Calendar: 1871-1872 Page 529

GENERAL LITERATURE AND SCIENCE 529 be equal and their other angles shall be equal each to each namely those to which the equal sides are opposite If two straight lines bisect each other at right angles any point in either of them is equi-distant from the extremities of the other If one side of triangle be produced the exterior angle shall be greater than either of the interior opposite angles Enunciate the propositions you employ in your proof Any two sides of triangle are together greater than the third side The sum of the distances of any point from the three angles of triangle is greater than half the sum of the sides of the triangle All the exterior angles of any rectilineal figure are together equal to four right angles If the sides of pentagon be produced both ways to meet in pairs forming five triangles find the sum of the vertical angles Describe square on given straight line Along the sides of square taken in order measure Λ Ε BF CG DH prove that EFGH is square If straight line be divided into two equal and also into two unequal parts the squares on the two unequal parts are together double of the square on half the line and of the square on the line between the points of section Divide straight line into two parts such that the sum of their squares may be the least possible In any triangle the sum of the squares on the two sides is equal to twice the square on half the base together with twice the square on the straight line which joins the middle point of the base to the opposite angle The sum of the squares on the sides of any quadrilateral is equal to the sum of the squares on its two diagonals together with four times the square on the line joining the middle points of the diagonals The straight line drawn at right angles to the diameter of circle from the extremity of it falls without the circle and no