Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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<
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">Productis enim contingentibus EB, NI vſque ad aſymptotos in S, T, fiat
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vt DB ad MI, ita BQ ad IV, & </
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">cum ſit DB maior
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MI, erit BQ, & </
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<
s
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">IR maior IV, eſtque FB maior OI (cum duplum DB ſit maior
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duplo MI) ergo tota FQ erit maior tota OV, & </
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<
s
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">QA ad VX erit vt DB
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MI, & </
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<
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xml:space
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">quoniam QB ad VI, eſt vt BD ad IM, vel vt dimidium BF ad dimi-
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dium IO, erit per-
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0093-01
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mutando, compo-
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nendo, & </
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">iterum
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permutando QF ad
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VO, vt BF ad IO,
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vel vt DB ad MI; </
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">& </
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cum ſit quadratum
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SB ad TI, vt rectan-
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gulũ DBE ad MIN,
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vtrunque enim eſt
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quarta pars ſuæ fi-
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guræ) vel vt qua-
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dratum DB ad qua-
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dratum MI; </
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<
s
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xml:space
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">ob rectangulorum ſimilitudinem) vel ſumptis ſubquadruplis, vt
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quadratum FB ad OI, erit quoque linea SB ad TI, vt linea FB ad OI, & </
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<
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">per-
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mutando SB ad BF, vt TI ad IO, ſed anguli SBF, TIO ſunt æquales per ſex-
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tam ſecundarum definitionum, & </
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<
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">per conſtructionem, quare triangula SBF,
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TIO erunt ſimilia, vti etiam triangula GQF, YVO, obidque homologa eo-
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rum latera proportionalia erunt, hoc eſt GQ ad YV, vt FQ ad OV, ſed eſt
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FQ maior OV, ergo, & </
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<
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">GQ erit maior YV, ſed FQ ad OV, eſt vt DB ad MI,
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item AQ ad XV, vt DB ad MI, vt ſupra oſtendimus, quare GQ ad YV erit
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vt AQ ad XV, & </
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<
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">permutando, & </
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">per conuerſionem rationis, & </
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">iterum per-
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mutando GQ ad YV, vt GA ad YX, ſed eſt GQ maior YV, ergo, & </
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<
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">G A
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maior YX, eſt autem YX maior PH, ergo eò magis GA erit maior PH. </
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<
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erat demonſtrandum.</
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">EX hac patet, in ſimilibus Hyperbolis aſymptotos ad partes æqualium in-
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clinationum ductas, æquales angulos cum diametris efficere, ac ideo
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angulos ab aſymptotis factos eſſe inter ſe æquales. </
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<
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">Cum enim demonſtrata
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ſint triangula SFB, TOI ſimilia, erunt anguli ad F, O, æquales; </
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<
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">eademque
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ratione æquales etiam anguli ab alijs aſymptotis cum diametris ad alteram
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partem conſtitutis; </
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<
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">vnde eorum aggregata, nempe anguli ab aſymptotis fa-
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cti in ſimilibus Hyperbolis inter ſe æquales erunt.</
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