firm adj.

late 14c., ferm, "strong, steady" (of things), "permanent, enduring" (of agreements), "steadfast, steady" (of persons), "sound, well-founded" (of arguments), from Old French ferm "strong, vigorous; healthy, sound; steadfast, loyal, faithful" (12c.), from Latin firmus "strong, steadfast, enduring, stable," figuratively "constant, steadfast, trusty, faithful," from suffixed form of PIE root *dher- "to hold firmly, support." The spelling return to -i- in late 1500s was modeled on Latin. Related: Firmly; firmness.

"business house," 1744, according to Barnhart from German Firma "a business, name of a business," originally "signature," from Italian firma "signature," from firmare "to sign," from Latin firmare "make firm, affirm," in Late Latin, "confirm (by signature)," from firmus "strong; stable," figuratively "constant, trusty" (see firm (adj.)).

c. 1300, fermen "make firm, establish," from Old French fermer "consolidate; fasten, secure; build, set up; fortify" (12c.) or directly from Latin firmare "make firm; affirm; strengthen, fortify, sustain; establish, prove, declare," from firmus "strong, steadfast, stable" (see firm (adj.)). Intransitive use, "become firm" is from 1879; with up (adv.) from 1956. Related: Firmed; firming.