# quaternion

### Definitions:

• A set of four persons or items.
• Any number of the form <em>a</em> + <em>bi</em> + <em>cj</em> + <em>dk</em> where <em>a, b, c,</em> and <em>d</em> are real numbers, <em>ij</em> = <em>k, i</em><sup>2</sup> = <em>j</em><sup>2</sup> = −1, and <em>ij</em> = −<em>ji.</em> Under addition and multiplication, quaternions have all the properties of a field, except multiplication is not commutative.
• In <em>book-making</em>, a set or ‘gathering’ of four sheets of paper or parchment folded in two.
• To divide into quaternions, files, or companies.
• A set, group, or body of four: applied to persons or things.
• A word of four syllables; a quadrisyllable.
• A fourfold quantity capable of being expressed in the form <em>xi</em> + <internalXref urlencoded="yj">yj</internalXref> + <internalXref urlencoded="zk">zk</internalXref> + <internalXref urlencoded="w">w</internalXref>, where <em>x, y, z, w</em> are scalars, or real numbers, while <em>i, j, k</em> are vectors, or quantities whose squares are negative scalars. The calculus of such quantities is termed <em>quaternions.</em>
• To divide into quaternions, files, or companies.
• The number four.
• A set of four parts, things, or person; four things taken collectively; a group of four words, phrases, circumstances, facts, or the like.
• A word of four syllables; a quadrisyllable.
• The quotient of two vectors, or of two directed right lines in space, considered as depending on four geometrical elements, and as expressible by an algebraic symbol of quadrinomial form.
• the cardinal number that is the sum of three and one