Calendar: 1873-1874 Page 610

610 THE SCHOOL and prove that χ Give the algebraical and geometrical definitions of propor- tion and prove that if quantities be proportional according to the algebraic definition they are proportional according to the geometric definition Prove that of and cf י ג י If and β be the roots of the equation ax2 bx prove that j3 and αβ el י hi β ι χ 1' Form the equation of which the roots are and β Divide Xs e4 a8 by ax a" and prove that 2n ן In 2n is divisible by ar2 aar a2 being positive integer Transform the number 18431 from the decimal scale to the scale whose base is and in the same scale multiply together the numbers 1432 and 653 certain number consisting of two digits is greater by than times the sum of its digits and if the order of the digits be reversed the number so formed is greater by 11 than times the sum of its digits find the number 10 Simplify the expression x2y xi Vary1 ζ fxy and find the square root of 141 18 Λ0