunc vllam contingentium ducere imposſibile eſt, & </
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<
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xml:space
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">du-
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cibiles lineæ ad conuexam Hyperbolæ peripheriam ſemper augentur, ideoque
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non datur MAXIMA; </
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xml:space
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">& </
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<
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xml:space
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">cum eſt in altero angulorum, qui deinceps ſunt
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aſymptotali, vel in ipſis aſymptotis Hyperbolen continentilem
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, tunc vnica
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tantùm contingens linea ab eo duci poteſt, & </
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<
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xml:space
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">hæc ad partem axis, quæ erit
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MAXIMA ad eandem partem ducibilium; </
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xml:space
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">ſed ad oppoſitam, ipſæ ducibiles
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ad Hyperbolæ conuexam peripheriam perpetuò pariter augentur. </
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<
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xml:space
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haud difficilis inueſtigationis ne ampliùs quæſo immoremur.</
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<
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pſi autẽ, MAXIMVM eſt axis maior, MINIMVM verò axis minor.</
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<
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xml:space
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B omnium tranſuerſorum eſſe _MINIMVM._</
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0216-01
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E A, & </
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G B F, quę axi perpendicu-
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laris erit, ac ſectionem con-
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tinget in B. </
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<
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xml:space
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pendicularis E B _MINIMA_
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ad peripheriam A B C:</
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quare E B minor erit E A,
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& </
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plo H A: </
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tranſuerſorum _MINIMVM._</
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<
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cuius centrum E, & </
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axis maior, & </
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A C _MINIMVM_, ex primo Coroll. </
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