Calendar: 1884-1885 Page 630

624 GENERAL LITERATURE AND SCIENCE Triangles that have one angle equal and the sides about the equal angles reciprocally proportional are equal to one another ABCD is parallelogram from Β straight line is drawn cutting the diagonal AC in the side DC in and AD produced in shew that the rectangle EF FG is equal to the square on BF If solid angle be contained by three plane angles any two of them must be greater than the third Prove that the perpendicular from the foot of the norma on the focal distance of conic cuts off from it part equal to the latus rectum chord of parabola normal at Ρ meets the axis in and is bisected in if AN be the abscissa of prove tha FG UN AN AS The ordinate at Ρ on an ellipse meets the auxiliar circle at ζ SZ perpendicular to SP meets the normal in ZR parallel to the minor axis meets CQ in prove that SR is perpendicular to CQ straight line cuts off constant area from two give11 straight lines prove that the locus of its middle point is hyperbola 10 Find the equation of the straight line joining the origin to the intersection of 'ox -f with 4x &y and the angles it makes with these lines 11 Find the equations of the diagonals of the quadrilateral Sx 4y 12 Express the area of polygon of η sides in terms of the coordinates of its angular points 13 Examine the conditions under which ax 1xy bf 2gx 2fy will represent two straight lines If the conditions be satisfied prove that the lines are χ be χ be ca sih ca VA2 ab