The term determiner is newish (about 80 years old), and hasn't had much uptake in school grammars. The study, in English, of French and other modern languages has employed the term DETERMINATIVE ADJECTIVE since at least 1806, when Dufief wrote,
"S. Why do you call them determinative?
M. Because, when they are expressed before nouns, we know how often the object represented by the noun is repeated" (p. 40).
In 1924, Palmer was the first to try to corral this group of theretofore-heterogeneous English words by adopting the concept from the French analysis.
"To group with the pronouns all determinative adjectives (eg
article-like, demonstratives, possessives, numerals, etc.), shortening
the term to determinatives (the "déterminatifs" of the French
grammarians) firstly because there are divergent opinions as to
whether they are adjectives or pronouns, and secondly, because most of
the members of this category may be used indifferently as pronouns or
as modifiers of nouns" (p 24).
And, in 1933, Bloomfield introduced the slightly different term, DETERMINER, into English linguistics when he wrote,
"our limiting adjectives fall into two sub-classes of determiners and
numeratives ... The determiners are defined by the fact that
certain types of noun expressions (such as house or big house) are
always accompanied by a determiner (as, this house, a big house)" (p