mid-14c., multiplicacioun, "any increase in size, number, or amount; act or process of increasing in number," from Old French multiplicacion (12c.) "multiplication, duplication; multiplicity, diversity," from Latin multiplicationem (nominative multiplicatio), noun of action from past-participle stem of multiplicare "to multiply, increase" (see multiply). The arithmetical sense of "process in which one number is considered as an operator on another" is attested from late 14c.

1857 as a term in biology, "reproduce, grow by multiplication of elementary parts;" see proliferation. General sense, of things, etc., "increase greatly in numbers," by 1961. Related: Proliferated; proliferating.

mid-15c., in mathematics, "the total or sum, the sum of an addition or product of a multiplication," from Medieval Latin resultantem (nominative resultans), present participle of resultare "to result" (see result (v.)). Sense in mechanics is from 1815.

late 14c., from Latin geometricus "of geometry" (from geometria; see geometry) + -al. Since 16c. it has been opposed to arithmetical in ratio, proportion, etc., reflecting the fact that problems of multiplication formerly were dealt with by geometry, not arithmetic. Related: Geometrically.

early 15c., "mathematical quantity obtained by multiplication," from Medieval Latin productum, in classical Latin "something produced," noun use of neuter past participle of producere "bring forth" (see produce (v.)). General sense of "anything produced" is attested in English from 1570s; political economy sense of "what is produced commercially for sale" is by 1890.

late 14c., divisioun, "act of separating into parts, portions, or shares; a part separated or distinguished from the rest; state of being at variance in sentiment or interest," from Old French division and directly from Latin divisionem (nominative divisio), noun of action from past-participle stem of dividere "to divide" (see divide (v.)).

Military sense "portion of an army, fleet, or ship's company" is from 1590s. Mathematical sense of "operation inverse to multiplication" is from late 14c. The mathematical division sign supposedly was invented by British mathematician John Pell (1611-1685) who taught at Cambridge and Amsterdam.

mid-12c., multeplien, "to cause to become many, cause to increase in number or quantity," from Old French multiplier, mouteplier (12c.) "increase, get bigger; flourish; breed; extend, enrich," from Latin multiplicare "to increase," from multiplex (genitive multiplicis) "having many folds, many times as great in number," from combining form of multus"much, many" (see multi-) + -plex "-fold," from PIE root *plek- "to plait."

Intransitive sense of "grow or increase in number or extent" (especially "to have children, produce offspring") is from mid-14c. Mathematical sense "perform the process of multiplication" is attested from late 14c. Related: Multiplied; multiplying.

"government by bureaus," especially "tyrannical officialdom," excessive multiplication of administrative bureaus and concentration of power in them, in reference to their tendency to interfere in private matters and be inefficient and inflexible, 1818, from French bureaucratie, coined by French economist Jean Claude Marie Vincent de Gournay (1712-1759) on model of democratie, aristocratie, from bureau "office," literally "desk" (see bureau) + Greek suffix -kratia denoting "power of" (see -cracy).

That vast net-work of administrative tyranny ... that system of bureaucracy, which leaves no free agent in all France, except for the man at Paris who pulls the wires. [J.S. Mill, Westminster Review vol. xxviii, 1837]

bureaucrat, &c. The formation is so barbarous that all attempt at self-respect in pronunciation may perhaps as well be abandoned. [Fowler]

"cold, factual person," from the name of the school-board superintendent and mill-owner in Dickens' "Hard Times" (1854):

THOMAS GRADGRIND, sir. A man of realities. A man of facts and calculations. A man who proceeds upon the principle that two and two are four, and nothing over, and who is not to be talked into allowing for anything over. Thomas Gradgrind, sir - peremptorily Thomas - Thomas Gradgrind. With a rule and a pair of scales, and the multiplication table always in his pocket, sir, ready to weigh and measure any parcel of human nature, and tell you exactly what it comes to. It is a mere question of figures, a case of simple arithmetic. ....

In such terms Mr. Gradgrind always mentally introduced himself, whether to his private circle of acquaintance, or to the public in general. In such terms, no doubt, substituting the words 'boys and girls,' for 'sir,' Thomas Gradgrind now presented Thomas Gradgrind to the little pitchers before him, who were to be filled so full of facts.

Indeed, as he eagerly sparkled at them from the cellarage before mentioned, he seemed a kind of cannon loaded to the muzzle with facts, and prepared to blow them clean out of the regions of childhood at one discharge. He seemed a galvanizing apparatus, too, charged with a grim mechanical substitute for the tender young imaginations that were to be stormed away.