Also 4–5 aungel, 4–7 angel, 5–6 -ule, -yll. [a. Fr. angle:—L. angul-um (nom. -us) corner, a dim. form, of which the prim. *angus is not in L.; cf. Gr. ἄγκος a bend, a hollow angle, and L. ang-ĕre to compress in a bend or fold, to strangle; Aryan root ank- to bend.]
1. The indefinite space included between two meeting lines or planes, the shape of which depends upon their mutual inclination; hence in Geom. the degree of inclination of two lines to each other, or of one line to a horizontal or vertical base-line.
The angle is measured by the portion of the circumference of a circle described from the intersection of the lines as center, which is intercepted between the two lines. The inclination of two lines in the same plane is a plane angle, which may be rectilineal or curvilineal, as it is formed by straight or curved lines; the inclination of two lines on the surface of a sphere is a spherical angle; the space included by more than two plane angles meeting at a point is a solid angle.
c. 1386. Chaucer, Sqrs. T., 222. By compositions of angles and of slie reflections.
1570. Billingsley, Euclid, I. def. 9. There are of angles thre kindes, a right angle, an acute angle, and an obtuse angle.
1571. Digges, Geom. Pract., I. B j. A Playne Angle is the inclination of two lines lying in one playne Superficies, concurring or meeting in a poynt.
1594. Blundevil, Exerc., III. I. (ed. 7), 272. Sphericall, that is to say, round Angels, which consist of two circular lines drawn upon a Sphericall superficies.
1646. Sir T. Browne, Pseud. Ep., IV. vi. 193. With man … in natation they [legs and arms] intersect and make all sorts of Angles.
1690. Locke, Hum. Underst., I. iv. (1695), 37. The three Angles of a Triangle are equal to two Right ones.
1878. Huxley, Physiogr., 60. The slope or inclination which one face [of a crystal] has to another; in other words the angle made by two neighbouring faces.
¶ Measurement by angle is used in many departments of physics, mechanics, etc., to estimate the position of bodies, the direction of forces, etc. Hence such phr. as angle of application, depression, deviation, elevation, incidence, inclination, position, reflection, refraction, repose, rest, traction, vision; and the vbl. phr. To take the angle.
1638. Wilkins, Discov. New World, I. (1684), 44. Where the Angel of Reflexion is Equal to the Angel of Incidence.
1790. Ray, in Phil. Trans., LXXX. 154. By the means of this piece of mechanism in the eye-end of the telescope … small angles of elevation or depression may be determined with great accuracy.
1805. Flinders, ibid., XCV. 190. Endeavoured to take the angles on shore with a … theodolite.
1812. Woodhouse, Astron., viii. 58. When through a Star great circles are drawn respectively from the poles of the equator and ecliptic, they form at the Star an angle called the Angle of Position.
1831. Brewster, Optics, iv. § 35. 29. The angular change of direction or the angle of deviation as it is called. Ibid. (1831), Nat. Magic, iv. 87. A prism with a small refracting angle.
1849. Weale, Dict. Terms, 17. Angle of application, the angle which the line of direction of a power gives the lever it acts upon. Angle of inclination, the angle an inclined plane makes with the horizon. Angle of traction, the angle which the direction of a power makes with the inclined plane.
1869. Phillips, Vesuv., vii. 180. The usual angle of rest in loose materials.
b. At angles with: so placed as to form an angle with, in opposition to parallel (and, unless qualified by right, to perpendicular) to. On the angle: obliquely.
1753. Hogarth, Anal. Beauty, iii. 19. The painter, if he is left to his choice, takes it on the angle rather than in front.
1779. J. Moore, Soc. in France, II. 169. Others which go off at right angles from that.
1862. Lytton, Str. Story, II. 11. Behind the portico of a detached house at angles with the street.
2. The meeting-point of two lines not in the same direction. Also fig.
1605. Bacon, Adv. Learn., II. v. § 2 (1873), 105. Several lines that meet in one angle, and so touch but in a point.
1677. Hale, Prim. Orig. Man., 362. He is nexus utriusque mundi, the common Angle wherein the highest and noblest of Material and Corporeal Nature is joyned to the Spiritual.
1870. Flower, Osteol. Mamm., 122. The angle of the jaw is the point at which the vertical hind edge of the ramus, descending from the condyle, meets the horizontal inferior border.
3. A corner viewed internally or as a receding space; a retreating corner, a corner into which one may withdraw, a coign. Also fig.
c. 1384. Chaucer, H. of Fame, 1959. Alle the houses Angles [v.r. aungelys] Ys ful of rovnynges and of Iangles.
1430. Lydg., Chron. Troy, I. vi. Not openly as ypocrytes praye In dyuers angels ioyning on the waye.
1509. Fisher, Wks. (1876), 171. We be thraste down into a very streyght angyll.
1607. Tourneur, Rev. Trag., III. i. Some darken’d blushless angle.
1655. Digges, Compl. Ambass., 321. For truth will seek no angles.
1826. Scott, Woodst., 187. In each angle of the ascent was placed … the figure of a Norman foot-soldier.
4. A spot lying out of the direct way, an out-lying spot or ‘corner,’ without reference to shape; a nook. Also fig. arch.
