DelMonte, Guidubaldo - In duos Archimedis aequeponderantium libros Paraphrasis : scholijs illustrata

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PROPOSITIO. XII.

Si duo triangula ſimilia fuerint, alterius verò
trianguli centrum grauitatis in rectalinea fuerit,
quæ ſit ab aliquo angulo ad dimidiam baſim du
cta; & alrerius trianguli centrum grauitatis erit in
linea ſimiliter ducta.

54[Figure 54]

Sint duo triangula ABC DEF ſimilia ſitquè AC ad DF, vt
AB ad DE, & BC ad FE. Diuiſaquè AC bifariam in G, iunga
tur BG. centrum verò grauitatis trianguli ABC ſit punctum H in li
nea BG. Dico centrum grauitatis trianguli EDF eſſe in recta linea ſi
militer ducta. ſecetur DF bifariam in puncto M. & iungatur EM.
& vt BG ad BH, ita fiat ME ad EN. connectanturquè AH
HC, DN NF. Quoniam enim eſt BA ad ED, vt AC ad DF, &
AG dimidia eſt ipſius AC; ipſius verò DF dimidiaest DM; erit BA
ad ED, vt AG ad DM. Quoniam autem ob triangulorum
ABC DEF ſimilitudinem angulus BAC angulo EDF eſt ę
qualis. & vt AB ad DE, ita AG ad DM; permutando〈que〉; AB
AG, vt DE ad DM; erit triangulum ABG triangulo DEM ſimile.
ſimilium ant triangulorum anguli sunt ęquales, et circa æquales angulos late

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