Calendar: 1858-1859 Page 474

476 THE SCHOOL would they take when working together to finish some work which alone could do in 24 days person having to walk 15 miles finds that by increasing his speed half mile an hour he might reach his journey's end 25 minutes sooner than he otherwise would what time will he take if he only begin to quicken his pace half-way Find the square root of 43 J30 and the sixth root of 99 70 Find the sum of terms of an Arithmetic series Ex The τ series whose rth term is Sum the series χ2 χ χ 2y ע &c to η terms 10 The sum of an infinite Geometric series is and the sum of the squares of the terms is find the sum of η terms II -eucift If two angles of triangle are equal the sides also which subtend them are equal Triangles on the same base and between the same parallels are equal Describe triangle equal to given quadrilateral figure its base being in the same straight line as that of the figure and its vertex at one of the angular points Squares are described on the two sides AB AC which contain the right angle of right-angled triangle and the sides opposite to AB AC meet in show that Ν produced cuts BC at right angles If straight line is divided into two equal and also into two unequal parts the rectangle contained by the unequal parts together with the square of the line between the points of section is equal to the square of half the line If straight line passing through the centre of circle cut another straight line which does not pass through the centre at right angles it shall also bisect it