# Calendar: 1878-1879 Page 597

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GENERAL LITERATURE AND SCIENCE 59S To describe an isosceles triangle baving each of tbe angles at the base double of the third angle Similar triangles are to one another in the duplicate ratio of their homologous sides If in triangle the line that bisects the base bisects also tlie vertical angle that triangle is isosceles Investigate the following forms of equation to straight line eiiooi arcosa ysina Draw the lines J3 V3 χ and find the area of the triangle formed by them Find the condition that three straight lines may pass through the same point 10 Apply the foregoing to prove that the straight lines drawn from the angles of triangle to the middle points of the opposite sides meet at point 11 Find the equations to the diagonals of the four-sided figure the sides of which are represented by the equations χ 2x 12 Transform the equation 1T-f y3 to axes inclined at 45 to the original axes 13 Find the equation to the circle referred to any oblique axes 14 Deduce the equation to the circle referred to pair of tangents as nxes meeting at an angle ω at 90 15 Find the magnitude of in order that the circles Cy and fi may touch each other 16 Interpret the equations bf xy χ1 χ2 ψ 2x 4y 30 7'-3r cos 2Θ sec θ 18 ρ

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