Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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">Si duo triangula ABC, DEF, habuerint circa angulos B, E,
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latera AB, BE, item@altera BC, EF inter ſe æqualia, & </
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<
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">in angulis
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BAC, EDF applicatæ ſint GH, IL parallelæ ad BC, EF, ſitque
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rectangulum BGH æquale rectangulo EIL. </
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inter ſe æqualia eſſe.</
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<
s
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">SEd conſultò omiſſa, præter mei inſtituti morem, affirmatiua demonſtra-
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tione, libet potiùs indirectam, ac breuiorem afferre, ſimulque egregiæ
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indolis ſpecimen exhibere nobiliſsimi, ac ingenioſiſsimi Romani Adoleſcentis,
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Bruti Annibali della Molara, ex ſelectiſsimis Ephebis SERENISSIMO
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MAGNO DVCI miniſtrantibus, de quo non auſim aſſerere, quæ ſint ei
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maioris oblectamenti, an equeſtrium exercitationum ornamenta, quibus
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elegantiſsimè inſignitur, an mathematicæ contemplationes, dum, etiam
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inter Aulæ ſtrepitus, pacatos ſubtilioris Geometriæ nouit inuenire receſſus,
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prout varia teſtantur problemata, ac theoremata, à me identidem ei propoſi-
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ta, & </
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<
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">ab ipſo quàm feliciter ſoluta, quorum, licet facillimum, poſteriori
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tamen inſeruiens hic habes.</
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<
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">ESto, ſi fieri poteſt, alterum ipſorum laterum, quale eſt BG, maius alte-
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ro EI: </
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">habebit ergo GB ad BA, maiorem rationem quam IE ad ED ipſi
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BA æqualem, & </
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ad AB maiorem rationem quàm ID
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ad DE, ſed GA ad AB, eſt vt GH ad
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BC, & </
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GH ad BC habet maiorem rationem
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quàm IL ad EF, hoc eſt ad ſibi æqua-
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lem BC, quare GH erit maior IL, & </
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ponitur BG maior EI, vnde rectan-
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gulum BGH maius eſt rectangulo
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EIL: </
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