Calendar: 1876-1877 Page 622

622 WARNEFORD SCHOLARSHIPS IX- £ucIiU Parallelograms upon the same base and between the same parallels are equal to one another To describe parallelogram that shall be equal to given triangle and have one of its angles equal to given rectilineal angle If the square described upon one of the sides of triangle be equal to the squares described upon the other two sides of it the angle contained by these two sides is right angle If straight line be divided into any two parts the square of the whole line is equal to the squares of the two parts to- gether with twice the rectangle contained by the parts To divide given straight line into two parts so that the rectangle contained by the whole and one of the parts shall be equal to the square of the other part If in circle two straight lines cut one another which do not both pass through the centre they do not bisect each other The straight line drawn at right anales to the diameter of circle from the extremity of it falls without the circle and no straight line can be drawn from ihe extremity between that straight line and the circumference so as not to cut the circle or which is the same thing no straight line can make so great an acute angle with the diameter at its extremity or so small an angle with the straight line which is at right angles to it as not to cut the circle If from any point without circle two straight lines be drawn one of which cuts the circle and the other touches it the rectangle contained by the whole line which cuts the circle and the part of it without the circle shall be equal to the square of the line which touches it -aigcfcra Find the continued product of χ 2a χ χ and χ 2a