Of Geometry, the seventh Booke, Of the comparison of Triangles.
1. Equilater triangles are equiangles. 8. p. j.
Thus forre of the Geometry, or affections and reason of one triangle; the comparison of two triangles one with another doth follow. And first of their rate or reason, out of their sides and angles: Whereupon triangles betweene themselves are said to be equilaters and equiangles. First out of the equality of the sides, is drawne also the equalitie of the angles.
Triangles therefore are here jointly called equilaters, whose sides are severally equall, the first to the first, the second, to the second, the third to the third; although every severall triangle be inequilaterall. Therefore the equality of the sides doth argue the equality of the angles, by the [7. e iij]. As here.
2. If two triangles be equall in angles, either the two equicrurals, or two of equall either shanke, or base of two angles, they are equilaters, 4. and 26. p j.
Or thus; If two triangles be equall in their angles, either
in two angles contained under equall feet, or in two angles, whose side or base of both is equall, those angles are equilater. H.
This element hath three parts, or it doth conclude two triangles to be equilaters three wayes. 1. The first part is apparent thus: Let the two triangles be aei, and ouy; because the equall angles at a, and o, are equicrurall, therefore they are equall in base, by the [7. e iij].