=Anghiari.= A city of Tuscany, where the Florentines under Berardino Ubaldini were defeated by the Milanese general Torello, in 1425, and in 1440 the Florentine general Orsini defeated the Milanese general Piccinino. =Angle.= In geometry, is the inclination of two lines meeting one another in a point, or the portion of space lying between two lines, or between two or more surfaces meeting in a common point called the _vertex_. Angles are of various kinds according to the lines or sides which form them. Those most frequently referred to in fortification and gunnery are: ANGLE, DIMINISHED, is that formed by the exterior side and the line of defense. ANGLE, FLANKED, or SALIENT, is the projecting angle formed by the two faces of a bastion. ANGLE, INTERIOR FLANKING, is that which is formed by the meeting of the line of defense and the curtain. ANGLE OF ARRIVAL. The angle of arrival is the angle which the tangent to the trajectory at the crest of the parapet makes with the horizon. ANGLE OF DEPARTURE, or ANGLE OF PROJECTION, is the angle which the tangent makes with the horizontal at the muzzle. ANGLE OF ELEVATION, or ANGLE OF FIRE, in gunnery, is that which the axis of the barrel makes with the horizontal line. ANGLE OF FALL, in gunnery, is the angle made at the point of fall by the tangent to the trajectory with a horizontal line in the plane of fire. ANGLE OF FIRE, in gunnery, is the angle included between the line of fire and horizon; on account of the balloting of the projectile, the angle of fire is not always equal to the angle of departure, or projection. ANGLE OF INCIDENCE is that which the line of direction of a ray of light, ball from a gun, etc., makes at the point where it first touches the body it strikes against, with a line drawn perpendicularly to the surface of that body. ANGLE OF REFLECTION is the angle intercepted between the line of direction of a body rebounding after it has struck against another body, and a perpendicular erected at the point of contact. ANGLE OF SIGHT, in gunnery, is the angle included between the line of sight and line of fire. Angles of sight are divided into natural and artificial angles of sight, corresponding to the natural and artificial lines of sight, which inclose them. See POINTING. ANGLE OF THE CENTRE is the angle formed at the centre of the polygon by lines drawn thence to the points of two adjacent bastions. ANGLE OF THE EPAULE, or SHOULDER, is formed by one face and one flank of the bastion. ANGLE OF THE FACE is formed by the angle of the face and the line of defense produced till they intersect each other. ANGLE OF THE FLANK is that formed by the flank and curtain. ANGLE OF THE LINE OF DEFENSE is that angle made by the flank and the line of defense. ANGLE OF THE POLYGON is that formed by the meeting of two of the sides of the polygon; it is likewise called the _polygon angle_.