Calendar: 1899-1900 Page 755

FACULTY OF SCIENCE cm When it is 12 noon at Greenwich it is 30 at place and 10 30 at place Find the longitudes of and Β respectively Give an account of Australia its divisions physical features chief towns and leading industries Describe the Gulf Stream II -JHatfjematt'cs Pteltmmatg Certificate Only six questions are to be attempted Prove that the line joining the middle points of two sides of triangle is parallel to the third side and equal to half of it Also prove that the line drawn from the middle point of the base of triangle parallel to one of the sides to meet the bisector of the vertical angle is equal to half the difference of the sides If straight line be divided into any two parts prove that the difference between the squares on the two parts is equal to the rectangle contained by the sum and difference of the parts Find the locus of the vertex of triangle the difference of the squares on whose sides is equal to the square on given line Is the triangle whose sides are acute-angled right-angled or obtuse-angled and what are the lengths of the segments into which the longest side is divided by per- pendicular from the opposite angle Prove that the opposite angles of cyclic quadrilatera are supplementary ABCD is such quadrilateral It is turned about BC as an axis till it returns into the plane in position A'BCD' This is turned about CD' into position CD'A"B' and this about A"D' into position A"B"C'D' Shew that A"B" is parallel to AB If two chords of circle intersect prove that the rect- angle contained by the segments of one is equal to that con- tained by the segments of the other