| 释义 |
▪ I. residue, n.|ˈrɛzɪdjuː|
Also 4–7 resydue (6 reasi-), 5–7 -dew(e, 6 -du; 5–6 resedew(e (6 resi-); 6 resideu.
[ad. F. résidu (14th c.), ad. L. residuum residuum.]
1. The remainder, rest; that which is left.
a. Of things.
Method of Residues: see Mill Logic (1843) iii. viii. §5.
1362Langl. P. Pl. A. v. 240 With þe Residue and þe remenaunt [of my living]..I schal seche seynt Treuþe. 1426Lydg. De Guil. Pilg. 17024 To Acomplysshe..the Resydue in effect, that Folweth in the same vers. 1484Caxton Fables of Poge viii, After this..the sellar demaunded of the byar the resydue. a1533Ld. Berners Huon lxvii. 231 In grete payne & mysery we must vse the resydew of our lyues. 1616R. C. Times' Whistle v. 1716 If with moderate fare they were contented They might..save the residue of all their wealth. 1656Sanderson Serm. (1689) 537 In the residue of the fifth verse. 1718Free-thinker No. 7. 47 Nothing farther could be done unless the Residue was forthcoming. 1780S. J. Pratt Emma Corbett (ed. 4) II. 41 If you looked him in the face, or, more properly,..in the residue of his face. 1826Faraday Exp. Res. (1859) 218 The residue supported combustion a little better than common air. 1878Huxley Physiogr. 199 Others assume that it is..the residue of the heat which the earth originally possessed.
b. Of persons.
1382Wyclif Zeph. ii. 9 The residues of my folc shuln welde hem. 1475Rolls of Parlt. VI. 139/1 The said Henry Bodrugan..the residue of the same Britons yet kepeth in prisone. 1526Pilgr. Perf. (W. de W. 1531) 266 b, On this maner the poore vnlerned fysshers Peter, John, Andrewe & James were taught, & the resydue of y⊇ holy couent. 1575Turberv. Trag. Tales (1837) 40 Both..promist not to faile Themselves to come, and bid the residue. 1610Holland Camden's Brit. (1637) 113 The residue of Britans remaining alive, withdrew themselves. 1719De Foe Crusoe ii. (Globe) 367 The Residue of the conquer'd People fled to their Canoes. 1836W. Irving Astoria III. 7 A number of men mounted guard,..while the residue..employed themselves below in dragging up the barges and canoes.
†c. The leavings of a destructive agent. Obs.
1560Bible (Genev.) Joel i. 4 The residue of the canker⁓worm hathe the caterpiller eaten.
†d. Phr. in, or for, the residue, for the rest, as to the remainder. Obs.
1548Bodrugan Epit. 249 In the residue it was not my mynde to trifle with the fine flowers of Rethorike. 1560J. Daus tr. Sleidane's Comm. 111 b, For the residue they committe all that ever they have unto the Emperour.
e. Sociol. A term used by Vilfredo Pareto (1848–1923) for fundamental impulses which motivate human conduct, and which are not the product of rational deliberation.
1933Harper's Mag. CLXVII. 573 In each of these two groups of phenomena we have found a constant element, the sentiment out of which both the actions and the explanations rise. The expression of such a sentiment is what Pareto calls a ‘Residue’. 1935Bongiorno & Livingston tr. Pareto's Mind & Society II. vi. 508 It might perhaps be advisable to give word-names to the things we have been calling a, b, and c... Suppose we call the things a, residues, the things b, derivations, and the things c, derivatives. Ibid. 509 Residues correspond to certain instincts in human beings, and for that reason they are usually wanting in definiteness, in exact delimitation. 1935L. J. Henderson Pareto's Gen. Sociol. v. 23 Theology and metaphysics and parts of law consist, in great measure, of systematic and extensive derivations from certain very important residues like those involving the words justice, duty, sanctity, and absolute. 1939F. Creedy Human Nature writ Large xix. 400 Public documents which have won high praise and wide acceptance..owe their acceptability to the fact that their Residues or fundamental assumptions coincide with those of the crowd. 1958W. Stark Sociol. of Knowl. viii. 320 These residues or drives determine all the comings and goings on the stage of life. The ‘derivations’, or thoughts and beliefs which, objectively speaking, derive from the residues, but which subjectively appear to the people who harbour them as ‘their ideas’, ‘their convictions’, ‘their philosophies’. 1966S. E. Finer V. Pareto: Sociol. Writings 38 Thus, if you strip from the theory its variable part you are left with a residuum. This is the constant element and Pareto therefore calls it a residue.
