Calendar: 1869-1870 Page 568

570 THE SCHOOL Find by the method of indeterminate multipliers the value of and then deduce that of and when ax by cz αϊχ a3x b3y c3 i3 If in finding the square root of number of -f- figures η be found show that the remaining η figures may be found by division only Ex -Find 12000000000 Divide by "- and being whole numbers and write down the la four terms of the quotient If ax2 bx and atx2 ff1 '1 ve cjmmon divisor tfjC ac atb a4 The quadrilateral whose diameters bisect each other is parallelogram Show how to divide an equilateral triangle into nine equal parts Show that the lines AD BE CF drawn from the angles of the triangle ABC to bisect the opposite sides intersect in and form the equal triangles AOB AOC BOC 10 To describe an isosceles triangle having each of the angles at the base double of the third angle Prove AB' BD1 AB BC 11 In any right-angled triangle the square which is described upon the side subtending the right angle is equal to the squares described upon the sides which contain the right angle Prove that BC and CH are parallel 12 Inscribe square in regular pentagon 13 Every solid angle is contained by plane angles which together are less than four right angles There are only regular solids 14 Find the quadratic factors of the equation a2 jT- a-f a4 15 Expand 10g1 according'to the powers of and compute loge to the 9th decimal place