multiplication
(ˌmʌltɪplɪˈkeɪʃən)
[a. F. multiplication (12th c.), ad. L. multiplicātiōn-em, n. of action f. multiplicāre to multiply.]
1. a. The act or process of multiplying, or increasing the quantity or amount of, a thing; the state of being multiplied or increased. Now rare exc. as coloured by sense 3.
| c 1384 Chaucer H. Fame ii. 312 (Fairf. MS.) Euerych ayre other stereth More and more and speche vpbereth..Ay through multiplicacion Til hyt be atte house of Fame. c 1450 Lovelich Grail xlviii. 364 Thus there As Alle these good men sete, Fulfylled they were with Alle Manere of Mete; but in place as the Synneris were, Non Multiplicacion was not there. 1593 R. Harvey Philad. 104 The ouerthrow of contraries is the generation of concord, and multiplication of consent. 1626 Bacon New Atl. (1900) 41 Wee represent also all Multiplications of Light, which wee carry to great Distance. 1644 Evelyn Diary 17 Nov., Looking-glasses, which render a strange multiplication of things resembling divers most richly-furnish'd roomes. 1758 Johnson Idler No. 85 ¶1 One of the peculiarities which distinguish the present age is the multiplication of books. 1863 E. V. Neale Anal. Th. & Nat. 37 The cottage becomes a mansion, the mansion a palace, the palace a town, simply by the multiplication of its parts. 1881 Westcott & Hort Grk. N.T. Introd. §8 Repeated transcription involves multiplication of error. 1888 Brackenbury Field Works 46 The..strength of the defence consisted in..Multiplication of tiers of fire [etc.]. |
b. of words. (
Cf. multiply v. 1 b.)
| 1651 Hobbes Leviath. ii. xxx. 182 Multiplication of words in the body of the Law, is multiplication of ambiguity. 1709 Berkeley Th. Vision §134 Wks. 1871 I. 97 No multiplication of words will ever suffice to make them understand the truth. 1709 Strype Ann. Ref. I. xxxviii. 396 After a multiplication of language on both sides, Malvisier departed. |
2. Propagation of animals and plants.
| 1387 Trevisa Higden (Rolls) I. 255 Þere is more multiplicacioun and encrese of men and children in þe norþ contray þan in þe south. 1398 ― Barth. De P.R. xvii. ii. (1495) 595 Some trees haue multyplycacyon by graffynge of stockes. 1426 Lydg. in Pol. Poems (Rolls) II. 140 That he may se his generacioun Unto the forteth multiplicacioun Victoriously for to regnen here. 1662 Stillingfl. Orig. Sacræ iii. iv. §9 Wee have yet cause to beleeve that there was a more than ordinary multiplication in the posterity of Noah after the flood. 1838 Penny Cycl. XI. 18/2 The artificial multiplication of that species in gardens. 1845 Mill Diss. & Disc. II. 198 If..it is intended that the law..should assume a control over the multiplication of the people. |
3. Math. a. The process of finding the quantity produced (see
product) by the summation of a given quantity (called the
multiplicand) taken as many times as there are units in another given quantity (called the
multiplier); or, in the case of a fractional multiplier, of finding the same fraction of the multiplicand as the multiplier is of unity.
compound multiplication:
† (
a) see
quot. 1706; (
b) see
quot. 1859 and
compound a. 2 b (b).
simple multiplication,
† single multiplication: see
quots. 1706, 1854.
| 1390 Gower Conf. III. 89 Be which [sc. Arithmetic] multiplicacioun Is mad and diminucioun Of sommes. c 1425 Crafte Nombrynge (E.E.T.S.) 21 Multiplicacioun is a bryngynge to-geder of 2 thynges in on nombur, þe quych on nombur contynes so mony tymes on, howe mony tymes þere ben vnytees in þe nowmbre of þat 2, as twyes 4 is 8. 1542 Recorde Gr. Artes (1575) 122 Multiplication is suche an operation, that by two summes produceth the thirde. 1690 Leybourn Curs. Math. 14 Multiplication may be fitly termed a Compendium of Addition. 1706 Phillips (ed. 6) s.v., Single Multiplication is when the Numbers given, consist each of them of one only Figure; as if 5 were to be multiply'd by 3, 9 by 6. Ibid. s.v., Compound Multiplication, is when either one or both Numbers given, consist of more Figures than one; as if 134 were to be multiply'd by 2, or 1232 by 23. Ibid. s.v., In Geometry, Multiplication, changes the Species or Kind; Thus a Right-line multiply'd by a Right-line, produces a Rectangle, or Plane; and that Rectangle, multiply'd again by another Line, produces a Solid. 1854 Orr's Circ. Sci., Math. 10 When the quantities are..all of one denomination, the operation is called simple multiplication. Ibid. 162 The sign × placed between two quantities denotes the multiplication of those quantities together. 1859 B. Smith Arith. & Algebra (ed. 6) 111 Compound Multiplication is the method of finding the amount of any proposed compound number, that is, of any number composed of different denominations. |
| fig. 1699 South Serm. (1823) III. 355 Society and converse..being a kind of multiplication of himself into every person of the company he converses with. |
† b. table of multiplication, multiplication table.
| 1594 Blundevil Exerc. i. iv. (1636) 10 Before I teach you the true order of multiplying, I thinke it good to set you downe a Table of Multiplication. 1706 W. Jones Syn. Palmar. Matheseos 18 All the variety that can happen..is express'd in the following Table of Multiplication. |
† c. Used for: Product.
