Calendar: 1863-1864 Page 528

528 GENERAL LITERATURE AND SCIENCE ab --- ac be -- 15 The roots of reciprocal equation of η dimensions may be solved by means of one of η dimensions Example 8z3 x2 8x 16 If Sm the sum of the Nth powers of the roots of an equation show that if the equation be ג χ S3 17 The equation to parabola being y1 ax and yv y2 y3 being the ordinates of the angular points of triangle in- scribed in it show that the area is 93 92 91 ύ93 Vx JUNIOR MATHEMATICAL SCHOLARSHIP -βιιάΐα 11 If two triangles have two sides of the one equal to two sides of the other each to each but the angle contained by the two sides of one of them greater than the angle contained by the two sides equal to them of the other the base of that which has the greater angle shall be greater than the base of the other Make parallelogram which shall be equal in area and perimeter to given triangle In any right-angled triangle the square which is described upon the side subtending the right angle is equal to the squares described upon the sides which contain the right angle If two exterior angles of triangle be bisected and from the point of intersection of the bisecting lines line be drawn to the opposite angle of the triangle it will bisect that angle In every triangle the square of the side subtending either of the acute angles is less than the squares of the sides con- taining that angle by twice the rectangle contained by either of