Calendar: 1857-1858 Page 433

THE SCHOOL 435 FIRST CLASS MATHEMATICAL SCHOLARSHIP -iSutltii anK iTrtg onomrtrD II -mgcbra The questions upon these subjects were the same as those set for the Junior Mathematical Scholarship in the Department of General Literature and Science SECOND CLASS MATHEMATICAL SCHOLARSHIP -eEucltU 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 decagon inscribed in the large circle and side of pentagon inscribed in the small circle In every triangle the square of the side subtending either of the acute angles is less than the squares of the sides con- tabling that angle by twice the rectangle contained by either of these sides and the straight line intercepted between the perpen- dicular 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 hexagonal figure thus formed is equal to four times the sum of the squares of the sides of the triangle If from point in the diameter Β of circle Ρ PR be drawn to the extremities of the chord QR which is parallel to then shall AP2 PB PQ' PR ε ε