Online Encyclopedia

ANGLE (from the Lat. angulus, a corne...

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Originally appearing in Volume V02, Page 15 of the 1911 Encyclopedia Britannica.
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ANGLE (from the
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Lat. angulus, a corner, a diminutive, of which the
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primitive form, angus, does not occur in Latin; cognate are the Lat. angere, to compress into a
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bend or to strangle, and the Gr. ayKOS, a bend; both connected with the
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Aryan root ank-, to
 
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bend: see
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ANGLING), in
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geometry, the inclination of one
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line or
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plane to another . Euclid (Elements,
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book I) defines a plane 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 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
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Antioch, who regarded it as the
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interval or space between the intersecting lines; Euclid adopted the third concept, although his
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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 . Frankland, The First Book of Euclid's Elements (ipo5) . Following Euclid, a right angle is formed by a straight line
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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
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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

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 curve ( mixed angle) or between two curves (
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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,
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convex) or cissoidal (Gr . Keavos, ivy), biconvex; xystroidal or sistroidal (Gr. vv-'rpis, a tool for scraping), concavo-convex; amphicoelic (Gr . KOiXn, a hollow) or angu.lus lunularis, biconcave .

End of Article: 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
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