#### For Angles of commutation at English => English (Websters 1913) Of Explained:

Angle \An"gle\ ([a^][ng]"g'l), n. [F. angle, L. angulus angle,

corner; akin to uncus hook, Gr. 'agky`los bent, crooked,

angular, 'a`gkos a bend or hollow, AS. angel hook, fish-hook,

G. angel, and F. anchor.]

1. The inclosed space near the point where two lines meet; a

corner; a nook.

Into the utmost angle of the world. --Spenser.

To search the tenderest angles of the heart.

--Milton.

2. (Geom.)

(a) The figure made by. two lines which meet.

(b) The difference of direction of two lines. In the lines

meet, the point of meeting is the vertex of the angle.

3. A projecting or sharp corner; an angular fragment.

Though but an angle reached him of the stone.

--Dryden.

4. (Astrol.) A name given to four of the twelve astrological

``houses.'' [Obs.] --Chaucer.

5. [AS. angel.] A fishhook; tackle for catching fish,

consisting of a line, hook, and bait, with or without a

rod.

Give me mine angle: we 'll to the river there.

--Shak.

A fisher next his trembling angle bears. --Pope.

{Acute angle}, one less than a right angle, or less than

90[deg].

{Adjacent} or {Contiguous angles}, such as have one leg

common to both angles.

{Alternate angles}. See {Alternate}.

{Angle bar}.

(a) (Carp.) An upright bar at the angle where two faces of

a polygonal or bay window meet. --Knight.

(b) (Mach.) Same as {Angle iron}.

{Angle bead} (Arch.), a bead worked on or fixed to the angle

of any architectural work, esp. for protecting an angle of

a wall.

{Angle brace}, {Angle tie} (Carp.), a brace across an

interior angle of a wooden frame, forming the hypothenuse

and securing the two side pieces together. --Knight.

{Angle iron} (Mach.), a rolled bar or plate of iron having

one or more angles, used for forming the corners, or

connecting or sustaining the sides of an iron structure to

which it is riveted.

{Angle leaf} (Arch.), a detail in the form of a leaf, more or

less conventionalized, used to decorate and sometimes to

strengthen an angle.

{Angle meter}, an instrument for measuring angles, esp. for

ascertaining the dip of strata.

{Angle shaft} (Arch.), an enriched angle bead, often having a

capital or base, or both.

{Curvilineal angle}, one formed by two curved lines.

{External angles}, angles formed by the sides of any

right-lined figure, when the sides are produced or

lengthened.

{Facial angle}. See under {Facial}.

{Internal angles}, those which are within any right-lined

figure.

{Mixtilineal angle}, one formed by a right line with a curved

line.

{Oblique angle}, one acute or obtuse, in opposition to a

right angle.

{Obtuse angle}, one greater than a right angle, or more than

90[deg].

{Optic angle}. See under {Optic}.

{Rectilineal} or {Right-lined angle}, one formed by two right

lines.

{Right angle}, one formed by a right line falling on another

perpendicularly, or an angle of 90[deg] (measured by a

quarter circle).

{Solid angle}, the figure formed by the meeting of three or

more plane angles at one point.

{Spherical angle}, one made by the meeting of two arcs of

great circles, which mutually cut one another on the

surface of a globe or sphere.

{Visual angle}, the angle formed by two rays of light, or two

straight lines drawn from the extreme points of an object

to the center of the eye.

{For Angles of commutation}, {draught}, {incidence},

{reflection}, {refraction}, {position}, {repose}, {fraction},

see {Commutation}, {Draught}, {Incidence}, {Reflection},

{Refraction}, etc.