单词 | quaternion |
释义 | quaternionn.adj. A. n. 1. a. A group or set of four persons or things. In quot. c1384: apparently understood as a Roman officer in charge of four soldiers. ΘΚΠ the world > relative properties > number > specific numbers > four > [noun] > group of four quaternionc1384 quadrivial?a1475 messa1529 quaternity1529 quaternio1601 mournival1631 quadrate1637 quaternarya1638 tetrad1653 quadruplet1795 quartetto1807 quatrain1862 quartet1882 quad1896 society > leisure > the arts > literature > poetry > poem or piece of poetry > [noun] > set of four poems quaternion1967 c1384 Bible (Wycliffite, E.V.) (Douce 369(2)) (1850) Deeds xii. 4 Bitakinge [Peter] to foure quaternyouns [1408 L.V. (Fairf.) Gloss.: a quaternion is he that hath foure kniȝtis vndir him; L. quaternionibus] of knyȝtis, that ech hadde foure men vndir him, for to kepe him. [1534 Tyndale quaternions of soudyers; 1535 quaternions of soudyers; 1611 King James quaternions of souldiers; 1961 New Eng. squads of four men each]. 1587 A. Fleming et al. Holinshed's Chron. (new ed.) III. 207/2 A quadrangle in geometrie compriseth in it a triangle, and a quaternion in arithmetike conteineth a ternion. 1648 W. Jenkyn Ὁδηγος Τυϕλος To Rdr. sig. A3 He puts his whole Booke under a quaternion of topicks. 1695 T. Tryon Treat. Dreams & Visions (ed. 2) x. 185 This..Elementary Quaternion of Earth, Air, Water and Fire. 1745 tr. L. J. M. Columella Of Husbandry iii. xx So let us be content with a certain Quaternion as it were of chosen vines. 1778 T. Reader Remarks on Revelation 25 So if this did not humble his enemies, they must expect to encounter that quaternion of destroyers the sword, famine, pestilence, and wild beasts, which will come yoked together under the next seal. 1815 W. Scott Guy Mannering 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. 1868 H. H. Milman Ann. St. Paul's Cathedral xii. 329 His great quaternion of English writers, Shakspeare, Hooker, Bacon, Jeremy Taylor. a1963 C. S. Lewis Discarded Image (1964) iv. 68 He accepts the classical quaternion of virtues, Prudence, Temperance, Fortitude and Justice. 1967 J. 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. 1989 W. Weaver tr. U. Eco Foucault's Pendulum lxvi. 379 Then comes the universal joint, the axle, the drive shaft, the differential—note the opposition/repetition of the quaternion of cylinders in the engine. ΘΚΠ society > leisure > the arts > literature > poetry > part of poem > [noun] > stanza > quatrain tetrastich1580 quatrain1584 quaternion1722 tetrachord1817 1722 J. Dennis Prosody in J. Greenwood Ess. towards Pract. Eng. Gram. (ed. 2) v. ii. 267 The Stanza of Sir William Davenant is, what they call the Quaternion, which consists of four Pentameters with alternate Rhyme. 1846 W. S. Landor Pentameron iv, in Wks. (1876) III. 517 You have given me a noble quaternion. 2. Also with capital initial. In Pythagorean philosophy: the number 4; (also) the sum of the first four numbers, namely 10. Cf. quaternary number n. at quaternary n. and adj. Compounds, tetractys n., tetrad n. 1. ΘΚΠ the world > relative properties > number > mathematical number or quantity > numerical arrangement > [noun] > set > elements in or parts of > specific number of hebdomad1545 quaternion1549 tetractys1603 quaternary number1605 tetrad1653 heptad1660 pentad1660 quaternary of numbers1809 tripair1878 trey1887 the world > relative properties > number > specific numbers > four > [noun] fourOE quaternaryc1450 cater1553 quaternion1768 rouf1950 1549 T. Chaloner tr. Erasmus Praise of Folie sig. Biv That, is the onely fountaine, whens all thynges receiue life, a great deale sooner than from Pythagoras quaternion [L. Pythagoricus quaternio]. 1577 J. Grange Golden Aphroditis sig. Iij Lady, the curtesie of Prometheus hath yeelded me a body shaped with moulde, whiche craueth lyfe not of Pythagoras quaternion, but of thy courteous harte. 1637 T. Heywood Londini Speculum sig. C1 The Pythagoreans expresse their holy oath in the quaternion. 1768 A. Tucker Light of Nature Pursued II. ii. xxiii. 241 Adore the sacred Quaternion: the Quaternion containeth under it One, Two, and Three, but One, Two, Three and Four compose Ten... The Quaternion Four alone is One and uncompounded. 1791 W. Anderson Philos. Anc. Greece ii. i. 51 The quaternion, or number four, was also considered as competing with the unite, in indicating the stability and power of the first cause. 1845 R. Cudworth True Intellect. Syst. Universe II. 20 If we assent to those, who suppose the Pythagoreans to have sworn by the inventor or author of the quaternion, we shall have again to consider who this inventor was, God or Pythagoras. 1905 F. Firth Golden Verses of Pythagoras (1993) 12 The knowledge of the Quaternion was one of the chief precepts among the Pythagoreans. 1961 Stud. Renaissance 8 18 The tetrad—sometimes called the ‘quaternion’—was the symbol which expressed this all-inclusive principle. 3. A quire of four sheets of paper or parchment folded in two. Formerly also: †a sheet of paper or parchment folded twice (obsolete). ΘΚΠ society > communication > printing > paper > [noun] > specific quantity of quatern?1533 ternion1609 quaternion1625 quinternion1652 bundle1724 ream1832 quinion1872 quire1879 sextern1885 society > communication > writing > writing materials > material to write on > paper > [noun] > large quantity of > specific quantity of milleOE reamc1390 quire1393 ternion1609 quaternion1625 quinternion1652 quinion1872 sextern1885 1625 J. Ussher Answer to Jesuite 398 The quaternion..in which I transcribed these things out of my table-booke. 