Calendar: 1852-1853 Page 334

330 GENERAL LITERATURE AND SCIENCE Describe an isosceles triangle having each of the angles at the base double of the third angle Describe rectilineal figure which shall be similar to one and equal to another given rectilineal figure Every solid angle is contained by plane angles which together are less than four right angles Find the length of the perpendicular from the vertex on the base of triangular pyramid the sides being equiangular triangles 10 The angles of quadrilateral inscribed in circle taken in order when multiplied by the numbers are in arith- metical progression find them 11 Prove that sin sin -f cos cos cos τ מ ל י sin If tan -- tan tan η sin 12 person wanting to find his distance from an inaccessible object discovers three places on level plane from which the elevation of the object is the same show that his distance £ cosec 13 If Af and -j Β be angles whose cosines are in harmonic proportion prove that cos ץ cos 14 If 2χύϊ θ χ sin φ χ sin φ θ find χ in terms of 15 Resolve a2 cos θ -j- into series of cosines of arcs multiples of Θ 10 Given the sum of two angles and the ratio of their tangents find the sine of the difference of the angles 17 If be the radius of the circle inscribed in triangle r2 r3 the radii of the circles inscribed between this circle and the sides prove that ץ r2 -f- rj ra ץ r3 r3