Calendar: 1885-1886 Page 679

general literature and science 671 In any right-angled triangle the square described on the side subtending the right angle is equal to the sum of the squares on the sides containing the right angle To describe square that shall be equal to given recti- lineal figure The base of triangle is given and is bisected by the centre of given circle if the vertex be at any point of the circumference show that the sum of the squares on the two sides of the triangle is invariable Equal straight lines in circle are equally distant from the centre and those which are equally distant from the centre are equal to one another Two circles have the same centre show that all chords of the outer circle which touch the inner circle are equal In circle the angle in semi-circle is right angle but the angle in segment greater than semi-circle is less than right angle and the angle in segment less than semi-circle is greater than right angle If two circles intersect at and and AC AD are two diameters the straight line CD will pass through To inscribe regular pentagon in given circle Any equilateral figure that is inscribed in circle is also equiangular 10 The sides about the equal angles of triangles which are equiangular to one another are proportionals triangle BC has its side greater than its side AC and from and perpendiculars BE CG are drawn on AG and AB respectively show that the sum of AB and CG is greater than the sum 01 AC and BE 11 The rectangle contained by the diagonals of quadri- lateral figure inscribed in circle is equal to both the rec- tangles contained by the opposite sides III Crigonomttrg The circular measure of an angle is equal to the ratio of the number of degrees in it to the number of grades find its magnitude in degrees