Determinans

Determinans is a historical term found in Latin mathematical literature to refer to what is nowadays called the determinant. In that sense, it designates a single scalar quantity associated with a square matrix, one that governs the solvability of linear systems, orientation, and volume scaling under linear transformations.

Etymology: from Latin determinans, the present participle of determinare, meaning "that which determines" or "deciding." In early Latin works the word could be used to describe a quantity which determines some property of a matrix or system rather than the English noun "determinant" itself; the sense evolved as the subject was translated into vernacular languages.

Historical usage: The concept of a determinant arose in the 17th–18th centuries in studies of linear systems and algebra. Foundational figures such as Leibniz and Cramer contributed to its development. In Latin editions of their work, determinans appeared as the term for what is now standardized as determinant; over the 19th century the modern English and European terminology settled on determinant, and determinans fell out of active use.

Modern status: Today determinans is largely of historical interest, encountered in discussions of the history of mathematics or in translations of older texts. In contemporary mathematics, the determinant is defined axiomatically as a multilinear alternating form or via upper-triangularization, with no use of the archaic term determinans in standard practice.