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. 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.
c. 1430. Art Nombryng (E.E.T.S.), 12. The nombre that shewith þe quocient.
1542. Recorde, 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.
1614. T. Bedwell, Nat. Geom. Numbers, i. 8. The quotients of 60, by 1, 2, 3,… are 60, 30, 20.
1695. Alingham, Geom. Epit., 73. If … I divide 54 by 3 the quotient is 18.
1727–41. Chambers, Cycl., s.v. Division, For 3 being only contained twice in 8, the last number in the quotient will be 2.
1840. Lardner, Geom., 124. Multiply b by c and divide the product by a, and the quotient will be d.
1884. A. 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, line, number; quotient representation (see quot. 1884 above).
c. 1430. Art Nombryng (E.E.T.S.), 12. Above þat figure … me most sette a cifre in ordre of the nombre quocient.
1542. Recorde, Gr. Artes, 48 b. That is called the quotiente numbre. Ibid. (1557), Whetst., K ij. The roote .2. I sette behind the quotiente line.
1709. J. Ward, Introd. Math., I. xi. § 7 (1734), 139. You must Increase … the Divisor with Thrice the Quotient Figure.
1889. F. H. Hill, in Universal Rev., 15 Jan., 7. Equal electoral districts, quotient representation of the population,… are a deduction from the democratic principle.
† 2. a. = QUOTUM. Obs. rare.
1621. Bp. Mountagu, Diatribæ, 511. The first of their Apples were offered to other gods: and for the quotient, it was a Tenth.
1641. H. L’Estrange, God’s Sabbath, 62–3. 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.
1659. T. Pecke, Parnassi Puerp., 82. God is but One. Hells Quotient, none assign.
