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In all plain Triangles; As the halfe sum of the sides, is to their halfe difference: so is the tangent of the half sum of their opposite angles, to the tangent if their half difference.
Demonst. In the triangle BCD let the sides be CB and CD, and CG = CB. wherefore ½ Z crur. = EG. & ½ × crur. = EC, draw CH bi-se∣cting BG at right angles, and make the angle GCI = D, then will the angle GCH = ½ Z angle B and D whose tangent is HG, and the angle
ICH = ½ × ang. B and D whose tan∣gent is HI.
But EG. EC ∷ HG. HI. that is. ½ Z crur. ½ × crur. ∷ t ½ Z ang t ½ X ang.