_Homologous_ ANGLES in similar figures are such as retain the same order, reckoning from the first in both figures. _Vertical_ ANGLES, are the opposite angles made by two lines cutting or crossing each other. When two lines cut or cross each other, the vertical angles are equal (15 _Eucl._ 1.) _Alternate_ ANGLES, are those cut or obtuse angles made by two lines cutting or crossing each other, and formed by a right line cutting or crossing two parallel lines. Alternate angles are always equal to each other (18. _Eucl._ 1.) _A rectilineal or right lined_ ANGLE, is made by strait lines, to distinguish it from the spherical or curvilineal angle. ANGLES _of contact_. Angles of contact may be considered as true angles, and should be compared with one another, though not with right lined angles as being infinitely smaller. ANGLE _of elevation_, in gunnery, is that which the axis of the hollow cylinder, or barrel of the gun, makes with a horizontal line. See ELEVATION. ANGLES _oblique_ are those which are greater than right angles. _Spherical_ ANGLE, is an angle formed by the intersection of two great circles of the sphere. All spherical angles are measured by an arch of a great circle described on the vertex as a pole, and intercepted between the legs which form the angle. ANGLE _lunular_ is an angle formed by the intersection of two curves, the one concave and the other convex. _Mixed-line_ ANGLE, is that comprehended between a right line and a curved line. _Curved-line_ ANGLE, is that intercepted between two curved lines meeting each other in one point, in the same plane. ANGLE _of a semi-circle_ is that which the diameter of a circle makes with the circumference. ANGLE _of Incidence_, is that which the line of direction of a ray of light, &c. makes at the point where it first touches the body it strikes against, with a line erected perpendicular to the surface of that body. ANGLE _of interval_ between two places is that formed by two lines directed from the eye to those places. 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 _at the centre_, in fortification, is the angle formed at the middle of the polygon, by lines drawn from thence to the points of the two adjacent bastions. ANGLE _of the curtain_, ANGLE _of the flank_, That which is made by, and contained between the curtain and the flank. ANGLE _of the polygon_, that which is made by the meeting of the two sides of the polygon, or figure in the centre of the bastion. See FORTIFICATION. ANGLE _of the triangle_, is half the angle of the polygon. ANGLE _of the bastion_, or _Flanked_ ANGLE, That which is made by the two faces, being the utmost part of the bastion most exposed to the enemy’s batteries, frequently called the point of the bastion. See FORTIFICATION.