xxii. A right-angled triangle is one that has one of its angles a right angle, as D. The side which subtends the right angle is called the hypotenuse. xxiii. An obtuse-angled triangle is one that has one of its angles obtuse, as E. xxiv. An acute-angled triangle is one that has its three angles acute, as F. xxv. An exterior angle of a triangle is one that is formed by any side and the continuation of another side. Hence a triangle has six exterior angles; and also each exterior angle is the supplement of the adjacent interior angle. The Polygon. xxvi. A rectilineal figure bounded by more than three right lines is usually called a polygon. xxvii. A polygon is said to be convex when it has no re-entrant angle. xxviii. A polygon of four sides is called a quadrilateral. xxix. A quadrilateral whose four sides are equal is called a lozenge. xxx. A lozenge which has a right angle is called a square. xxxi. A polygon which has five sides is called a pentagon; one which has six sides, a hexagon, and so on. The Circle. xxxii. A circle is a plane figure formed by a curved line called the circumference, and is such that all right lines drawn from a certain point within the figure to the circumference are equal to one another. This point is called the centre. xxxiii. A radius of a circle is any right line drawn from the centre to the circumference, such as CD. xxxiv. A diameter of a circle is a right line drawn through the centre and terminated both ways by the circumference, such as AB. From the definition of a circle it follows at once that the path of a movable point in a plane which remains at a constant distance from a fixed point is a circle; also that any point P in the plane is inside, outside, or on the circumference of a circle according as its distance from the centre is less than, greater than, or equal to, the radius. Postulates. Let it be granted that— i. A right line may be drawn from any one point to any other point. When we consider a straight line contained between two fixed points which are its ends, such a portion is called a finite straight line. ii. A terminated right line may be produced to any length in a right line. Every right line may extend without limit in either direction or in both. It is in these cases called an indefinite line. By this postulate a finite right line may be supposed to be produced, whenever we please, into an indefinite right line. iii. A circle may be described from any centre, and with any distance from that centre as radius.