Calendar: 1875-1876 Page 542

538 FREAKE EXHIBITIONS to another of which the characteristic only shall be negative and then find the corresponding number having given log 3325 1246672 and log 3326 1246998 IV tomttri The angles at the base of an isosceles triangle are equal to one another and if the equal sides be produced the angles 011 the other side of the base shall be equal to one another The opposite sides and angles of parallelogram are equal to one another and the diameter bisects the parallelogram that is divides it into two equal parts Show that quadrilateral which has its opposite sides equal is parallelogram In any right-angled triangle the square which is described on the side subtending the right angle is equal to the sum of the squares described on the sides which contain the right angle If two exterior angles of triangle be bisected and from the point of intersection of the bisecting lines line be drawn to the opposite angle of tbe triangle it will bisect that angle If straight line be divided into two equal and also into two unequal parts the squares on the two unequal parts are together double of the square on half the line and of the square on the line between the points of section In every triangle the square on the side subtending an acute angle is less than the squares on the sides containing that angle by twice the rectangle contained by either of these sides and the straight line intercepted between the perpendicular let fall on it from the opposite angle and the acute angle In any quadrilateral tbe squares on the diagonals are together equal to twice the sum of the squares on the straight lines joining the middle points of opposite sides The opposite angles of any quadrilateral inscribed in circle are together equal to two right angles Prove the converse of this proposition To describe an isosceles triangle having each of the angles at the base double of the third angle