Valerio, Luca
,
De centro gravitatis solidorvm libri tres
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EF. quæ ſuntin latera homologa duorum triangulorum
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ABC, DEF. </
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>Ex definitione igitur, duo puncta G, H,
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in triangulis ABC, DEF, ſimiliter poſita erunt. </
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<
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enim ſi fieri poteſt ſit aliud punctum K, in triangulo
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DEF, ſimiliter poſitum puncto G. </
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<
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>Vel igitur punctum
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K in aliquo triangulorum, quorum eſt communis vertex
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H, vel in aliquo eorundem latere cadet. </
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<
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FH, & iungatur DK: triangulum ergo DFK, ſimile
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erit triangulo ACG. </
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>Sed & triangulum EDF, ſimile
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eſt triangulo BAC; vtraque igitur horum ad illorum ſi
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bi reſpondens triangulorum duplicatam eorundem late
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rum homologorum AC, DF, habebunt proportionem:
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vt igitur eſt triangulum EDF, ad triangulum BAC, ita
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erit triangulum DFK, ad triangulum ACG: & per
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mutando, vt triangulum ACG, ad triangulum ABC,
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ita triangulum DFK, ad triangulum EDF: eadem ra
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tione, vt triangulum ACG, ad triangulum ABC, ita
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erit triangulum DFH, ad triangulum DEF: vt igitur
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triangulum DFK, ad triangulum EDF; ita erit trian
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gulum DFH, ad triangulum EDF; triangulum ergo
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DFK, triangulo DFH, æquale erit, pars toti, quod eſt
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abſurdum: idem autem abſurdum ſequeretur, ſi punctum
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K
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, poneretur in aliquo prædictorum triangulorum, vt in
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triangulo DFH; Non igitur aliud punctum à puncto H,
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in triangulo EDF, ſimiliter poſitum erit puncto G.
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PROPOSITIO V.
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>Cuilibet figuræ planæ rectangulum æquale
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poteſt eſſe. </
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