quaternion

From Middle English quaternioun, from Late Latin quaterniō, from quaternī (ablative form of quater, “four times”) + -iōn, “-ion”.[1][2][3]

• (UK) IPA^(key): /kwəˈtəːni.ən/

quaternion (plural quaternions)

1. A group or set of four people or things.
   • 1526, William Tyndale, trans. Bible, Acts XII:

     Then wer the dayes of unlevended breed, and when he had caught hym, he put him in preson, and delyvered hym to iiij. quaternions off soudiers to be kept, entendynge after ester to brynge hym forth to the people.

   • 1885, Alexander Roberts, James Donaldson (original translators and editors), Arthur Cleveland Coxe (editor of American edition, unauthorized; author of annotations, notes, and introductions), Philip Schaff (also credited as editor), Nicene and Post-Nicene Fathers: Series II:

     This quaternion of revilers has traduced Origen, but not on the same grounds, one having found one cause of accusation against him, and another another; and thus each has demonstrated that what he has taken no objection to, he has fully accepted.

   • 2004, Jason Glenn, Politics and History in the Tenth Century: The Work and World of Richer of Reims, Cambridge: Cambridge University Press, →ISBN, page 140:

     We saw above that the fourth quire consists of ten folios, two of which (folios 29 and 31) Richer added to a quaternion (folios 23 to 28, 30, 32). Most of the folios Richer added to his manuscript supplement, elaborate, or amend text that he had already composed in the codex.

2. A word of four syllables.
   • Sir Walter Scott

     The triads and quaternions with which he loaded his sentences.

3. (mathematics) A four-dimensional hypercomplex number that consists of a real dimension and 3 imaginary ones (i, j, k) that are each an independent square root of -1. They are commonly used in vector mathematics and in calculating the rotation of three-dimensional objects.
   • 2004, David H. Eberly, 3D Game Engine Architecture: Engineering Real-Time Applications with Wild Magic:

     The right-hand side of the quaternion equation requires scalar multiplication and quaternion addition.

• hypercomplex number

• quaternionic

• (mathematics): octonion