# Calendar: 1875-1876 Page 586

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582 GENERAL LITERATURE AND SCIENCE tained by those sides equal to one another they shall also have their bases or third sides equal and the two triangles shall be equal and their other angles shall be equal each to each namely those to which the equal sides are opposite If side of any triangle be produced the exterior angle is equal to the two interior and opposite angles and the three interior angles of every triangle are together equal to two right angles If the straight lines bisecting the angles at the base of an isosceles triangle are produced to meet they contain an angle equal to an exterior angle of the triangle In any right-angled triangle the square which is described on the side subtending the right angle is equal to the squares described on the sides which contain the right angle If any point be joined to the angular points of rectangle the squares on OA and OC are together equal to the squares on 0Î’ and OD 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 cf the line between the points of section In any triangle the sum of the squares on the sides is equal to twice the square on half the base together with twice the square on the straight line drawn from the vertex to the middle point of the base In any quadrilateral the sum of the squares on the sides is greater than the sum of the squares on the diagonals by four times the square on the straight line joining the middle points of the diagonals The diameter is the greatest straight line in circle and of all others that which is nearer to the centre is always greater than one more remote Through given point within circle draw the shortest chord The opposite angles of any quadrilateral figure inscribed in circle are together equal to two right angle No parallelogram but rectangle can be inscribed in circle If straight line touch circle and from the point of contact straight line be drawn cutting the circle the angles

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