Calendar: 1861-1862 Page 502

GENERAL LITERATURE AND SCIENCE 503 straight lines drawn from to the diameter prove that the sum of the squares of the reciprocals of the dividing lines 16 The sides of triangle are proportional to the roots of the equation χ3 -ρ χ" χ show that the sum of the cotangents of the semi-angles UPON the same base and on the same side of it there cannot be two triangles that have their sides which are termi- nated in one extremity of the base equal to one another and likewise those which are terminated in the other extremity The opposite sides and angles of parallelograms are equal to one another and the diameter bisects them that is divides them into two equal parts If the corner of leaf of book be twice turned down so that the creases are parallel and the triangular fold of the same breadth as the other show that the space included in the second fold is three times that in the first If the diagonals of quadrilateral bisect each other the figure is parallelogram If straight line be divided into any two parts the squares of the whole line and of one of the parts are equal to twice the rectangle contained by the whole and that part together with the square of the other part To draw straight line from given point either without or in the circumference which shall touch given circle If straight line touches circle and from the point of contact straight line be drawn cutting the circle the angles which this line makes with the line touching the circle shall be equal to the angles which are in the alternate segments of the circle in-emiia -m