Calendar: 1880-1881 Page 684

684 CLOTHWORKERS SCIENCE EXHIBITIONS Inscribe regular pentagon in given circle Similar triangles are to one another in the duplicate ratio of their homologous sides 10 The rectangle contained by the diagonals of quadri- lateral inscribed in circle is equal to both the rectangles contained by its opposite sides 11 If the tangent to the parabola at any point Ρ intersect the directrix in then SZ is at right angles to SP 12 If QV be an ordinate to the diameter PF then QV2 4SP PF 13 In an ellipse if CD be conjugate to CP then CP will be conjugate to CD 14 Find the area of triangle in terms of the coordinates of its angular points Draw the straight lines 2y 2x 2x 43 2y Sx and find the area of the triangle formed by either set of lines 15 The straight lines drawn from the angles of triangle to the middle points of the opposite sides meet at point 16 Find the equation to the circle referred to any oblique axes Deduce the equation to the circle referred to pair of tangents meeting at an angle ω III -i&tcbank State the conditions of equilibrium of three forces Can forces of 11 balance one another Find the resultant of 115 lbs and 56 lbs acting at an angle of 60 What is the moment of force about point and how is it calculated uniform beam weighing cwt and 26 ft long is laid on table ft broad with 10 ft projecting on one side and 12 on the other-how far can man of 1£ cwt walk on the beam on either side of the table