Calendar: 1887-1888 Page 667
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GENERAL LITERATURE AND SCIENCE 671 any spherical triangle having arcs of great circles for its sides if one side and its opposite angle are each then another side and its opposite angle must be equal to In any right-angled spheiical triangle having the right angle at prove cos cot cot β If be the central point of triangle ABO having each זל side prove cos AO If be the side of an equilateral triangle and ρ the perpendicular from one corner on the opposite side prove cos cos 2a cos 2a State Gauss's theorems and prove one of them 10 If be the number of solid angles the number of faces and Ε the number of edges in polyhedron prove Έ 11 Having given that is root of the equation x4 8x3 26x2 52x 48 solve the equation 12 Divide δχ3 6x2 ix 20 by χ three times in succession and shew that the remainders obtained are the coefficients of the successive powers of χ in the expansion of 20 II -algebra If prove that each is equal to ί 3-y3 Solve the equation 2x 4z 4y2 124
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