| 释义 |
▪ I. infinite, a. (adv.) and n.|ˈɪnfɪnɪt|
Forms: 4–6 infynyt(e, 4–7 infinit, (5 infenite, 6 infinyte, infynit(e, Sc. infineit), 4– infinite.
[ad. L. infīnīt-us unbounded, unlimited, f. in- (in-3) + fīnīt-us finite; perh. orig. through OF. infinit, -ite (13th c. in Hatz.-Darm.), later infini (Oresme, 14th c.). In hymns sometimes rimed with (-aɪt).]
A. adj.
1. a. Having no limit or end (real or assignable); boundless, unlimited, endless; immeasurably great in extent, duration, or other respect. Chiefly of God or His attributes; also of space, time, etc., in which it passes into the mathematical use (4 b).
1413Pilgr. Sowle (Caxton) v. i. (1859) 71 The largenes therof may not be comprehended by thought of mannes wytte; for it is Infynyte. 1477Earl Rivers (Caxton) Dictes 1 Releued by thynfynyte grace & goodnes of our said lord. 1535Coverdale Ps. cxlvi[i]. 5 Greate is oure Lorde, and greate is his power, yee his wyszdome is infinite. 1557N. T. (Genev.) Ep. *iij, That he might shewe more manifestly his goodnes and infinit mercie among men. 1651Hobbes Leviath. i. iii. (1886) 22 No man can have in his mind an image of infinite magnitude; nor conceive infinite swiftness, infinite time, or infinite force, or infinite power. 1754Edwards Freed. Will i. iv. 22 That Power is not Infinite; and so goes not beyond certain Limits. 1811Heber Hymn, Lord of mercy and of might..Maker, Teacher, Infinite; Jesus, hear and save! 1849Froude Nemesis Faith 130 The doctrine of the infinite divisibility of matter must be called in to help you in your dividings. 1860Tyndall Glac. i. ii. 15 An infinite series of images of the candle will be seen.
b. In loose or hyperbolical sense: Indefinitely or exceedingly great; exceeding measurement or calculation; immense, vast.
c1385Chaucer L.G.W. 1675 Hypsip., Why lykede me..of thyn tunge the infynyt graciousnesse. c1440Gesta Rom. i. xxxii. 122 (Harl. MS.) He shulde wed hir with goodis infinite. 1527R. Thorne in Hakluyt Voy. (1589) 255 Infinite nomber of Iewes that were expelled out of Castill. 1596Shakes. Merch. V. i. i. 114 Gratiano speakes an infinite deale of nothing. 1602― Ham. ii. ii. 316 What a piece of worke is a man! how Noble in Reason? how infinite in faculty? 1748Anson's Voy. Introd., Of infinite importance to the commercial and sea-faring part of mankind. 1857Maurice Ep. St. John xvii. 281 We owe them infinite thanks for it. 1865R. W. Dale Jew. Temp. xxi. (1877) 233 A truth this of infinite importance.
†c. Occupying an indefinitely long time; immensely long, very tedious, ‘endless’. (Used predicatively, with inf. or with personal subj.: cf. long.) Obs.
1575–85Abp. Sandys Serm. (Parker Soc.) 26 It were infinite to recite what huge sums of money they have..gathered. 1608Topsell Serpents (1658) 667 All which..I will (lest I should seem to be infinite) passe over with silence. 1620E. Blount Horæ Subs. 363, I dare walke no farther in this Labyrinth, for feare of growing too infinite. 1638Chillingw. Relig. Prot. i. ii. §116. 97 Lastly, not to be infinite, it is taught by Mr. Knot himselfe, not in one page only..but all his Book over.
d. infinite regress (see quots.).
1836–7[see regress n. 1 fig.]. 1934A. C. Ewing Idealism iv. 149 If we once view relations as terms we are involved in Bradley's infinite regress. 1946P. Harrison Oxf. Marmalade i. iii. 27 George's criterion of niceness, however, might be described as an infinite regress. Every girl he met was nice, until he met another, and she was nicer. 1968E. H. Gombrich Art & Illusion (ed. 3) ix. 268 Are we not led into what philosophers call an infinite regress, the explanation of one thing in terms of an earlier which again needs the same type of explanation? 1973A. Quinton Nature of Things 109 The concept of an axiom..solves the problem of the infinite regress of justification.
