See also:bend: see
See also:ANGLING), in
See also:geometry, the inclination of one
See also:line or
See also:plane to another . Euclid (Elements,
See also:book I) defines a plane
See also:angle as the inclination to each other, in a plane, of two lines which meet each other, and do not lie straight with respect to each other (see GEOMETRY, EUCLIDEAN) . According to
See also: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, who regarded it as the
See also:interval or space between the intersecting lines; Euclid adopted the third concept, although his
See also: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, The First Book of Euclid's Elements (ipo5) . Following Euclid, a right angle is formed by a straight line
See also: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 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 article TRIGONOMETRY . A solid angle is definable as the space contained by three or more planes intersecting in a
See also: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 asphere, 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 ( mixed angle) or between two curves (
See also: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) or cissoidal (Gr . Keavos, ivy), biconvex; xystroidal or sistroidal (Gr. vv-'rpis, a
See also:tool for scraping), concavo-convex; amphicoelic (Gr . KOiXn, a hollow) or angu.lus lunularis, biconcave .
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