Calendar: 1868-1869 Page 499

GENERAL LITERATURE AND SCIENCE 501 11 person observes the elevation of tower and the angle which spire on the tower makes at the place of observation he walks feet perpendicularly to his first position and makes similar observations thence find the height of the tower of the spire and his distance from the tower 12 From the vertex of triangle AD is drawn perpendicular to Β and δ Ε from Β perpendicular to join Show that ABDE may be inscribed in circle and prove DE cos 13 If ABC he triangle and A1 Bl Cx be another formed of the three perpendiculars from C3 on the opposite sides show that cos A1 cos B1 coe -f -- 14 If η π show that sin sin 4- sin &c 4- sin na cot η 7r 27r 3jt 47r 67r 7r coe cos cos cos cos cos 15 15 15 15 15 15 15 If AD be perpendicular to the base BC of the triangle ABC and DE DF perpendicular to AB and AC and radius of the circumscribed circle show that the area of the triangle EF 16 If straight line be drawn parallel to one of the sides of triangle it shall cut the other sides or these produced pro- portionally and if the sides or the sides produced be cut pro- portionally the straight line which joins the points of section shall be parallel to the remaining side of the triangle 17 Similar triangles are to one another in the duplicate ratio of their homologous sides 18 The rectangle contained by the diagonals of quadrilateral figure inscribed in circle is equal to both the rectangles con- tained by its opposite sides 19 If two straight lines be at right angles to the same plane they shall be parallel to one another 20 To draw straight line perpendicular to plane from given point above it