Calendar: 1851-1852 Page 321

APPLIED SCIENCES 325 Given the perimeter of triangle and one angle find when its area is the greatest possible Express the area of triangle in terms of the coordinates of its angular points Trace the curve defined by the equation x2 a2 and find the area between the curve and asymptote 0" Ρ and are drawn at right angles to each other from the centre of an ellipse find when their rectangle is greatest If be positive for all values of χ between and then -J- -is also positive Apply the Integral Calculus to sum the series Rr '5 Of all cones inscribed in sphere find that which has the greatest convex surface γ dx xadx 10 Integrate ---- and---r 11 Where must an eye be placed between two given objects both perpendicular to the horizon that the sum of their apparent magnitudes may be the greatest 12 Find the differential of the surface of solid of revolution and apply it to find the surface generated by the semicycloid round its base II 42 r2 Deduce the equation p2 -- -- to the a2 epicycloid and show that the arc corresponding to one revolu- tion of the generating circle