See also:

• ANGLE (from the Lat. angulus, a corner, a diminutive, of which the primitive form, angus, does not occur in Latin; cognate are the Lat. angere, to compress into a bend or to strangle, and the Gr. ayKOS, a bend; both connected with the Aryan root ank-, to

ANGLE (from the See also:

• LAT

Lat. angulus, a corner, a diminutive, of which the See also:

• PRIMITIVE

primitive See also:

• FORM (Lat. forma)

form, See also:

• ANGUS, EARLS OF

angus, does not occur in Latin; cognate are the Lat. angere, to compress into a See also:

• BEND

bend or to strangle, and the Gr. ayKOS, a bend; both connected with the See also:

• ARYAN

Aryan See also:

• ROOT (late O.E. rot, adopted from Scand., cf. Norw. and Swed. rot, Dan. rod; the true O.E. word was wyrt, plant, represented in Ger. Wurz or Wurzel; the ultimate root is the same in both words, and is seen in Lat. radix)
• ROOT, ELIHU (1845– )

root ank-, to  See also:

• BEND

bend: see See also:

• ANGLING

ANGLING), in See also:

• GEOMETRY

geometry, the inclination of one See also:

• LINE

line or See also:

• PLANE

plane to another . See also:

• EUCLID
• EUCLID [EucLEIDES]

Euclid (Elements, See also:

• BOOK

book I) defines a plane See also:

• ANGLE (from the Lat. angulus, a corner, a diminutive, of which the primitive form, angus, does not occur in Latin; cognate are the Lat. angere, to compress into a bend or to strangle, and the Gr. ayKOS, a bend; both connected with the Aryan root ank-, to

angle as the inclination to each other, in a plane, of two lines which meet each other, and do not See also:

• LIE, JONAS LAURITZ EDEMIL (1833—1908)
• LIE, MARIUS SOPHUS (1842–1899)

lie straight with respect to each other (see GEOMETRY, EUCLIDEAN) . According to See also:

• PROCLUS, or PROCULUS (A.D. 410-485)

Proclus an angle must be either a quality or a quantity, or a relationship . The first concept was utilized by Eudemus, who regarded an angle as a deviation from a straight line; the second by Carpus of See also:

• ANTIOCH

Antioch, who regarded it as the See also:

• INTERVAL

interval or space between the intersecting lines; Euclid adopted the third concept, although his See also:

• DEFINITIONS

definitions of right, acute, and obtuse angles are certainly quantitative . A discussiocl of these concepts and the various definitions of angles in Euclidean geometry is to be found in W . B . See also:

• FRANKLAND, SIR EDWARD (1825-1899)

Frankland, The First Book of Euclid's Elements (ipo5) . Following Euclid, a right angle is formed by a straight line See also:

• STANDING

standing upon another straight line so as to make the adjacent angles equal; any angle less than a right angle is termed an acute angle, and any angle greater than a right angle an obtuse angle . The difference between an acute angle and a right angle is termed the See also:

• COMPLEMENT (Lat. complementum, from complere, to fill up)

complement of the angle, and between an angle and two right angles the supplement of the angle . The generalized view of angles and their measurement is treated in the See also:

• ARTICLE (from Lat. articulus, a joint)

article See also:

• TRIGONOMETRY (from Gr. rpiywvov, a triangle, /ATpov, measure)

TRIGONOMETRY . A solid angle is definable as the space contained by three or more planes intersecting in a See also:

• COMMON

common point; it is familiarly represented by a corner . The angle between two planes is termed dihedral, between three trihedral, between any number more than three polyhedral .

A spherical angle is a particular dihedral angle; it is the angle between two intersecting arcs on a See also:

• SPHERE (Gr. vclsa?pa, a ball or globe)

sphere, and is measured by the angle between the planes containing the arcs and the centre of the sphere . The angle between a line and a See also:

• CURVE (Lat. curvus, bent)

curve ( mixed angle) or between two curves (See also:

• CURVILINEAR

curvilinear angle) is measured by the angle between the line and the tangent at the point of intersection, or between the tangents to both curves at their common point . Various names (now rarely, if ever, used) have been given to particular cases:—amphicyrtic (Gr . 401, on both sides, Kvpros, See also:

• CONVEX

convex) or cissoidal (Gr . Keavos, See also:

• IVY (A.S. ifig, Ger. Epheu, perhaps connected with apium, anent)

ivy), biconvex; xystroidal or sistroidal (Gr. vv-'rpis, a See also:

• TOOL (0. Eng. tdl, generally referred to a root seen in the Goth. taujan, to make, or in the English word " taw," to work or dress leather)

tool for scraping), concavo-convex; amphicoelic (Gr . KOiXn, a hollow) or angu.lus lunularis, biconcave .