| 释义 |
quaternion|kwəˈtɜːnɪən|
[ad. late L. quaternio, -iōn-em, f. quaternī four together: cf. obs. F. quaternion (Godef.).]
1. a. A group or set of four persons or things; spec. a set of four poems.
1382Wyclif Acts xii. 4 Bitakinge [him] to foure quaternyouns of Knyȝtis..for to kepe him. [Tindale and later versions, quaternions of soudiers (souldiers).] 1599B. Jonson Cynthia's Rev. v. iii. (Masque i), The fitter to conduct this quaternion [= these four fair virgins]. 1648W. Jenkyn Blind Guide Pref. A iij, He puts his whole Booke under a quaternion of topicks. 1695Tryon Dreams & Vis. x. 185 This..Elementary Quaternion of Earth, Air, Water and Fire. 1745tr. Columella's Husb. iii. xx, So let us be content with a certain Quaternion as it were of chosen vines. 1815Scott Guy M. III. iii. 42 A species of florid elocution, which often became ridiculous from his misarranging the triads and quaternions with which he loaded his sentences. 1868Milman St. Paul's xii. 329 His great quaternion of English writers, Shakspeare, Hooker, Bacon, Jeremy Taylor. 1964C. S. Lewis Discarded Image iv. 68 He accepts the classical quaternion of virtues, Prudence, Temperance, Fortitude and Justice. 1967J. Hensley Wks. Anne Bradstreet p. xxiv, The Quaternions follow the structure of Thomas Dudley's own ‘On the Four Parts of the World’, now lost. 1976Times Lit. Suppl. 27 Aug. 1049/1 The formal elegies and quaternions she [sc. Anne Bradstreet] laboured over in imitation of Du Bartas.
b. A quatrain. rare—1.
1846Landor Pentam. iv. Wks. 1876 III. 517 You have given me a noble quaternion.
2. Of paper or parchment:
a. A quire of four sheets folded in two.
†b. A sheet folded twice.
1625Ussher Answ. Jesuit 398 The quaternion..in which I transcribed these things out of my table-booke. 1656Blount Glossogr., Quaternion,..a Quire with four sheets, or a sheet foulded into four parts. 1816Singer Hist. Cards 167 Before they had completed the third quaternion (or gathering of four sheets) 4000 florins were expended. 1882–3Schaff Encycl. Relig. Knowl. I. 268 The books were mostly made up of quaternions, i.e. quires of four sheets, doubled so as to make sixteen pages.
3. The number 4 or 10 (cf. quaternary).
1637Heywood Lond. Spec. Wks. 1874 IV. 310 The Pythagoreans expresse their holy oath in the quaternion. 1768–74Tucker Lt. Nat. (1834) I. 462 Adore the sacred quaternion: the quaternion containeth under it one, two, and three... The quaternion four alone is one and uncompounded.
4. Math.
a. The quotient of two vectors, or the operator which changes one vector into another, so called as depending on four geometrical elements, and capable of being expressed by the quadrinomial formula w + xi + yj + zk, in which w, x, y, z are scalars, and i, j, k are mutually perpendicular vectors whose squares are —1.
b. pl. That form of the calculus of vectors in which this operator is employed, invented by Sir W. R. Hamilton in 1843.
1843Sir W. R. Hamilton Let. in Philos. Mag. XXV. 493 We have, then, this first law for the multiplication of two quaternions together. 1858― Let. 15 Oct. ibid. 436 To-morrow will be the 15th birthday of the Quaternions. They started into life, or light, full grown on the 16th of October, 1843. 1866― (Title) Elements of Quaternions. 1873H. Spencer Stud. Sociol. (1882) 7 The value of Quaternions for pursuing researches in physics.
c. quaternion group, the group which is generated by multiplication of the unit quaternions, i, j, and k.
1911W. Burnside Theory of Groups of Finite Order (ed. 2) viii. 132 The group defined by these relations is known as the quaternion-group. 1949H. Zassenhaus Theory of Groups iv. 116 We wish to find non-abelian groups of order pn which contain only one subgroup of order p. An example is the quaternion group. By the theorem of Hölder it is defined by the relations A4 = 1, BAB-1 = A-1, B2 = A2. 1972F. J. Budden Fascination of Groups xv. 245 The simplest group in this class is Q4 of order 8 (n = 4), and this is usually known as the quaternion group, though in fact all the dicyclic groups may be realised as groups of quaternions.
5. attrib. or as adj. Consisting of four persons, things, or parts.
1814Cary Dante, Purgatory xxxiii. 3 The trinal now, and now the virgin band Quaternion, their sweet psalmody began. 1849Ticknor Span. Lit. I. 27 When and where this quaternion rhyme, as it is used by Berceo, was first introduced, cannot be determined.
Hence † quaˈternion v., to arrange in quaternions (only in pa. pple. quaˈternioned); quaterniˈonic a., pertaining to quaternions; quaˈternionist, one who studies quaternions.
1641Milton Ch. Govt. i. i, Yea, the Angels themselves..are distinguish'd and quaternion'd into their Celestial Princedoms, and Satrapies. 1873Tait Quaternions (ed. 2) 266 It would be easy to give this a more strictly quaternionic form. 1881J. Venn Symbolic Logic 91 Do we depart wider from the primary traditions of arithmetic than the Quaternionist does? |