"to keep moving round and round without purpose in a mass," 1874 (originally of cattle, implied in milling), originally of cattle, from mill (n.1) on resemblance to the action of a mill wheel. Related: Milled.
Old English stempan "to pound in a mortar," from Proto-Germanic *stamp- (source also of Old Norse stappa, Danish stampe, Middle Dutch stampen, Old High German stampfon, German stampfen "to stamp with the foot, beat, pound," German Stampfe "pestle"), from nasalized form of PIE root *stebh- "to support, place firmly on" (source also of Greek stembein "to trample, misuse;" see staff (n.)). The vowel altered in Middle English, perhaps by influence of Scandinavian forms.
Sense of "strike the foot forcibly downwards" is from mid-14c. The meaning "impress or mark (something) with a die" is first recorded 1550s. Italian stampa "stamp, impression," Spanish estampar "to stamp, print," French étamper (13c., Old French estamper) "to stamp, impress" are Germanic loan-words. Related: Stamped; stamping. To stamp out originally was "extinguish a fire by stamping on it;" attested from 1851 in the figurative sense. Stamping ground "one's particular territory" (1821) is from the notion of animals. A stamped addressed envelope (1873) was one you enclosed in a letter to speed or elicit a reply.
mid-15c., "instrument for crushing, stamping tool," from stamp (v.). Especially "instrument for making impressions" (1570s). The meaning "downward thrust or blow with the foot, act of stamping" is from 1580s.
The sense of "official mark or imprint" (to certify that duty has been paid on what has been printed or written) dates from 1540s; it was transferred 1837 to designed, pre-printed adhesive labels issued by governments to serve the same purpose as impressed stamps. U.S. postage stamps were issued under the Post Office Act of March 3, 1847; Britain had them earlier, under the Postage Act of 1839. German Stempel "rubber stamp, brand, postmark" represents a diminutive form. Stamp-collecting is by 1862 (compare philately).
Middle English mille, "building fitted to grind grain," Old English mylen "a mill" (10c.), an early Germanic borrowing from Late Latin molina, molinum "mill" (source of French moulin, Spanish molino), originally fem. and neuter of molinus "pertaining to a mill," from Latin mola "mill, millstone," related to molere "to grind," from PIE root *mele- "to crush, grind." The -n- gradually was lost in English but survives in the surname Milner. Also from Late Latin molina, directly or indirectly, are German Mühle, Old Saxon mulin, Old Norse mylna, Danish mølle, Old Church Slavonic mulinu.
The meaning "mechanical device for grinding grain for food" is from 1550s. The broader sense of "machine for grinding or pulverizing any solid substance" is attested from 1670s. Other types of manufacturing machines driven by wind or water, that transform raw material by a process other than grinding began to be called mills by early 15c. Sense of "large building fitted with machinery for manufacturing" is from c. 1500. In old slang also "a typewriter" (1913); "a boxing match or other pugilistic bout" (1819).
1550s, "subject to mechanical operations carried on in a mill;" 1560s, "to grind in or as in a mill, reduce to fine particles;" from mill (n.1). Meaning "to flute the edge (of a coin, etc.) is from 1724. Related: milled; milling.
"one-tenth of a cent," 1786, an original U.S. currency unit but now used only for tax calculation purposes, shortening of Latin millesimum "one-thousandth part," from mille "a thousand" (see million). Formed on the analogy of cent, which is short for Latin centesimus "one hundredth" (of a dollar). Compare mil.
1879, "instrument for stamping by hand with ink, having letters or numbers cast in vulcanized rubber," from rubber (n.1) + stamp (n.). The figurative sense of "thing or institution whose power is formal but not real" is by 1901 (on the notion of rubber-stamping "approved" or some such thing on everything given to it by the real powers). The verb is by 1889; in the figurative sense by 1912. As an adjective by 1931. Related: Rubber-stamped; rubber-stamping.