Calendar: 1893-1894 Page 885

WARNEFORD SCHOLARSHIPS clxvii 13 Write down the general term in the expansion of binomial raised to any power If the index of the power be an integer prove that the sum of the coefficients is half the sum of the coefficients of the next higher power Candidates for Warneford Scholarship and Sambrooke Ex- hibition omit Questions 10 for Clothworkers9 Exhibition omit Questions 10 for Entrance Exhibition omit Enunciate the propositions that you employ to prove that the lines joining the extremities of two straight lines that bisect one another at right angles form rhombus If straight lines be drawn perpendicular to the sides of an equilateral triangle each to each prove that they in general form an equilateral triangle Shew how to describe square that shall be equal to given pentagon Prove that the angle in segment greater than semi- circle is less than right angle Shew how to inscribe regular octagon in given circle Two radii of circle are at right angles through the middle point of each straight line is drawn parallel to the other to intersect the circle Prove that the line joining their nearer extremities is the side of regular dodecagon inscribed in the circle Define similar figures and state under what circum- stances two triangles may be proved to be similar Prove that parallelograms that are equiangular to one another have to one another the ratio compounded of the ratios of their sides Prove that two straight lines that are perpendicular to the same plane are parallel 10 Prove that the shortest distance between two straight lines is perpendicular to both