Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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<
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B E F ſuperare rectangulum B G H maiori exceſſu quàm ſit qua-
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dratum G E.</
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">COmpletis enim rectangulis B E F I, B G H L, productiſque E F, L H
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vſque ad occurſum in O; </
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">cum ſit A E pluſquàm dimidium ipſius
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A B, vt ſupra oſtendimus, erit A E maior E B; </
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">cumque ſit B A ad A E,
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ita B C ad E F, vel ad B I, erit diuidendo B E ad E A, vt C I ad I B,
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ſed eſt B E minor ipſa E A, ergo, & </
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">C I minor erit ipſa I B, quare ſum-
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pta L M æquali ipſi C I punctum M non pertinget ad B.</
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<
s
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xml:space
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">Iam cum M L, I C ſint ęquales, erit
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M L ad N H, vt I C ad N H, vel vt I F
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ad F N, vel vt L O ad O H, quare pun-
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cta M, N, O erunt in vna, eademque
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recta M N O. </
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M P Q parallela ad B E. </
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">Erunt in re-
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ctangulo Q L ſupplementa Q N, L N
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inter ſe æqualia, quibus addito com-
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muni rectangulo B N, fiet gnomon G I
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Q æqualis rectangulo B H, ſed exceſ-
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ſus rectanguli B F ſupra gnomonem G I
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Q, eſt rectangulum G Q, quare exceſ-
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ſus quoque rectanguli B F, ſupra B H,
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erit idem rectangulum G Q. </
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ſit C B minor B A, & </
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">vt C B ad B A,
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ita C L ad L H, erit quoque C L, vel M I, vel Q F minor L H, vel BG;
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</
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<
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">eſtque tota E F, maior tota E B, vt ſuperiùs oſtendimus, ergo reliqua
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Q E maior erit reliqua E G, vnde rectangulum G E Q, quod eſt exceſ-
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ſus rectanguli B E F ſupra B G H maius erit quadrato G E. </
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<
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">conſtructis, concipiatur quoque
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alia B R maior quidem B E, ſed minor adhuc dimidio ipſius B
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A, & </
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<
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">Dico tandem exceſſum
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rectanguli B E F ſupra rectangulum B G H, quod eſt G E Q,
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maius eſſe exceſſu quadrati G R ſupra R E.</
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">NAm, vt primo loco ſuperiùs demonſtrauimus, erit tota linea E F
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maior aggregato B R, cum R E, ſed pars Q F minor eſt parte BG
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prædicti aggregati (nam eſt Q F æqualis M I, ſiue L C, & </
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eſt L H, eſtque C L minor L H, cum ſit data C B minor quoque B A) er-
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go reliqua E Q maior erit reliquo eiuſdem aggregati, quod eſt G R cum
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R E; </
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<
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">E G, quod eſt exceſſus rectanguli B
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E F ſupra B G H, maius erit rectangulo ſub G E cum R E, in eadem G E:
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</
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<
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">ſed rectangulum ſub G R cum R E, in G E, eſt exceſſus quadrati G
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ſupra R E, ideoque rectangulum B E F ſuperat rectangulum B G H maio-
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ri exceſſu, quo quadratum G R ſuperat quadratum RE. </
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