1447. Bokenham, Lyvys of Seyntys, 2. For this the[y] soun Throwyn it [this book] in the angle of oblyvyoun.
1480. Caxton, Descr. Brit., 3. Anglia hath that name as it were an angle and a corner of the world.
1563. Grindal, Rem. (1843), 256. That little angle where I was born, called Cowpland.
1610. Shaks., Temp., I. ii. 223. Whom I left … In an odde Angle of the Isle.
1641. Milton, Ch. Govt., II. iii. (1851), 171. To search the tenderest angles of the heart.
1656. S. Holland, in Shaks. Cent. Praise, 302. The fire of Emulation burnt fiercely in every angle of this Paradise.
5. A corner viewed externally or as a projection, a projecting corner (of a building, etc.). Also fig.
1532. More, Confut. Barnes, VIII. Wks. 1557, 783/1. That corner stone that is layed in the hed of the angle.
1589. Puttenham, Eng. Poesie (Arb.), 111. The Roundell hath no bonch nor angle, which may his course stay or entangle.
1624. Wotton, Archit. (1672), 20. That the Angles be firmly bound, which are the Nerves of the whole Edifice.
1756. Burke, Subl. & B., Wks. I. 184. There is nothing more prejudicial to the grandeur of buildings than to abound in angles.
1842. E. Wilson, Anat. Vade M., 18. The superior angle is received into the interval formed by the union of the posterior and superior angles of the parietal bones.
6. An angular or sharp projection; hence an angular fragment. Also fig.
1684. Dryden, Ovid’s Met., XIII. (1717), 476 (R.).
| Though but an Angle reach’d him of the Stone, | |
| The mighty Fragment was enough alone. |
1844. Kinglake, Eöthen, ii. (1878), 21. The angle of the oriental stirrup is a very poor substitute for spurs.
1850. Tennyson, In Mem., lxxxix. 40. We rub each other’s angles down.
1853. Kane, Grinnell Exp., xxviii. (1856), 229. We trod on the fractured angles of upturned ice.
7. Astrol. A name given to the four astrological ‘houses,’ at the cardinal points of the compass.
c. 1386. Chaucer, Sqrs. T., 263. Phebus hath laft the Angle [v.r. angel] meridional.
1594. Blundevil, Exerc., IV. xxxvi. (ed. 7), 493. Or which 12 houses the foure principall are foure points of the Zodiaque, whereof two do fall upon the Horizon, and the other two upon the Meridian, and are called principall points, Poles, or Angles.
1727–51. Chambers, Cycl., s.v., The horoscope of the first house is termed the angle of the East.
1819. J. Wilson, Dict. Astrol., 6. Ptolemy gives the preference to the south angle.
8. Comb., chiefly attrib.: a. of shape (= ANGULAR), as angle-leg, -piece, -taper; b. of position (at or in an angle), as angle-bracket, -column, -niche, -rafter, -rib, -stone, -turret.
Also angle-bar, the upright bar at the angle of a polygonal window, also (= angle-iron); angle-bead, a vertical bead, usually of wood, fixed to an exterior angle, flush with the surface of the plaster; angle-brace, a piece of timber fixed to the adjacent sides of a quadrangular framing; angle-iron, an L-shaped piece of iron, used to secure or strengthen all kinds of framework; angle-meter, an instrument for measuring angles, esp. for ascertaining the dip of geological strata, a CLINOMETER; angle-staff (= angle-bead); angle-tie (= angle-brace). Also ANGLE-WISE, q.v.
1649. Lovelace, Lucaste. Like flyes Caught by their angle-legs.
1793. Smeaton, Edystone L., § 295. Sixteen angle pieces of iron … in the nature of knee timbers of a ship.
1649. Blith, Eng. Improver Impr. (1653), 131. The other two run towards an Angle-taper, declining from twelve Inches in the But or bottom, to six Inches at the mouth.
1880. J. Middleton, in Academy, 21 Aug., 139/3. The angle columns have the least weight to bear, owing to the pyramidical form of the pediment.
1879. G. Scott, Archit., II. 185. The angle ribs of the outer half meet the transverse ribs of the inner half of the vault.
1867. A. Barry, Sir C. Barry, iv. 110. The elevated angle-turrets.
1842. Gwilt, Encycl., 1181. Angle beads of wood round the intradosses of circular arches are difficult to bend without cutting or steaming them.
1862. Smiles, Engineers, III. 422. Cells formed of boiler-plates riveted together with angle-iron.
1869. Sir E. Reed, Ship-build., ii. 25. The vertical flanges of the angle-irons were bolted through all.
1881. Greener, Gun, 415. A wooden frame … strengthened by an angle-iron facing.
1782. in Phil. Trans., LXXII. 368. from the place into which this holdfast was driven to the outer end of the angle-tie.
