Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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Apoll. Pergæi.</
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">_A_NTEQV AM inſtitutum opus aggrediamur, ſiquidem in
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ipſo frequenter accider vti, proferreque affectiones propoſi-
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tionum 11. </
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<
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<
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">non erit fortaſſe omninò
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incongruum meas earundem demonſtrationes hic exhibere,
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quales olim, cum primùm ad elementa conica me conuerte-
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rem, aliter ac breuius vnico tantùm Theoremate concludi poſſe animaduer-
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ti, eaſque proponi enunciationibus, vtirebar genuinis, ac proximis ad trium
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coni-ſectionum, Parabolæ, nempe, Hyperbolæ, & </
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tionem. </
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<
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">Verùm antea mihi detur, vt quibuſdam morem gerens, qui tres
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prædictas Apollonij propoſitiones difſiciles admodum exiſtimant, ob nimium
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in ea vſum 23. </
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afferre poſsim eodem penitus modo, quo aliquibus, voce, & </
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care ſolitus fui, hoc eſt ſine compoſita proportione, quam, neſcio quaratione
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faſtidiant.</
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">Stantibus igitur ijſdem hypoteſibus, expoſitionibus, ac conſtructionibus
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prædictarum Apoll. </
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">propoſitionum, adhibitiſque figuris, quæ ibi in Comman-
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dini verſione.</
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">poſt ea verba_ Rectangulum igitur MLN æquale eſt
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quadrato K L ſequatur ſic.</
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ad FA ex conſtructione, & </
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ad BC, vel vt ablata BF ad ablatam BG, hoc eſt vt reliqua FA ad reliquam
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GC, ſiue ad LN, ergo ex æquo quadratum BC ad rectangulum ACB, vel
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recta BC ad CA, vel BG ad GF, vel ML ad LF, erit vt HF ad LN, ideoque
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rectangulum ſub extremis ML, LN, ſiue quadratum KL æquatur rectangu-
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lo HFL. </
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_drato_, ſic dicatur.</
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