2. with n. pl. Unlimited or indefinitely great in number; innumerable, very many, ‘no end of’. Now arch. or rare.
c1386Chaucer Knt.'s T. 1969 Infinite been the sorwes and the teeres Of olde folk and eek of tendre yeeres. 1483Caxton Cato I ij, Many and Infynyte euyles and inconuenientes. 1555Eden Decades 88 Not onely..infinite hundredes and legions but also myriades of men. 1556Aurelio & Isab. (1608) L j, She and heir ladeis shedde infinite teares. 1611Bible Transl. Pref. 5 Now the Latine Translations were too many to be all good, for they were infinite. 1668Hale Pref. Rolle's Abridgm. b ij, Infinite other Instances of like nature may be given. 1709Addison Tatler No. 119 ⁋2 There are infinite Parts in the smallest Portion of Matter. 1775Harris Philos. Arrangem. Wks. (1841) 265 Thus there are..infinite ways of being vicious, though but one of being virtuous. 1858Carlyle Fredk. Gt. iii. xviii. (1872) I. 253 The Swedes..found infinite ‘pigs, near Insterburg’.
†3. Indefinite in nature, meaning, etc.; indeterminate. Obs.
1520Whitinton Vulg. (1527) 6 Nownes infinyte as quisquis, quicunque. 1553T. Wilson Rhet. 1 Either it is an infinite question and without ende, or els it is definite and comprehended within some ende. 1663J. Spencer Prodigies (1665) 111 It is a blind, confused, infinite, giddy thing.
4. Math.
†a. Having no determined limit; of indefinite length or magnitude. Obs.
1660Barrow Euclid i. xii, Upon an infinite right line. Ibid. xxii, From the infinite line DE.
b. Of a quantity or magnitude: Having no limit; greater than any assignable quantity or magnitude (opp. to finite). Of a line or surface: Extending indefinitely without limit, and not returning into itself at any finite distance (opp. to closed).
1692Halley in Phil. Trans. No. 195 (title) Of the several Species of Infinite Quantity, and of the Proportions they bear to one another. 1743Emerson Fluxions 277 To find the Force wherewith an infinite Solid, plain on one Side Ll, attracts a Corpuscle placed at C. 1836De Morgan Calculus Elem. Illustr. 61 When we say, a + 1 / x is equal to a when x is infinite, we only mean that as x is increased a + 1 / x becomes nearer to a and may be made as near to it as we please, if x may be as great as we please. 1840Lardner Geometry 278 When the ellipse becomes a parabola, the further focus will be removed to an infinite distance. 1869Todhunter Plane Trigon. (ed. 4) iv. §58 As the angle increases from 0 to 90° the tangent increases from 0 without limit, so that by taking an angle sufficiently near to 90° we can make the tangent as great as we please; this is usually expressed for the sake of abbreviation thus, the tangent of 90° is infinite. 1875― Algebra (ed. 7) lii. §706 The number of prime numbers is infinite. 1885Watson & Burbury Math. The. Electr. & Magn. I. 4 If u become infinite at any point within S, we cannot include in the integration the point at which the infinite value occurs.
c. infinite series: a series of quantities or expressions which may be indefinitely continued without ever coming to an end (but may or may not have a finite value or ‘limit’ to which it approaches as more and more terms are taken: see converging 2, divergent 4). So infinite decimal.
1706W. Jones Syn. Palmar. Matheseos 44 The Operation may either be terminated..or else continued on in an Infinite Series. 1763Emerson Increments p. vi, The Method of Increments will help us to this term, either expressed in finite quantities, or by an infinite series. 1796Hutton Math. Dict. s.v., Infinite Decimals, such as do not terminate, but go on without end. 1875Todhunter Algebra (ed. 7) xl. §557 An infinite series in which all the terms are of the same sign is divergent if each term is greater than some assigned finite quantity, however small.
