ternions's Usage Examples:

With this notation the values of x and y may be expressed in the forms x q q /N q ', gg /Nq', which are free from ambiguity, since scalars are commutative with quaternions.

In addition to his political pamphlets Pourquoi et comment je suis Boulangiste (1887) and L'Anarchie bourgeoise (1887), he published mathematical works, among them Introduction a l'etude des quarternions (1881) and Theorie et applications des equipollences (1887).

As will be seen later, the fundamental i, j, k of quarternions, with their reciprocals, furnish a set of six quantities which satisfy the conditions imposed by Servois.

- There are three fairly wellmarked stages of development in quaternions as a geometrical method.

Thus e 1 e 2 - e2ei, and if q, q are any two quaternions, qq is generally different from q'q.

Quaternions (as a mathematical method) is an extension, or improvement, of Cartesian geometry, in which the artifices of co-ordinate axes, 'c.

(Note that the z here occurring is only required to ensure harmony with tri-quaternions of which our present biquaternions, as also octonions, are particular cases.

This applies also to quaternions, but not to extensive quantities, nor is it true for linear algebras in general.

In addition, quaternions was one of the themes of his address as president of the mathematical section of the British Association in 1871.

Neither of these men professed to employ the calculus itself, but they recognized fully the extraordinary clearness of insight which is gained even by merely translating the unwieldy Cartesian expressions met with in hydrokinetics and in electrodynamics into the pregnant language of quaternions.

Hamilton's Quaternions.

The comparative motion of two points at a given instant is capable of being completely expressed by one of Sir William Hamiltons Quaternions,the tensor expressing the velocity ratio, and the versor the directional relation.

Thus every quaternion may be written in the form q Sq+Vq, where either Sq or Vq may separately vanish; so that ordinary algebraic quantities (or scalars, as we shall call them) and pure vectors may each be regarded as special cases of quaternions.

Synonyms:

3, triplet, terzetto, trinity, trio, III, tierce, tercet, trine, deuce-ace, digit, ternary, leash, triad, trey, troika, three, threesome, figure,

Antonyms:

ordinal, single, untie, integrate, differentiate,