2. Law. That which remains of an estate after all charges, debts, and bequests have been paid.
1411E.E. Wills (1882) 20 Þ⊇ residue of alle my godes. 1454Ibid. 134 Yf my seide goodes, Residues, and dettis may not suffice. 1529Cromwell Will in Merriman Life & Lett. (1902) I. 63 The residue of all my goodes, catalles, and debttes not bequethed..I will shalbe sold. 1590Swinburne Testaments 115 He to whom all or the residue is bequeathed, is thereby vnderstood to be made executor. 1766Blackstone Comm. II. 492 Then the residue of the goods shall go to the executor to perform the will of the deceased. 1818Cruise Digest (ed. 2) V. 499 It was still the same residue remaining in the wife, which she had not disposed of before. 1865Dickens Mut. Fr. iii. vii, He, John Harmon,..gives the whole rest and residue of his property to the Crown. 1967E. Rudinger Wills & Probate 9 After disposing of specified items and sums of money, you give the remainder—the residue, lawyers call it—to some named person... You could, of course, provide that your residue should be divided..among a number of people.
attrib.1838W. Bell Dict. Law Scot. 585 Legacy and Residue Duties.
3.
†a. Math. = remainder 4 a. Obs.
c1430Art Nombryng 17 Thow shalt fynde the same figures that thow haddest before; And so that nought be the residue. And yf thow have any residue [etc.]. 1570Billingsley Euclid v. prop. 19. 146 If the whole be to the whole, as the part taken away is to the part taken away: then shall the residue be vnto the residue, as the whole is to the whole. 1636Mellis Recorde's Gr. Artes 154 From the last subtract the first, and the residue diuide by a number lesse by 1, then the number of the places.
b. Number Theory. A remainder left when a given number is divided into some integer; also, a number congruent to a given number modulo a third number; quadratic residue, cubic, etc., residue, a remainder left when a given number is divided into the square, cube, etc., of some integer; residue class, the class of integers congruent to one another modulo a given number (e.g. 2, 5, 8, 11, etc., are members of a residue class modulo 3).
1860Rep. Brit. Assoc. Adv. Sci. 1859 i. 231 The set of numbers 0, 1, 2{ddd}P - 1 (or any set of P numbers respectively congruous for the modulus P to those numbers) is termed a complete system of residues for the modulus P. 1899Q. Jrnl. Math. XXX. 363 The same representation of the coefficients also determines the residue when the coefficient is not a multiple of the modulus. 1939Uspensky & Heaslet Elem. Number Theory vi. 134 Of two numbers congruent for the modulus m, each is called a ‘residue’ of the other modulus m. Ibid. x. 270 A number a is said to be a quadratic residue of another number m if the congruence x2 = a (mod m) can be satisfied by some integer x. 1948O. Ore Number Theory & its Hist. ix. 214 Since these are the numbers that correspond to the same remainder r when divided by m, we say that they form a residue class (mod m). There are m residue classes (mod m). 1963W. W. R. Ball Math. Recreations & Ess. (ed. 12) ii. 60 There is an arithmetic of residues, closely analogous to the arithmetic of ordinary numbers. 1966Ogilvy & Anderson Excursions in Number Theory iv. 43 If we identify every integer, positive, negative, or zero, with its remainder modulo m, we thus have all the integers partitioned into congruence classes, or residue classes, modulo m. 1977Sci. Amer. July 127/2 Gauss used complex numbers of the form a + bi..to formulate and prove a version of the law of quadratic reciprocity for biquadratic residues. The number k is said to be a biquadratic residue of another number m if k is congruent modulo m to the fourth power of an integer. Thus the biquadratic residues of 10 are 0, 1, 5 and 6.
c. Theory of Functions. (See quots.)
