Dictionary.net

[Gr.] The portion of the surface of a sphere inclosed by arcs (each less than a semicircle) of three great circles is a Spherical triangle. The relations between the sides and angles of spherical triangles is the subject of Spherical excess geometry ; those between the trigonometrical functions of the sides and angles, of Spherical excess trigonometry. The excess of the sum of the three angles of a spherical triangle above two right angles is its Spherical excess. A Spherical excess segment is the part of a sphere cut off by a plane ; a Spherical excess sector is the part of a sphere inclosed within a conical surface whose vertex is at the centre.