1656 T. Blount Glossographia Quaternion,..a Quire with four sheets, or a sheet foulded into four parts. 1732 S. Palmer Gen. Hist. Printing i. ix. 71 Before they had finish'd the third quaternion (or quire of four sheets,) the charges amounted already to four thousand florins, a prodigious sum in those days. 1816 S. W. Singer Researches Hist. Playing Cards 167 Before they had completed the third quaternion (or gathering of four sheets) 4000 florins were expended. 1882 P. Schaff et al. Relig. Encycl. I. 268 The books were mostly made up of quaternions, i.e. quires of four sheets, doubled so as to make sixteen pages. 1927 E. K. Rand in W. M. Lindsay Palaeographia Latina v. 53 A quinion may consist of a quaternion ruled four leaves at a time plus an extra leaf. 1953 D. C. C. Young in Scriptorium 8 15 There is an inbound quaternion of blanks. 1996 Speculum 71 838 Each quaternion had 4 bifolia, or 8 leaves. 4. Mathematics. A kind of number of the form w + xi + yj + zk, where w, x, y, z are real numbers, and i, j, k are unit imaginary numbers satisfying the conditions ij = −ji = k, jk = −kj = i, ki = −ik = j, and i2 = j2 = k2 = ijk = −1.Quaternions were invented by Sir William Hamilton and were originally considered as the abstract quotient of two vectors (or an operator which changes one vector into another), which depends on four elements (a scalar and three geometrical elements) and can be expressed in terms of generalized complex numbers. ΘΚΠ the world > relative properties > number > mathematical number or quantity > tensor > [noun] > vector > quaternion quaternion1844 biquaternion1852 1844 W. R. Hamilton Let. in London, Edinb. & Dublin Philos. Mag. 25 493 We have, then, this first law for the multiplication of two quaternions together. 1873 H. Spencer Study Sociol. (1882) 7 The value of Quaternions for pursuing researches in physics. 1972 M. Kline Math. Thought xxxii. 786 By Maxwell's time a great deal of vector analysis was created by treating the scalar and vector parts of quaternions separately. 1996 J. H. Conway & R. K. Guy Bk. Numbers viii. 232 The appropriate measure of the ‘size’ of a typical quaternion a + bi + cj + dk is its norm a2 + b2 + c2 + d2. Consisting of four persons, things, or parts. Obsolete. ΘΚΠ the world > relative properties > number > specific numbers > four > [adjective] > group of four foursome15.. tetradic1788 quaternion1814 quad1881 1814 H. F. Cary tr. Dante Vision II. xxxiii. 3 The trinal now, and now the virgin band Quaternion, their sweet psalmody began. 1849 G. Ticknor Hist. Spanish Lit. I. 27 When and where this quaternion rhyme, as it is used by Berceo, was first introduced, cannot be determined. Compounds quaternion group n. Mathematics the group which is formed under multiplication by the unit quaternions, 1, i, j, and k, and their negatives. ΘΚΠ the world > relative properties > number > mathematical number or quantity > numerical arrangement > [noun] > set > in abstract algebra > groups syntheme1844 group1854 substitution group1861 quaternion group1881 subgroup1881 Abelian group1892 permutation group1893 quotient group1893 factor group1895 order1897 symmetric group1897 point group1903 Sylow subgroup1905 module1927 Lie group1939 symmetry group1956 Weyl group1961 stabilizer1965 1881 Amer. Jrnl. Math. 4 345 The object of the present paper is to determine all the possible finite quaternion groups. 1949 H. 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. 1972 F. 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. 2002 Amer. Math. Monthly 109 183 Another group that can be given by generators and relations is the quaternion group H of order 8. Derivatives quaterniˈonic adj. Mathematics involving or relating to quaternions. ΚΠ 1873 P. G. Tait Elem. Treat. Quaternions (ed. 2) xi. 266 It would be easy to give this a more strictly quaternionic form. 1937 J. J. Thomson Recoll. & Refl. i. 14 Many physical laws, notably those of electrodynamics, are most concisely expressed in Quaternionic Notation. 2002 New Scientist 9 Nov. 32/4 So we have four candidate string theories here: real, complex, quaternionic, and octonionic. quaˈternionist n. Mathematics (now historical) a person who studies or uses quaternions, esp. (in later use) instead of the modern system of vector analysis. ΚΠ 1881 J. Venn Symbolic Logic 91 Do we depart wider from the primary traditions of arithmetic than the Quaternionist does? 1970 Isis 61 123/1 The famous debate between quaternionist and vectorialist which took place in the early 1890's. 1989 Math. Mag. 62 302 Not only was this construction ignored by the quaternionists but it is not even mentioned in modern books on the rotation group. This entry has been updated (OED Third Edition, December 2007; most recently modified version published online June 2022). † quaternionv. Obsolete. rare. transitive. To arrange in quaternions or groups of four. ΚΠ 1641 J. Milton Reason Church-govt. 4 Yea the Angels themselves..are distinguisht and quaterniond into their celestiall Princedomes, and Satrapies. This entry has been updated (OED Third Edition, December 2007; most recently modified version published online December 2021). < n.adj.c1384v.1641 |
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