De*ter"mi*nant (?), *a.* [L.
*determinans*, p. pr. of *determinare*: cf. F.
*déterminant*.] Serving to determine or limit;
determinative.

De*ter"mi*nant, *n.* **1.**
That which serves to determine; that which causes
determination.

**2.** *(Math.)* The sum of a series of
products of several numbers, these products being formed according to
certain specified laws; thus, the *determinant* of the
nine numbers

a, b, c,

a′, b′,
c′,

a′′, b′′,
c′′,

is *a b′ c′′ - a b′′ c′ +
a′ b′′ c] - a′ b c′′ +
a′′ b′ c*. The determinant is written by placing
the numbers from which it is formed in a square between two vertical
lines. The theory of *determinants* forms a very important
branch of modern mathematics.

**3.** *(Logic)* A mark or attribute,
attached to the subject or predicate, narrowing the extent of both,
but rendering them more definite and precise. *Abp.
Thomson.*