Definition - The dependence of one clause upon another clause.

1. The traditional name for it was hypotaxis.

Example -
I went to bed because I was sick.
(The highlighted clause is dependent on the other, thus it is called a subordinate clause.)

Etymology -
The term derives from the Latin subordinare, place in a lower order (from Latin sub, under + ordinare, arrange).

Oxford English Dictionary -
Its first citation is from 1857:
"When two propositions … are so united into a single thought or sentiment, that one proposition … forms the complement of the other proposition, the former proposition is said to be subordinate to the latter, and this kind of union is called subordination."
(J. W. Gibbs Philol. Studies 115)

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