Calendar: 1877-1878 Page 629

WARNEFORD SCHOLARSHIPS 627 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 and of one of the parts are equal to twice the rectangle contained by the whole and that part together with the square of the other part In obtuse-angled triangles if perpendicular be drawn from either of the acute angles to the opposite side produced the square of the side subtending the obtuse angle is greater than the squares of the sides containing the obtuse angle by twice the rectangle contained by the side upon which when produced the perpendicular falls and the straight line intercepted without the triangle between the perpendicular and the obtuse angle To draw straight line from given point either without or in the circumference which shall touch given circle If straight line touches circle and from the point of contact straight line be drawn cutting the circle the angles which this line makes with the line touching the circle shall he equal to the angles which are in the alternate segments of the circle -Hgeftra If ρ find the numerical value of" cb bc Divide p3 Zp'q Zpq q3 i13 by ρ Resolve a3 -f- b3 into two factors and multiply by β2 ah