Calendar: 1859-1860 Page 448

GENERAL LITERATURE AND SCIENCE 449 Any rectangle is equal to half the rectangle contained by the diagonals of the squares upon its two sides To describe square that shall be equal to given rec- tilineal figure If straight line drawn through the centre of circle bisect straight line in it which does not pass through the centre it shall cut it at right angles and if it cuts it at right angles it shall bisect it Draw circle which shall pass through two points and have its centre in given line The opposite angles of any quadrilateral figure inscribed in circle are together equal to two right angles £ State and prove the converse of the above Upon given straight line to describe segment of circle which shall contain an angle equal to given rectilineal angle In circle draw an isosceles triangle having one of the equal sides the diagonal of the square of which the base is side 10 To describe an isosceles triangle having each of the angles at the base double of the third angle 11 If two triangles have one angle of the one equal to one angle of the other and the sides about the equal angles propor- tionals the triangles shall be equiangular and shall have those angles equal which are opposite to the homologous sides 12 Similar triangles are to one another in the duplicate ratio of their homologous sides 13 To find mean proportional between two given straight lines 14 Describe square in given segment of circle Ill-ffiutlfo -$lane Crtgonometrg If two straight lines he at right angles to the same plane they shall be parallel to one another Every solid angle is contained by plane angles which together are less than four right angles