Part 11

An Acute ANGLE, is that which is less than a right angle, or 90°.

An Obtuse ANGLE, is that which is greater than a right angle.

Adjacent ANGLES, are such as have the same vertex, and one common side contained beyond the angular point. The sum of the adjacent angles is always equal to two right angles (13. Eucl. 1.) and therefore, if one of them be acute, the other will be obtuse; and the contrary: whence, if either of them be given, the other is also given, it being the complement of the former to 180°.

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.

Diminished ANGLE, only used by some engineers, especially the Dutch, is composed of the face of the bastion, and the exterior side of the polygon.

ANGLE of the shoulder, or ANGLE of the épaule, Is formed by one face, and one flank of the bastion. See FORTIFICATION.

ANGLE of the tenaille, ANGLE rentrant, Is made by two lines fichant, that is, the faces of the two bastions extended till they meet in an angle towards the curtain, and is that which always carries its point towards the out-works. See FORTIFICATION.

ANGLE of the flank exterior, is that which is before the centre of the curtain, formed by the prolongation of the faces of the bastion, or by both the fichant lines of defence, intersecting each other on planning a fortification.

ANGLE of the flank interior, is formed by the flanked line of defence and the curtain; being that point where the line of defence falls upon the curtain.