Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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<
s
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xml:space
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">Iam in Parabola, quam exhibet prima huius ſchematis ſigura, cum ſint
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BC, EF diametri ipſæ erunt inter ſe parallelæ, BA verò eas ſecat,
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">cõuerſ.
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46. pr. co-
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nic.</
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angulus GBF æquatur angulo EFA, ſed eſt GBF obtuſus, cum GBE ſit re-
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ctus (nam eſt CB axis Parabolæ) ergo angulus quoque EFA obtuſus erit,
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ſiue maior conſequenti BFE.</
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<
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<
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<
s
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xml:space
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">In Hyperbola verò ſecundæ ſiguræ, cum angulus CBA externus triangu-
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li DBF ſit acutus, (nam CBE rectus eſt) ſitque maior interno BFE, is quidem
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acutus erit, & </
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<
s
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xml:space
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">qui ei deinceps EFA erit obtuſus, ſiue maior ipſo BFE.</
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<
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</
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<
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<
s
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">In Ellipſi tandem tertiæ ſiguræ iuncta DA, cum in trianguiis DFB, DFA
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ſit BF ęqualis AF, & </
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<
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xml:space
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">communis FD baſis verò BD maior DA, erit
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BFD maior angulo DFA, & </
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<
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xml:space
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">eiad verticẽ EFA maior angulo ad verticẽ BFE.</
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">In triangulis itaq; </
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0158-01
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cuiuslibet harum ſigurarum, cum
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ſit latus A F æqualis FB, & </
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commune, augulus verò E F A
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demonſtratus ſit maior angulo
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BFE, erit baſis A F maior baſi
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BE. </
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<
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xml:space
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">Quare contingens B E ex
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termino maioris axis, minor eſt
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altera contingente A E. </
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<
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primò probandum erat.</
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<
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xml:space
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">Si verò, in Ellipſi ABC, quar-
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tæ ſiguræ, axis BC fuerit minor.
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</
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">conſtructis ijſdem. </
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">Cum in triangulis AFD, BFD ſit latus AF æ-
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qualle lateri BF, & </
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<
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">commune FD, baſis verò AD maior baſi DB (cum minor
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ſemi-axis DB ſit _MINIMA_ ſemi-diametrorum) erit angulus AFD, ſiue
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">ibidem.</
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maior angulo BFD, hoc eſt AFE, ſuntque in triangulis BFE, AFE latera BF,
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AF inter ſe æqualia, & </
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<
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">quare baſis BE, erit maior
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conic.</
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AE Quod ſuit vltimò demonſtrandum.</
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à tactu erigatur contingenti perpendicularis, hæc neceſſariò cum
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axe conueniet, in Ellipſi cum vtroque axe, ſed priùs cum maiori;
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</
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<
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">occurſum cum axe,
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qui tamen in Ellipſi ſit axis maior, ſemper minor erit eo axis ſe-
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gmento, quod inter occurſum, & </
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<
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">Cum autem in Ellipſi, contingens linea minori axi occurret,
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tunc prædicta perpendicularis inter contactum, & </
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<
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intercepta, maior ſemper erit ſegmento minoris axis, quod inter
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occurſum, & </
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<
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<
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">prima ſigura Parabolen, aut Hy-
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perbolen repræſentet, ſecunda verò Ellipſim, cuius axis maior, ſit </
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