Calendar: 1857-1858 Page 400

402 GENERAL LITERATURE AND SCIENCE 12 If and β be tbe roots of the equation -f- bx -f- α β b' 2ac show that ό --- pa ac 13 The sum of the squares of two numbers divided by their ratio equals 10 the difference of their squares multiplied by their ratio equals 24 Find the numbers 14 If S' be tbe perimeter and Ρ the product of tbe three sides of triangle ABC Ρ τ the area cos cos Β cos cos Ή 15 If cos י ע- show that -4 VK--2 16 What integral values of χ and will satisfy the equation xy x1 χ 3y -f 29 17 The number of different combinations of η things taken at time of which there are ρ of one sort of another and of another -f II Budia ants Crigononutrg Describe an isosceles triangle having each of the angles at the base double of the third angle Shew that the base of the triangle is side of the decagon inscribed in the large circle and side of the pentagon inscribed in the small circle and compare their areas In every triangle the square of the side subtending either of the acute angles is less than the squares of the sides containing that angle by twice the rectangle contained by either of these sides and the straight line intercepted between the perpendicular let fall upon it from the opposite angle and the acute angle If squares be described on the sides of any triangle and the angular points be joined the sum of the squares of the sides