Calendar: 1870-1871 Page 511

GENERAL LITERATURE AND SCIENCE 511 If lines be drawn through the ends of the base of an isosceles triangle making angles with it on the side remote from the vertex each equal to one-third of one of the equal angles and meeting the sides produced prove that three of the triangles thus formed are isosceles If side of triangle be produced the exterior angle is equal to the two interior and opposite angles and the three interior angles of every triangle are equal to two right angles If ABC be triangle in which Ο is right angle show how to draw straight line parallel to given straight line so as to be terminated by OA and CB and bisected by AB If straight line fall upon two parallel straight lines it makes the alternate angles equal to one another Through two given points draw two lines forming with line given in position an equilateral triangle Triangles upon equal bases and between the same parallels are equal to one another If quadrilateral figure have two sides parallel and the parallel sides be bisected the line joining the points of bisection shall pass through the point in which the diagonals cut one another If straight line be divided into any two parts the sum of the square on the whole line and one of the parts is equal to twice the rectangle contained by the whole line and that part together with the square on the other part Produce straight line so that the sum of the squares on the given litie and the part produced may be equal to twice the rectangle contained by the whole line thus produced and the produced part The opposite angles of quadrilateral inscribed on circle are together equal to two right angles If the chords which bisect two angles of triangle inscribed in η circle be equal prove that either the angles are equal or the third angle is equal to tbe angle of an equilateral triangle Divide straight line into two parts so that the square of one part may be double the square of the other In circle the angle in semicircle is right angle The greatest rectangle that can be inscribed in circle is tquave