5. Mus. Applied to a form of musical structure which can be repeated infinitely.
1869Ouseley Counterp. xv. 105 If [the canon] is made continually to recur to the beginning, so as never to come to a regular close, it is called Infinite, or Circular. 1876Stainer & Barrett Dict. Mus. Terms s.v. Canon, The above is also an infinite canon, because, anyone having such a remarkable desire as to play it for ever, could do so. 1880Grove Dict. Mus. s.v. Canon, Many canons lead back to the beginning and thus become ‘circular’ or ‘infinite’. 1959Collins Mus. Encycl. s.v. Canon, If..each part, on coming to the end of the melody, goes back to the beginning again and repeats, the result is a ‘perpetual’ or ‘infinite’ canon.
6. Law. distress infinite: see distress n. 3 b.
1495Act 11 Hen. VII c. 24 §1 In the same atteynte there shalbe awarded ageynst the petite Jurie the party and the graund Jury somons and resomons and distres infynyte. 1531–2Act 23 Hen. VIII, c. 3 §1. 1641, 1768 [see distress n. 3 b]. 1882Scriven's Copyholds (ed. 6) vi. §2. 227 The proper remedy for neglect of suit of court, as well as for refusal to do fealty, was a distress infinite of the beasts or other personal property of the defaulter.
7. Gram. Applied to those parts of the verb which are not limited by person or number; viz. those verbal ns. and adjs. which have certain verbal properties, the Infinitive ‘Mood’, Gerunds, Supines, and Participles. Opposed to finite.
1871Roby Lat. Gram. ii. xvi. 183 The forms of the verb proper are often called collectively the Finite Verb; the verbal nouns above named are sometimes called the Infinite Verb. 1871Publ. Sch. Lat. Gram. §35 The forms of the Verb Infinite are not limited by Mood and Person. It comprises..(1) The Infinitive, a Verbal Substantive: as, amare, to love..(2) Participles, which are Verbal Adjectives.
8. Logic. A rendering of Schol.L. infinitus, applied to a negative term, etc.; infinitated.
1860Sir W. Hamilton Logic xiv. I. 253 Aristotle denominated the negative terms, such as non-B, non-homo, non-albus, etc., ὀνόµατα ἀόριστα, literally indefinite nouns. Boethius however unhappily translated..ἀόριστος by the Latin infinitus. The Schoolmen..thus called the ὀνόµατα ἀόριστα..nomina infinita: and the non- they styled the particula infinitans.
†B. adv. = infinitely: usually in hyperbolical sense = very greatly. Obs.
1526Pilgr. Perf. (W. de W. 1531) 298 Infinyte ryche in glory. 1642Rogers Naaman 616 Are there not infinite many passages in thy life? 1658W. Sanderson Graphice 60 Nature is so infinite various in the Colours and shadows of the face. 1673Dryden Marr. à la Mode i. i, I set a good face upon the matter, and am infinite fond of her before company.
C. absol. or as n.
1. That which is infinite, or has no limit; an infinite being, thing, quantity, extent, etc. Now almost always in sing. with the; esp. as a designation of the Deity or the absolute Being.
1587Golding De Mornay ii. 14 Two infinites cannot be abidden, no nor imagined together,..therefore, as there must needes be one Infinite, so must there be but onely one. a1711Ken Hymnarium Poet. Wks. 1721 II. 1 No Rival Infinite could share thy Throne, There no more Infinites can be but one. 1712H. More's Antid. Ath. i. viii. Schol. 151 Since every part of an Infinite is infinite, there may be supposed something more infinite than an Infinite. 1830Herschel Stud. Nat. Phil. §106 The telescope and the microscope laid open the infinite in both directions. 1843J. Martineau Chr. Life (1867) 455 The Presence-chamber of the Infinite. 1856Vaughan Mystics (1860) I. 44 Hindoo mysticism..aims at ultimate absorption in the Infinite.
2. In hyperbolical use: An exceedingly large amount or number; a very great quantity or multitude; very much or many; ‘no end’.
†a. absol. (from A. 2: always in plural sense.) Obs.
a1568R. Ascham Scholem. i. (Arb.) 69 Infinite shall be made cold in Religion by your example. 1577J. Northbrooke Dicing (1843) 170 Infinite from thence haue returned home vnchast. 1656Ridgley Pract. Physick 120 Infinite have been cured by it.
