1832 in mathematics and physics, "a quantity which is assumed to be invariable throughout," from constant (adj.), which is attested from 1753 in mathematics. The general sense "that which is not subject to change" (1856) is a figurative extension from this.
late 14c., "steadfast, resolute; patient, unshakable; fixed or firm in mind," from Old French constant (14c.) or directly from Latin constantem (nominative constans) "standing firm, stable, steadfast, faithful," present participle of constare"to stand together," from assimilated form of com "with, together" (see con-) + stare "to stand," from PIE root *sta- "to stand, make or be firm."
Meaning "steadfast in attachment to a person or cause" is from early 15c. Of actions and conditions, "fixed, not varying" (1540s); "continual, enduring" (1650s). Meaning "regularly recurring" is from 1817. Related: Constantly.
"attentive, devoted, constant in application," 1530s, from Latin assiduus "attending; continually present, incessant; busy; constant," from assidere/adsidere "to sit down to, sit by" (thus "be constantly occupied" at one's work); from ad "to" (see ad-) + sedere "to sit," from PIE root *sed- (1) "to sit." The word acquired a taint of "servile" in 18c. Related: Assiduously; assiduousness.
"diligent and assiduous application, constant attention," 1540s, from Latin sedulitas "assiduity, application," noun of quality from sedulus "attentive, diligent, busy" (see sedulous).