| 释义 |
quotient|ˈkwəʊʃənt|
Forms: 5 quocient, (quocyens), 6– quotient.
[f. L. quotiens how many times, how often (f. quot how many), erron. taken as a ppl. stem in -ent; cf. F. quotient (earlier quotiens), It. quoziente, Sp. quociente.]
1. Math.
a. The result obtained by dividing one arithmetical or algebraic quantity by another; the number of times one number is contained in another as ascertained by division.
14..Mann. & Househ. Exp. (Roxb.) 439 Owt of that nowmber take as many tymes clx. as ye may, beyinge for euery tyme a quocyens. c1430Art Nombryng (E.E.T.S.) 12 The nombre that shewith þe quocient. 1542Recorde Gr. Artes 129 Then I seke howe often the diuisor maye be founde in the diuident, and that I fynde 3 tymes, then set I 3 in the thyrde lyne for the quotient. 1614T. Bedwell Nat. Geom. Numbers i. 8 The quotients of 60, by 1, 2, 3,..are 60, 30, 20. 1695W. Alingham Geom. Epit. 73 If..I divide 54 by 3 the quotient is 18. 1727–41Chambers Cycl. s.v. Division, For 3 being only contained twice in 8, the last number in the quotient will be 2. 1840Lardner Geom. 124 Multiply b by c and divide the product by a, and the quotient will be d. 1884A. Paul Hist. Reform ii. 29 The total was to be divided by 558, and the quotient to be deemed the proportion of voters entitled to elect one member.
b. attrib., as quotient figure, quotient line, quotient number, quotient ring; quotient representation (see quot. 1884 above); quotient group = factor group s.v. factor n. 9.
c1430Art Nombryng (E.E.T.S.) 12 Above þat figure..me most sette a cifre in ordre of the nombre quocient. 1542Recorde Gr. Artes 48 b, That is called the quotiente numbre. 1557― Whetst. K ij, The roote .2. I sette behind the quotiente line. 1709J. Ward Introd. Math. i. xi. §7 (1734) 139 You must Increase..the Divisor with Thrice the Quotient Figure. 1889Universal Rev. 7 Jan., Equal electoral districts, quotient representation of the population,..are a deduction from the democratic principle. 1893Bull. N.Y. Math. Soc. III. 74 The quotient-group of any two consecutive groups in the series of composition of any group is a simple group. 1911W. Burnside Theory of Groups of Finite Order (ed. 2) iii. 39 Herr Hölder has introduced the symbol G/H to represent this group; he calls it the quotient of G by H, and a factor-group of G. 1958R. V. Andree Mod. Abstract Algebra iv. 101 The order of the quotient group is the order of G divided by the order of H, providing G is finite. Ibid. viii. 188 The term quotient ring is also used because of the similarity to the concept of quotient groups. 1965Patterson & Rutherford Elem. Abstract Algebra iii. 101 If S is an ideal in the ring R... The set of all cosets of S in R is a ring:..this is called the..quotient ring of R by S. 1972F. J. Budden Fascination of Groups xxi. 409 A group which resolves into a succession of cyclic quotient groups in this way is called a ‘soluble’ group.
†2.
a. = quotum. Obs. rare.
1621Bp. R. Montagu Diatribæ 511 The first of their Apples were offered to other gods: and for the quotient, it was a Tenth. 1641H. L'Estrange God's Sabbath 63 The fourth Commandment..declareth also his will concerning the quotient..so that one [day] in a week he must have.
†b. Number, total. Obs. rare—1.
1659T. Pecke Parnassi Puerp. 82 God is but One. Hells Quotient, none assign. |