early 14c., "person under control or dominion of another," specifically a government or ruler, from Old French sogit, suget, subget "a subject person or thing" (12c., Modern French sujet), from noun use of Latin subiectus "lying under, below, near bordering on," figuratively "subjected, subdued," past participle of subicere, subiicere "to place under, throw under, bind under; to make subject, subordinate," from sub "under" (from PIE root *upo "under") + combining form of iacere "to throw" (from PIE root *ye- "to throw, impel"). In 14c., sugges, sogetis, subgit, sugette; form re-Latinized in English 16c.
Meaning "person or thing regarded as recipient of action, one that may be acted upon" is recorded from 1590s. Grammatical sense is recorded from 1630s, from Latin subjectum "grammatical subject," noun use of the neuter of the Latin past participle. Likewise some restricted uses in logic and philosophy are borrowed directly from Latin subjectum as "foundation or subject of a proposition," a loan-translation of Aristotle's to hypokeimenon. Meaning "subject matter of an art or science" is attested from 1540s, probably short for subject matter (late 14c.), which is from Medieval Latin subjecta materia, a loan translation of Greek hypokeimene hylē (Aristotle), literally "that which lies beneath."