# quaternion

[kwuh-tur-nee-uh n] /kwəˈtɜr ni ən/
noun
1.
a group or set of four persons or things.
2.
Bookbinding. four gathered sheets folded in two for binding together.
3.
Mathematics.
1. an expression of the form a + bi + cj + dk, where a, b, c, and d are real numbers; i 2 = j 2 = k 2 = −1; and ij = −ji = k, jk = −kj = i, and ki = −ik = j.
2. a quantity or operator expressed as the sum of a real number and three complex numbers, equivalent to the quotient of two vectors. The field of quaternions is not commutative under multiplication.
Origin of quaternion
1350-1400
1350-1400; Middle English quaternioun < Late Latin quaterniōn- (stem of quaterniō), equivalent to Latin quatern(ī) four at a time + -iōn- -ion
Dictionary.com Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2016.
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Examples from the Web for quaternion
Historical Examples
• As regard class of the first quaternion, like Sancho Panza I have no intention of indicating how old these may be.

Lewis Spence
• Should neither player be able to form a quaternion, then the game is drawn.

• The quaternion was a gathering of four sheets of vellum, each folded once; thus forming sixteen pages.

J. Henry Middleton
• Next, to assign the distinction between the first and the second quaternion in propositions tertii adjacentis.

George Grote
• William Hare, the second of our quaternion, was also a native of Ireland, having been born in the neighbourhood of Londonderry.

Alexander Leighton
• These last words are incorrect in fact, for οὐκ ἄνθρωπος does not appear in the first quaternion, but is reserved for the second.

George Grote
• Even then the captain of the gate was replying to a question from the quaternion.

William O. Stoddard
• Four soldiers formed a quaternion; four quaternions therefore were sixteen men, who were especially appointed to guard Peter.

• His days are thus described: from dawn to the third hour he copied rapidly, filling a (quaternion) each day.

Henry Osborn Taylor
• There was no sound of trumpet at the sun's rising, but a quaternion of legionaries came and the guard was changed.

William O. Stoddard
British Dictionary definitions for quaternion

## quaternion

/kwəˈtɜːnɪən/
noun
1.
(maths) a generalized complex number consisting of four components, x = x0 + x1i + x2j + x3k, where x, x0x3 are real numbers and i² = j² = k² = –1, ij = –ji = k, etc
2.
another word for quaternary (sense 5)
Word Origin
C14: from Late Latin quaterniōn, from Latin quaternī four at a time
Collins English Dictionary - Complete & Unabridged 2012 Digital Edition
Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012
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quaternion in Science
 quaternion   (kwə-tûr'nē-ən)    Any number of the form a + bi + cj + dk where a, b, c, and d are real numbers, ij = k, i2 = j2 = -1, and ij = -ji. Under addition and multiplication, quaternions have all the properties of a field, except that multiplication is not commutative.
The American Heritage® Science Dictionary
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quaternion in the Bible

a band of four soldiers. Peter was committed by Herod to the custody of four quaternions, i.e., one quaternion for each watch of the night (Acts 12:4). Thus every precaution was taken against his escape from prison. Two of each quaternion were in turn stationed at the door (12:6), and to two the apostle was chained according to Roman custom.

Easton's 1897 Bible Dictionary
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### Word Value for quaternion

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