2 The second thus: Let the said two triangles aei, and ouy, be equall in two angles a peece, at e, and i, and at u, and y. And let them be equall in the shanke ei, to uy. I say, they are equilaters. For if the side ae, (for examples sake) be greater than the side ou, let es, be cut off equall unto it; and draw the right line is. Here by the antecedent, the triangles sei, and ouy, shall be equiangles, and the angles sie, shall be equall to the angle oyu, to which
also the whole angle aie, is equall, by the grant. Therefore the whole and the part are equall, which is impossible. Wherefore the side ae, is not unequall but equall to the side ou: And by the antecedent or former part, the triangles aei, and ouy, being equicrurall, are equall, at the angle of the shanks: Therefore also they are equall in their bases ai, and oy.
3 The third part is thus forced: In the triangles aei, and ouy, let the angles at e, and i, and u, and y, be equall, as afore: And ae, the base of the angle at i, be equall to ou, the base of angle at y: I say that the two triangles given are equilaters. For if the side ei, be greater than the side uy, let es, be cut off equall to it, and draw the right line as. Therefore by the antecedent, the two triangles, aes, and ouy, equall in the angle of their equall shankes are equiangle: And the angle ase, is equall to the angle oyu, which is equall by the grant unto the angle aie. Therefore ase, is equall to aie, the outter to the inner, contrary to the [15. e. vj]. Therefore the base ei, is not unequall to the base uy, but equall. And therefore as above was said, the two triangles aei, and ouy, equall in the angle of their equall shankes, are equilaters.
3. Triangles are equall in their three angles.
The reason is, because the three angles in any triangle are
equall to two right angles, by the [13. e vj]. As here, the greatest triangle, all his corners joyntly taken, is equall to the least.