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单词 quaternion
释义

quaternionn.adj.

Brit. /kwəˈtəːnɪən/, U.S. /kwəˈtərniən/, /kwɑˈtɛrniən/
Forms: Middle English quaternyoun, Middle English– quaternion.
Origin: A borrowing from Latin. Etymons: Latin quaternion-, quaternio.
Etymology: < post-classical Latin quaternion-, quaternio squad of four soldiers (Vulgate), gathering of four leaves of parchment, quire (4th cent.; from 8th cent. in British sources), the number four (5th cent.) < classical Latin quaternī four each (see quatern adj.) + (see -oon suffix). Compare Middle French quaternion set of four (1537; compare Old French quaregnon, caregnon a sheet of paper folded twice, a letter (12th cent.)).In sense A. 2 ultimately after Hellenistic Greek τετρακτύς tetractys n. With sense A. 3 compare earlier quatern n. Compare apparent earlier borrowing of post-classical Latin quaternio (specific sense unclear) into Old English as quatern, although the two glossarial attestations may perhaps represent a scribal error for classical Latin quaternī (compare the reading in Erfurt Gloss.):eOE Épinal Gloss. (1974) 45 Quaternio, quatern [eOE Erfurt Gloss. Quaternio, quaterni].eOE Corpus Gloss. (1890) 99/2 Quaternio, quatern.
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.
b. A quatrain. Obsolete. rare.
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.
B. adj.
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.

Origin: Formed within English, by conversion. Etymon: quaternion n.
Etymology: < quaternion n.
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).
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n.adj.c1384v.1641
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