1893A. R. Forsyth Theory of Functions x. 223 The sum of the residues of a doubly-periodic function relative to a fundamental parallelogram of periods is zero. 1957T. M. Apostol Math. Analysis xvi. 524 In many cases it is relatively easy to evaluate the residue at a point without the use of integration. 1959G. & R. C. James Math. Dict. 334/1 If f(z) is an analytic function of the complex variable z in the ‘deleted’ neighbourhood consisting of all z satisfying 0 0{vb} 0 is 1 / 2πi ∫C f(z)dz , where C is a simple closed rectifiable curve about z0 in the ‘deleted’ neighbourhood. The value of the residue is..the coefficient of (z - z0)-1 in the Laurent expansion of f(z) about z0. 1973Rauch & Lebowitz Elliptic Functions, Theta Functions, & Riemann Surfaces i. 19 A differential of the first kind is one whose set of Laurent expansions has no poles. Differentials of the second kind have poles but with zero residue at each pole while differentials of the third kind allow poles with non-vanishing residues.
4. = residuum 3. Also attrib.
1807T. Thomson Chem. (ed. 3) II. 357 The liquid being now filtered, boiled, and evaporated to dryness, left a residue, which may be considered as tannin. 1838― Chem. Org. Bodies 287 The aqueous residue was decanted off a resinous precipitate. 1887A. M. Brown Anim. Alkaloids 82 The tissue-residue is then retreated with alcohol at 99°; this when evaporated gives a new residue. 1899tr. Jaksch's Clin. Diagn. (ed. 4) 418 Inflammatory fluids are comparatively rich in fibrin..and in dry residue products.
5. Chem. (See quot. 1873.) In mod. use applied to any molecule when incorporated without major alteration in a larger one; esp. in Biochem., an amino-acid, sugar, or other molecule incorporated in a polymer such as a protein, carbohydrate, etc.
1852H. Watts tr. Gmelin's Hand-bk. Chem. VII. 76 The compound thus formed by substitution contains therefore the residues of the two compounds united, that is to say, the first compound + the second, minus an equal number of H- and O-atoms. Ibid. 77 Oxamide..may be regarded as a compound of the two residues, C4H2O4 and 2NH. 1873― Fownes' Chem. 251 Suppose one or more of the component atoms of a fully saturated molecule to be removed: it is clear that the remaining atom or group of atoms will no longer be saturated... Such unsaturated groups are called residues or radicals. 1886E. F. Smith tr. V. von Richter's Org. Chem. 30 Ordinarily, radicals are groups containing carbon, while all others, like OH, SH, NH2, NO2, are residues or groups. 1903Jrnl. Chem. Soc. LXXXIV. i. 214 The (albumin) molecule may be regarded as made up of 125 groups or residues. 1934W. R. Fearon Introd. Biochem. xv. 231 The test is believed to depend on the hydrolytic unmasking of an aldehyde group in the hexose residue. 1955H. R. Downes Chem. Living Cells v. 186 In one sample of lactoglobulin, for example, there were found 20 serine residues, 36 from aspartic acid, and 50 from leucine. 1975Nature 27 Feb. 694/2 Even the smallest protein (say 50 residues) is extremely complicated.
▪ II. † ˈresidue, a. Obs. rare.
[ad. L. residuus: see prec.]
Remaining, surviving.
1382Wyclif 1 Macc. iii. 37 The kyng toke to a part of the residue oost. 1382― 1 Thess. iv. 14 We that lyuen, that ben residue, or left [L. qui residui sumus], in the comynge of the Lord. 1432–50tr. Higden (Rolls) I. 29 Þat the weye may be patente to the residu peple of God. |