▪ I. concave, n.
(ˈkɒnkeɪv)
[a. OF. concave, f. concave adj.: cf. L. concava hollows. Appears to be earlier in Eng. than the adj.; but in later uses it is only an absolute use of the adj. Not unfrequently stressed conˈcave by poets.]
† 1. A hollow; a cavity. Obs.
| 1541 R. Copland Guydon's Quest. Chirurg, In the fyrste concaue is receyued the roundnes of Cohas aforesayd. c 1590 Marlowe Faust. (ed. Rtldg.) 95/2 Bred in the concave of some monstrous rock. 1602 Marston Ant. & Mel. iii. Wks. 1856 I. 35, I will warble to the delicious concave of my mistresse eare. 1747 Hooson Miner's Dict. W j, [Miners] in the Bowels and Concaves of the Earth. 1814 Cary Dante's Inf. ix. 16 Doth ever any Into this rueful concave's extreme depth Descend? |
† b. A cylindrical or spherical cavity; the bore of a gun, etc. Obs.
| 1597 Daniel Civ. Wares vi. xlix, They minerals combustible do find, Which, in stopped concaves placed cunniningly, They fire. 1627 Capt. Smith Seaman's Gram. xiv. 65 The Sillinder or Concaue..is the bore of the Peece. 1703 Moxon Mech. Exerc. 54 Then put into the two Concaves a round Bullet, that will just fill them both. |
c. A concave part of a machine, as of a thresher.
| 1874 Knight Dict. Mech. I. 604/2 The example shows a concave in which each slat rests upon a spring, and the grain escapes through the intervening spaces. |
2. A concave surface, or the structure presenting it; a vault, arch, hemisphere, etc., as viewed from the centre; often applied to the vault of the sky.
| 1552 Lyndesay Monarche 6247 All dede thyngis corporall, Onder the Concaue of the Heuin Impyre. 16.. Evelyn Mem. (1857) I. 127 The inside, or concave, is covered with most exquisite Mosaic. 1651 H. More in Enthus. Triumph. (1656) 191 All to the very concave [i.e. ‘sphere’] of the Moon. 1660 Barrow Euclid iii. viii, Those lines that fall on the concave of the circumference. 1813 Shelley Q. Mab 232 The chariot's way Lay through the midst of an immense concave. 1870 Proctor Other Worlds ii. 45 Every single star that shines upon us from the celestial concave. |
b. spec. The vault of heaven.
| 1635 Swan Spec. M. iv. §2 (1643) 70 On high within the concave, as are the..starres. 1770 E. Nicklin in Monthly Rev. 406 Loud clamour rising rends the vast concave. 1808 J. Barlow Columb. x. 504 Let..all the concave flame in one clear sun. 1864 Skeat tr. Uhland's Poems 21 Around me spreads the blue concave. |
† 3. A concave lens, speculum, etc. Obs.
| 1621 Burton Anat. Mel. ii. ii. iv. (1651) 284 To represent solid bodies, by Cylinders and Concaves, to walk in the air. 1685 Boyle Effects of Motion viii. 96 An expert Artificer, that made metalline Concaves. 1797 Brougham in Phil. Trans. 377 Glass concaves were freer from these hairs. |
4. A card prepared for cheating by being cut slightly concave on two edges: cf. quot. 1873.
| 1825 C. M. Westmacott English Spy I. 271 Every leg and Greek who play the concave suit. 1873 Slang Dict., Concaves and convexes, a pack of cards contrived for cheating, by cutting all the cards from the two to the seven concave, and all from the eight to the king convex. Then by cutting the pack breadthwise a convex card is cut, and by cutting it lengthwise a concave is secured. |
▪ II. concave, a.
(ˈkɒnkeɪv)
[a. F. concave (14th c. Oresme), ad. L. concavus, f. con- + cavus hollow: see cave.]
† 1. Having an internal hole or cavity; hollow.
| 1571 Digges Pantom. i. xxx, The concaue Cylinders. 1600 Shakes. A.Y.L. iii. iv. 26, I doe thinke him as concaue as a couered goblet, or a Worme-eaten nut. 1659 Willsford Archit. 24 A concave vessel containing a cubical yard. |
2. Having the outline or surface curved like the interior of a circle or sphere; having a curvature that presents a hollow to the point of observation; the reverse of convex; incurvated.
| 1594 Blundevil Exerc. iii. i. (ed. 7) 271 The upper part of such a Vault is sayd to be Convex and the inward part Concave. 1656 Hobbes' Elem. Philos. (1839) 279 If two strait converging lines..fall upon the concave circumference of a circle. 1753 Hogarth Anal. Beauty xii. 101 It will..appear concave like a bason. 1816 J. Smith Panorama Sc. & Art I. 39 The screw cut by a tap is called an inside or concave screw. 1822 J. Imison Sc. & Art I. 72 The grinding surface of the under [mill-] stone is a little convex..and that of the upper stone a little concave. 1880 Gunther Fishes 51 The vertebra..with a concave anterior and posterior surface. |
b. esp. used of glasses, lenses, mirrors, etc., made in this form for optical purposes.
| 1571 Digges Pantom. i. vi, Playne, conuex, or concaue glasses. 1662 Hobbes 7 Philos. Probl. Wks. 1845 VII. 30 How comes the light of the sun to burn almost any combustible matter by refraction through a convex glass, and by reflection from a concave? 1833 Brewster Nat. Magic iv. 61 The concave mirror is the staple instrument of the magician's cabinet. 1869 Tyndall Notes on Light §156 Double concave, with both surfaces concave. Plano-concave, with one surface plane and the other concave. 1878 T. Bryant Pract. Surg. I. 301 Until we have found the weakest concave lens with which distant letters can be most plainly seen. |
3. Comb., as concave-planned adj.
| 1879 Sir G. Scott Lect. Archit. I. 84 A rudimental relic of the concave-planned abacus. |
Add: [2.] c. Math. Of a plane figure, a solid, a set (of points), etc.: not convex (*convex a. 1 c). Of a function: such that its negative is convex.
| 1942 G. & R. C. James Math. Dict. 41/1 An arc of a curve is concave toward a point (or line) if every segment of the arc cut off by a secant lies on the opposite side of the secant from the point (or line). 1974 Adby & Dempster Introd. Optimization Methods i. 10 The function f is concave if -f is convex. 1986 Oxf. Econ. Papers July 344 The production functions are concave and homogeneous of degree one. |
▪ III. concave, v.
(ˈkɒnkeɪv)
[f. concave a.: cf. L. concavāre in same sense.]
trans. To make concave; † to vault, arch over or round.
| 1652 Benlowes Theoph. x. lxvi, Pride concav'd Satans hall. 1795 A. Seward Lett. 16 Nov. IV. 118 That western bay [Cardigan] concaved by vast mountains. 1818 J. Brown Psyche 15 A smile (tho' none for sundry years Concav'd her cheek) for once appears. |