Calendar: 1857-1858 Page 399

GENERAL LITERATURE AND SCIENCE 401 Exhibit as binomial surds the square root of 12 γ ץ 67 and the cube root of γ -f- passenger in railway carriage observes train moving in the opposite direction to pass him in 2" and also that another train moving in the same direction as his with the same speed as the former but twice its length takes 40" to pass him compare the speeds of the two trains If Ν and η be the number of balls in the length and breadth of the base of rectangular pile show that the number of balls 3iV- If be the radius of the inscribed circle of the triangle ABC Α Β area r2 cot cot cot If be in geometrical progression then Divide an odd number into two whole numbers so that their product may be the greatest If four quantities be proportionals according to Euclid's definition prove that they will be so according to the algebraic definition and show that if β ז &c then am bu cp &c alm bln clp Sec If be the first and be the last of series of η quantities in geometric progression prove that the continued product of the terms β 10 Two clocks point to 12 at the same instant one of them gains 7" the other loses 6" in twelve hours When will one have gained half-an-hour on the other and what time will it show 11 If χ 15 χ find