▪ I. inverse, a. and n.
(ɪnˈvɜːs, ˈɪnvɜːs)
[ad. L. invers-us inverted, pa. pple. of invertĕre, f. in- (in-2) + vertĕre to turn: orig. sense app., To turn outside in. Cf. F. inverse.]
A. adj.
1. Turned upside down; inverted.
| a 1658 Cleveland News fr. Newcastle 86 A Coal-pit is a Mine of every thing..An inverse Burse, an Exchange under Ground. 1661 Lovell Hist. Anim. & Min. 345 Also things seeme inverse, by reason of the mutation of the site of the crystalline humour. 1703 Moxon Mech. Exerc. 256 Make from these Piers inverse Arches. 1709 Berkeley Th. Vision §100 Whether objects were erect or inverse. a 1845 Hood Two Swans ii, A tower builded on a lake, Mock'd by its inverse shadow. |
2. Inverted in position, order, or relations; that proceeds in the opposite or reverse direction or order; that begins where something else ends, and ends where the other begins.
| 1831 Brewster Newton (1855) II. xxii. 298 The first who gave the analysis of the inverse truth, without supposing the direct one to be already known. 1848 Clough Amours de Voy. iv. 32 What shall I do?..Go on..Seeking, an inverse Saul, a kingdom to find only asses. 1868 Lockyer Guillemin's Heavens (ed. 3) 65 The same appearances are observed, but in an inverse order. 1869 J. Martineau Ess. II. 19 It must follow an inverse order. |
3. Math. a. Arith. and Alg. Of such a nature in respect to another operation, relation, etc. that the starting-point or antecedent of the one is the result or conclusion of the other, and vice versa; opposite in nature or effect. Opp. to direct; e.g. Inverse Method of Fluxions: see quot. 1807.
inverse ratio: (a) a ratio related to another ratio in the way defined above, i.e. one in which the terms are reversed; (b) the ratio of two quantities which vary inversely, i.e. one of which increases in the exact proportion in which the other decreases, and vice versa; so inverse proportion. (In popular language often loosely extended to the case of two things one of which decreases, or is less, as the other increases, or is greater.) inverse square: often used for the relation of two quantities one of which varies inversely as the square of the other. Rule of Three Inverse: that case of the Rule of Three in which the antecedent of each of the ratios corresponds to the consequent of the other.
| 1660 Barrow Euclid v. Def. xiii, Inverse ratio is when the consequent is taken as the antecedent and so compared to the antecedent as the consequent. 1790 Burke Fr. Rev. 139 The operation of opinion being in the inverse ratio to the number of those who abuse power. 1793 Beddoes Math. Evid. 19 A balance of which one arm should be ten inches, and the other one inch long, and each arm should be loaded in an inverse proportion to its length. 1806 Hutton Course Math. I. 44 Rule of Three Inverse, is when more requires less, or less requires more. 1807 Ibid. II. 279 The direct method [of fluxions] consists in finding the fluxion of any proposed fluent..; and the inverse method..consists in finding the fluent of any proposed fluxion. 1816 Playfair Nat. Phil. II. 295 The attraction of a spheroid, in the plane of its equator, does not decrease exactly in the inverse ratio of the square of the distance. 1816 tr. Lacroix's Diff. & Int. Calculus 547 By substituting for x the inverse function of a (x), by which is understood that function which written instead of x in the expression of a (x) produces x as the final result. Ibid., ex and log x are inverse functions of each other, since log (ex) = x. 1834 M. Somerville Connex. Phys. Sc. viii. (1849) 70 The inverse problem had now to be solved. 1865 F. Oakeley Historical Notes 51 The ratio of its extent appeared to be inverse with the degree in which it was sought. 1882 Minchin Unipl. Kinemat. 161 Matter attracting according to the law of the inverse square of distance. |
b. Geom. inverse point, inverse line, inverse curve, etc., one related to another point, line, curve, etc. in the way of geometrical inversion (see inversion 3 b).
| 1873 B. Williamson Diff. Calc. (ed. 2) xii. §181 By aid of this property the tangent at any point on a curve can be drawn, whenever that at the corresponding point of the inverse curve is known. Ibid. xvii. §227 If two curves be inverse to each other with respect to any origin. 1881 Casey Sequel to Euclid 95 If X be a circle, O its centre, P and Q two points on any radius such that the rectangle OP. OQ = square of the radius, then P and Q are called inverse points with respect to the circle. |
4. Cryst. Opposed to direct: see quot.
| 1878 Gurney Crystallogr. 65 The second class of rhombohedrons may be called inverse..The unequal index is algebraically less than the other two. 1895 Story-Maskelyne Crystallogr. 141 and 312. |
5. inverse spelling, an unetymological spelling based on the spelling of another word containing an element that is no longer pronounced, e.g. limb from OE. lim after lamb (from OE. lamb).
| 1933 L. Bloomfield Lang. xvii. 294 So-called inverse spellings tell the same story... When we find the word deleite..spelled delight, then we may be sure that the [χ] was no longer spoken in words like light. 1956 N. E. Eliason Tarheel Talk v. 194 Occasionally inverse spellings occur, for example forks for folks,..and polk for pork. |
6. Cryst. Designating a spinel structure, B[AB]O4, in which half the B (trivalent) cations are in tetrahedral holes and the A (bivalent) cations together with the other half of the B cations are in octahedral holes in the array of oxide ions (in contrast to the normal structure A[B2]O4).