Obs. rare—1.
| 1586 T. B. La Primaud. Fr. Acad. (1587) 531 The number of 63. which is the multiplication of seven by nine. |
d. In
Higher Algebra, used in extended sense for: The successive application of operators.
| 1843 Sir W. R. Hamilton in Trans. Royal Irish Acad. (1848) XXI. 257 We have now the system of the two equations, q{pp} = q{p}q; q{pp} = qq{p}; q{pp} and q{pp} being those two distinct quaternion products which arise from the multiplication of the same two quaternion factors, q and q{p}, with two different arrangements of those factors. |
† 4. Alch. The art of ‘multiplying’.
Obs.| 1390 Gower Conf. II. 88 This Ston..makth multiplicacioun Of gold, and the fixacioun It causeth. 1471 Ripley Comp. Alch. xi. i. in Ashm. (1652) 181 Multyplycacyon..ys..dyfynyd, Augmentacyon yt ys of that Elixer indede, In goodnes, in quantyte, both for Whyt and Rede. 1543 [see multiply v. 6]. 1584 R. Scot Discov. Witchcr. xiv. i. (1886) 294 The art or rather the craft of Alcumystrie, otherwise called Multiplication. 1612 Woodall Surg. Mate Wks. (1653) 273 Multiplication by projection, is of a body amalgamated from 7. to 10. from 10. to 50. from 50. to 100. &c. according to the force and quantity of the tincture. a 1661 Fuller Worthies (1662) iii. 204 1696 in Phillips. |
5. Bot. Increase in the number of whorls or in the number of organs in a whorl.
| 1849 Balfour Man. Bot. §653 Multiplication, or an increase of the number of parts, gives rise to changes in plants. Ibid., Multiplication causes a repetition of successive whorls, which still follow the law of alternation. 1880 A. Gray Struct. Bot. vi. §3 (ed. 6) 179. |
6. attrib.:
multiplication constant or
factor Nuclear Physics, in nuclear fission, the ratio by which the number of neutrons increases during a period equal to the lifetime of a neutron;
multiplication sign, the sign × placed between two quantities to denote their multiplication; also
fig.;
multiplication table, a table of products of factors taken in pairs, usually beginning with ‘twice one are two’ (2 × 1
= 2) and going up to some assumed limit. (See also 3 b.)
| 1956 A. H. Compton Atomic Quest 137 These ‘delayed’ neutrons..make the difference between a multiplication constant of less than one and greater than one. 1962 Newnes Conc. Encycl. Nucl. Energy 111/1 The actual number of neutrons per fission varies considerably, but has an average value of 2·5. This is a high enough gain per cycle to suggest that a chain-reacting system of uranium could be made with a multiplication constant of at least unity. |
| 1941 E. Fermi Coll. Papers (1965) II. 89 The chain reaction may reach a steady state only when the multiplication factor of the neutrons (including neutron losses due to diffusion outside of the reacting mass) is equal to 1. 1974 Encycl. Brit. Macropædia XIII. 305/1 If a fission bomb is to be made, the multiplication factor must be as large as possible. |
| 1907 W. D. Eggar Elem. Algebra i. 4 When a number is written in front of a bracket without a sign following it, thus 10(6 + 5), the multiplication sign is understood, just as when we write 10a. 1908 W. Owen Let. 20 July (1967) 46 Best love, and a ‘multiplication sign’ (×) from your ever loving W. 1973 P. M. Aitchison et al. Form Two Maths. vi. 67 Remember that a multiplication sign connects factors. |
| 1674 S. Jeake Arith. (1696) 22 To learn by heart the Table commonly called Multiplication Table. 1709 J. Ward Yng. Math. Guide i. ii. §4 (1734) 15 Multiplication Table. 1864 Bowen Logic xi. 356 Our conclusions..are as absolute as the truths of the multiplication-table. 1871 Routledge's Ev. Boy's Ann. 277 Some young scamp who has learned the whole multiplication table of mischief..before he can repeat the sevens' column in arithmetic. |
Hence
multipliˈcational a.| 1868 A. Sandeman Pelicotetics 47 The laws of multiplicational equivalence. |