†b. Const. of, with no defining word prefixed.
1591Shakes. Two Gent. ii. vii. 70 A thousand oathes, an Ocean of his teares, And instances of infinite of Loue. 1613Purchas Pilgrimage iv. xvi. (1614) 428 There are infinite of Frier-like companions passing to and fro. 1661Pepys Diary 1 June, There was infinite of new cakes placed. 1677A. Yarranton Eng. Improv. 115 Down the Elb to Hamborough, is sent infinite of Corn. 1697Congreve Mourn. Bride iv. i, No term, no bound, but infinite of woe.
c. With article or other defining word prefixed; usually const. of. Formerly also in pl. (cf. mod. colloq. lots, heaps, oceans).
1563Winȝet Wks. (1890) II. 64 Thow may se an infinit of exemplis. 1595Markham Sir R. Grinvile xciii, Shee lesse great shot in infinets did hide. 1611Heywood Gold. Age iii. i. Wks. 1874 III. 36 We haue assembled infinites of men. 1615J. Wright Acc. Lady J. Grey in Phenix (1708) II. 28 She brought forth her Increase in such abundance of Infinites, that the least of her Excellencys were impossible to be circumscrib'd. 1647R. Stapylton Juvenal 279 The ibes, that kill infinites of serpents. 1662Glanvill Lux Orient. Pref. (1682) 10 What an infinite of Books are written upon almost all subjects. 1748F. Smith Voy. Disc. I. 188 You have an Infinite to lose, should you be defeated. 1856Ruskin Mod. Paint. IV. v. i. §3 That Calais tower has an infinite of symbolism in it.
†3. Phr. in infinite, to infinite, = L. in or ad infinitum (see infinitum); endlessly. Obs.
a1631Donne Elegy to Lady Bedford Poems (1633) 299 Diffus'd, and spread in infinite. 1651Life Father Sarpi (1676) 71 Mischiefs have their terminations, but fears go in infinite. 1651Jer. Taylor Serm. for Year i. vii. 87 And so on to infinite.
4. Math. An infinite quantity: see A. 4 b.
Different orders of infinites are distinguished, each infinitely greater than the preceding: cf. infinitesimal B. 1.
1656Hobbes Consid. Wallis Wks. 1845 VII. 446 This arguing of infinites is but the ambition of school-boys. 1677Plot Oxfordsh. 288 Dr. John Wallis..first demonstrated the impossibility of squaring the Circle, Arithmetically,..having apply'd his method of Infinites in order thereunto. 1692Halley in Phil. Trans. XVII. 556 That among themselves each of those Species of Infinites are in given Proportions, is what I now intend to make plain. 1706W. Jones Syn. Palmar. Matheseos 205 Of Infinites 'tis hence plain, that some are equal, others unequal. 1710Berkeley Princ. Hum. Knowl. §130 Of late the speculations about Infinites have..grown to such strange notions, as have occasioned no small scruples and disputes among the geometers. 1831Brewster Newton (1855) II. xvii. 127 He then proceeds to correct an error of Dr. Bentley's in supposing that all infinites are equal. 1858Buckle Civiliz. (1869) II. iv. 190 The geometry of infinites applied to the ordinates and tangents of curves. 1864Plucker New Geom. Space in Phil. Trans. (1865) 727 The number of rays constituting a configuration, a congruency, a complex and space, are infinites of first, second, third, and fourth order. 1864Reader 21 May 657 The symbol 1/0, the infinite of common algebra, represents an extreme of infinite.
▪ II. ˈinfinite, v. rare.
[f. infinite a.]
†1. to infinite it: to proceed to an ‘infinite’ or indefinite extent. Obs. nonce-use.
1656S. H. Gold. Law 72 Suppose that any King..should..Solomon-like, infinite it in Wives and Concubines.
2. trans. To render infinite; to infinitate.
1868H. Bushnell Serm. Living Subj. 105 They are creatures to be somehow infinited, to be eternized in their continuance of good. 1868Contemp. Rev. VIII. 617 Those very elements of diversity by which..spirit in its last individual forms infinites and unifies the manifold. |