Valerio, Luca
,
De centro gravitatis solidorum
,
1604
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AH, ita fiat ED, ad DK: & quoniam angulus BAG,
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æqualis eſt angulo EDF: quorum angulus EDK,
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æqualis eſt angulo BAH, erit reliquus angulus
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K
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DF,
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æqualis reliquo angulo HAC; ſed angulus HAC, eſt
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maior angulo BAH; ergo & angulus KDF, maior erit
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angulo BAH; poſito igitur angulo FDL, æquali an
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gulo BAH, ac proinde minori, quàm ſit angulus FD
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K
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,
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fiat vt BA, ad AH, ita FD, ad DL. Dico, in triangu
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lo EDF, duo puncta K, L, ſimiliter poſita eſse ac pun
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ctum H, in triangulo BAC. </
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<
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>Iungantur enim rectæ AH,
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BH, CH, EK, KF, FL, LE. </
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>Quoniam igitur an
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gulus ED
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K
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, eſt æqualis angulo BAH, qui lateribus
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homologis continentur; erit angulus DE
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K
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, æqualis an
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gulo ABH: ſed totus angulus DEF, æqualis eſt toti an
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gulo ABC; reliquus igitur angulus KEF, æqualis erit
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reliquo HBC: ſed ex æquali eſt vt CB, ad BH, ita
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FE, ad EK; igitur vt antea erit angulus KFE, æqualis
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angulo HCB, & angulus DFK, æqualis angulo ACH,
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& angulus FDK, æqualis angulo CAH; punctum igi
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tur K, ſimiliter poſitum erit in triangulo EDF, ac pun
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ctum H, in triangulo ABC. </
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<
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>Rurſus quoniam angulus
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FDL, æqualis eſt angulo BAH, & latus AB, homo
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logum lateri DF, (eſt enim vt BA, ad AC, ita FD, ad
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DE) ſed vt BA, ad AH, ita eſt FD, ad DL, per con
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ſtructionem; ſimiliter vt ante, oſtenderemus, punctum L,
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in triangulo EDF, ſimiliter poſitum eſse puncto H; in
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uenta igitur ſunt duo puncta in triangulo DEF, ſimili
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ter poſita ac punctum H, in triangulo BAC. </
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<
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poſitum erat. </
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