| [1947 Verwey & Heilmann in Jrnl. Chem. Physics XV. 175/2 For the sake of convenience, the first arrangement will be indicated as characteristic for ‘normal spinels’, the Barth and Posnjak arrangement as that of ‘inversed spinels’.] 1957 Jrnl. Physics & Chem. Solids III. 313 These energies..may be sufficient to determine whether a given spinel shall be normal or inverse. 1970 R. G. Burns Mineral. Applications Crystal Field Theory vi. 112 Ni2+ and Cu2+ have a strong tendency to form inverse spinels. Ions such as Fe3+ and Mn2+, which have zero octahedral site preference energies, form both normal and inverse spinels. |
B. n.
1. An inverted state or condition; that which is in order or direction the direct opposite of something else; thus CBA is the inverse of ABC.
| 1681 tr. Willis' Rem. Med. Wks. Vocab., Inverse, a turning inside out, or outside in, upside down, quite contrary. 1794 G. Adams Nat. & Exp. Philos. IV. lii. 456 Rain, which is the inverse of evaporation. 1823 H. J. Brooke Introd. Crystallogr. 74 Proceeding in an order the inverse of that by which the modified crystal has been formed. 1891 Gladstone Sp. 2 Oct., The foreign policy of the present Administration has been well-nigh the inverse and the reverse to that of the Administration of Lord Beaconsfield. |
2. The result of inversion: a. Math. A ratio, proportion, or process in which the antecedents and consequents are interchanged. Also, short for inverse function.
| 1695 W. Alingham Geom. Epit. 101 By the other two, the inverses of both are proved, for as a: A::b:B, also as b:a::B:A. 1839 Penny Cycl. XIII. 5 From all the inverses of a function ϕχ..we separate that one, αχ, which gives both ϕαχ = χ and αϕχ = χ, and call it the convertible inverse. |
b. Geom. Short for inverse curve, point, etc.
| 1873 B. Williamson Diff. Calc. (ed. 2) xii. §180 If on any radius vector OP, drawn from a fixed origin O, a point P{nfacu} be taken, such that the rectangle OP, OP{nfacu} is constant, the point P{nfacu} is called the inverse of the point P; and if P describe any curve, P{nfacu} describes another curve called the inverse of the former. 1887 R. A. Roberts Integ. Calc. i. 315 The central inverse of a conic. |
c. Logic. The proposition obtained by inversion.
| 1896 [see inversion 2 e]. |
3. Rouge et Noir. The section at the end of the table in which are placed bets wagering that the colour of the card that wins the coup will not be the same as that first dealt for a colour.
| 1850 Bohn's Hand-bk. Games 343 If the player..be determined to try his luck on the inverse, he must place his money on a yellow circle, or rather a collection of circles, situated at the extremity of the table. Ibid., The punters place on the Rouge, the Noir, the Couleur, or the Inverse, the sum they wish to risk. 1909 [see couleur 2]. 1950 Hoyle's Games Modernized (ed. 20) 291 The tailleur never mentions the words ‘Black’ or ‘Inverse’, but always says that Red wins or Red loses, and that the colour wins or the colour loses. |
4. Math. An element which, when combined with a given element by a given operation, produces the identity element for that operation.
E.g. the inverse of any number with respect to multiplication is the reciprocal of that number, and with respect to addition the negative of it.
| 1900 Ann. Math. II. 48 For every element Tκ exists an element (denote it by Tκ-1) such that TκTκ-1 = Tκ-1Tκ = 1. Tκ-1 is called the inverse of Tκ. 1905 Trans. Amer. Math. Soc. VI. 187 The identity, z, of this group, is called the zero-element of the field, and is denoted by 0; while the inverse of an element a is here called the negative of a, and is denoted by -a. 1951 N. Jacobson Lect. Abstr. Algebra I. i. 22 If the operation in 𝔊 is denoted as +, we denote the identity as 0. The inverse of a if it exists is written as -a. 1953 Birkhoff & MacLane Survey Mod. Algebra (ed. 2) vi. 122 Hence ϕψ = I and ψ is a right-inverse of ϕ. 1965 Patterson & Rutherford Elem. Abstr. Algebra i. 19 Let {logicand} be the closed binary operation in R defined by x {logicand} y = x + y - 2x2y2... Show..that every..non⁓zero element x of R such that x > -½ has two inverses but that if x < -½, then x has no inverse. |
▪ II. inverse, v. Now rare.
(ɪnˈvɜːs)
[f. prec. or f. invers-, ppl. stem of invertĕre: cf. reverse vb.]
trans. To turn upside down; to invert; to reverse in order or direction.
| 1611 Florio, Inuersare, to inuert, to inuerse. 1663 Power Exp. Philos. ii. 115 We therefore fill'd our Glass-Tubes..half with Water, and the rest with Ayr, and afterwards invers'd it into a pail of water. 1694 Loyal Satirist in Somers Tracts VII. 68 You would think the church as well as religion, were inversed, and the anticks which were used to be without were removed into the pulpit. a 1701 Sedley Happy Pair Wks. 1766 I. 17 From hence the baffled world has been inverst, Princes involv'd in war, and people curst. 1849 C. Brontë Shirley vii, Inversing the natural order of insect existence. |