Calendar: 1883-1884 Page 629

GENERAL LITERATURE AND SCIENCE G25 likewise have their bases or third sides equal and the two triangles shall be equal and their other angles shall be equal each to each viz those to which the equal sides are opposite Any two sides of triangle are together greater than the third side The four sides of any quadrilateral are together greater than the two diagonals together In any right-angled triangle the square which is de- scribed upon the side subtending the right angle is equal to the squares described upon the sides which contain the right angle If two exterior angles of triangle are bisected and from the point of intersection of the bisecting lines line be drawn to the opposite angle of the triangle it will bisect that angle If straight line be divided into two equal and also into two unequal arts the squares of the two unequal parts are together double of the square of half the line and of tho square of the line between the points of section The sum of the squares of the sides of triangle 18 equal to double the square of the bisector of the base together with double the square of half the base The opposite angles of any quadrilateral figure inscribed in circle are together equal to two right angles Prove the converse of this theorem In equal circles the angles which stand upon equal cir- cumferences are equal to one another whether they be at the centres or circumferences 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 10 If Λ he point within circle BC the diameter and through he drawn AD perpendicular tu BC and BAF