Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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<
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que Conoide, aut Sphæroide _MINIM A_ eſt ea illius portionis, cuius axis
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ſit ſegmentum axis, & </
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">pro Sphæroide ſit ſegmen tum maioris axis genitricis
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ſectionis dati ſolidi. </
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">_MAXIM A_ verò eius, cuius axis ſit ſegmentum mino-
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ris axis eiuſdem ſectionis genitricis.</
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">INter altitudines æqualium portionum de eodem Cono recto, ſiue de quo-
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libet Conoide, aut Sphæroide, _MAXIMA_ eſt ea illius portionis, cuius
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axis congruat cum maiori axe genitricis ſectionis dati ſolidi, & </
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de _MINIM A_ eius, cuius axis cum minori axe eiuſdem genitricis ſectionis
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conueniat.</
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<
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">Quæ omnia, ex hucuſque demonſtratis, paucis oſtendentur (vti factum
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fuit in præfato Scholio, & </
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<
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">h.) </
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<
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">conſimilibus, ac ibi
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argumentis, veruntamen circa ſolidas portiones verſantibus, è quibus de-
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nique vniuſcuiuſque trium proximè præcedentium propoſitionum veritas
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iterum eluceſcet. </
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">PLacuit SERENO, Antinſ enſi Philoſopho, in quibuslibet Conis
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terminatis MAXIMV M, & </
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">MINIMV M triangulum
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per verticem ductum inquirere, liceat nobis tanti Geometræ
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veſtigia inſequentibus in Cono pariter terminato quocunque
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MAXIMAM, & </
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">MINIMAM Paraboæ portionem aſsignare, pro
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cuius indigatione nonnulla circa plana, nec præter ſuſceptam materiam,
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nec ſcitu iniucunda occurrunt afferenda.</
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">Si duo triangula habuerint latus lateri æquale, atque alterum
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adiacentium angulorum in vno triangulo, alteri adiacentium in
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reliquo æqualem, ſitque reliquus angulus adiacentium in primo,
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maior reliquo adiacentium in altero, & </
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">latus illi oppoſitum, late-
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re huic oppoſito maius erit.</
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rum latera B C, E F ſint æqualia, & </
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anguli pariter A B C, D E F æquales, an-
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gulus verò A C B maior ſit angulo D F E.
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maius eſſe latere D E oppoſitum minori.</
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