[ad. late L. quaternio, -iōn-em, f. quaternī four together: cf. obs. F. quaternion (Godef.).]
1. A group or set of four persons or things.
1382. Wyclif, Acts xii. 4. Bitakinge [him] to foure quaternyouns of Knyȝtis … for to kepe him. [Tindale and later versions, quaternions of soudiers (souldiers).]
1599. B. Jonson, Cynthia’s Rev., V. iii. (Masque i). The fitter to conduct this quaternion [= these four fair virgins].
1648. Jenkyn, Blind Guide, Pref. A iij. He puts his whole Booke under a quaternion of topicks.
1695. Tryon, Dreams & Vis., x. 185. This … Elementary Quaternion of Earth, Air, Water and Fire.
1745. trans. Columella’s Husb., III. xx. So let us be content with a certain Quaternion as it were of chosen vines.
1868. Milman, St. Paul’s, xii. 329. His great quaternion of English writers, Shakspeare, Hooker, Bacon, Jeremy Taylor.
b. A quatrain. rare–1.
1846. Landor, 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.
1625. Ussher, Answ. Jesuit, 398. The quaternion … in which I transcribed these things out of my table-booke.
1656. Blount, Glossogr., Quaternion,… a Quire with four sheets, or a sheet foulded into four parts.
1816. Singer, Hist. Cards, 167. Before they had completed the third quaternion (or gathering of four sheets) 4000 florins were expended.
1882–3. Schaff, 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).
1637. Heywood, Lond. Spec., Wks. 1874, IV. 311. The Pythagoreans expresse their holy oath in the quaternion.
1768–74. Tucker, 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 that 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.
1843. Sir W. R. Hamilton, Lett., in Philos. Mag., XXV. 493. We have, then, this first law for the multiplication of two quaternions together. Ibid. (1858), Lett., 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. Ibid. (1866) (title), Elements of Quaternions.
1873. H. Spencer, Stud. Sociol. (1882), 7. The value of Quaternions for pursuing researches in physics.
5. attrib. or as adj. Consisting of four persons, things or parts.
1814. Cary, Dante, Purgatory, XXXIII. 3. The trinal now, and now the virgin band Quaternion, their sweet psalmody began.
1849. Ticknor, Span. Lit., I. 27. When and where this quaternion rhyme, as it is used by Berceo, was first introduced, cannot be determined.
Hence † Quaternion v., to arrange in quaternions (only in pa. pple. Quaternioned); Quaternionic a., pertaining to quaternions; Quaternionist, one who studies quaternions.
1641. Milton, Ch. Govt., I. i. Yea, the Angels themselves … are distinguish’d and quaternion’d into their Celestial Princedoms, and Satrapies.
1873. Tait, Quaternions (ed. 2), 266. It would be easy to give this a more strictly quaternionic form.
1881. J. Venn, Symbolic Logic, iv. 91. Do we depart wider from the primary traditions of arithmetic than the Quaternionist does?
