SPHERICAL EXCESS
\sfˈɛɹɪkə͡l ɛksˈɛs], \sfˈɛɹɪkəl ɛksˈɛs], \s_f_ˈɛ_ɹ_ɪ_k_əl ɛ_k_s_ˈɛ_s]\
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[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.
By Henry Percy Smith
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