Calendar: 1848-1849 Page 251

GENERAL LITERATURE AND SCIENCE 249 The sides of triangle are in arithmetical proportion and the distance between the centres of the inscribed and circum- scribed circles is mean proportional between the greatest and least find the sides If Ρ be the sum of the series formed by taking the 1st and every p"' term of an infinite geometric series first term unity Ο the sum by taking the 1st and every term prove that P" as Qp An ellipse slides between two rectangular axes find the curve traced by its centre Sum the series tan &c to η terms a8 sin χ a2 sin χ sin χ &c to infinity person at known distance from two towers observes that their apparent altitudes are the same he then walks given distance towards them till the angle of elevation of one is double that of the other find the heights of the towers 10 Find the point of contrary flexure in spiral γ 11 Trace the curve defined by cos Θ cos Θ and find its area 12 In the arc Β of circle centre AC is taken sine AB then will sector Ο Β segment Β 13 Expand ee according to the powers of and find co-efficient of xn 14 Inscribe the greatest parabola in given isosceles triangle 15 If θ be the angle which the normal to an ellipse makes with the axis major the radius of curvature α2 δ2 Ex θ a2cos 20 δ2 sin Θ 16 The shadows of two vertical walls at right angles to each other and which are and in height are observed at 12 o'clock