Calendar: 1873-1874 Page 547

GENERAL LITERATURE AND SCIENCE 547 If ttie same straight line ect the base and the vertical angle the triangle is isosceles 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 All the interior angles of any rectilineal figure together with four right angles are equal to twice as many right angles as the figure has sides The diagonals of square bisect one another at right angles Half the base of triangle is greater than equal to or less than the bisector of the base according as the vertical angle is greater than equal to or less than right angle 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 straight line be divided into any two parts the square on the whole line is equal to the squares on the two parts together with twice the rectangle contained by the two parts In every triangle the square on the side subtending an acute angle is less than the squares on the sides containing that angle by twice the rectangle contained by either of these sides and the straight line intercepted between the perpendicular let fall on it from the opposite angles and the acute angle The sum of the squares on the sides of triangle is equal to twice the square on half the base together with twice the square on the bisector of the base The angles in the same segment of circle are equal to one another If two triangles with equal vertical angles stand on the same base and on the same side of it the circle circumscribing one of the triangles will also circumscribe the other If from any point without circle two straight lines be drawn one of which cuts the circle and the other touches it the rectangle contained by the whole line which cuts the circle and the part of it without the circle shall be equal to the square on the line which touches it Μ Μ