5. a. Math. Applied to quantities or ratios which can be expressed without the use of radical signs. {dag}rational to (see quot. 1614). Also rational fraction (see quot. 1823).
1570 BILLINGSLEY Euclid v. def. iii, Such magnitudes or quantities, which may be expressed by numbre, are called rationall. 1614 T. BEDWELL Nat. Geom. Numbers i. 2 The Base and Height are said to be rational one to another, when as the rate or reason of both may be expressed by a number of the same measure given. 1660 BARROW Euclid x. prop. lxi. 237 The square of a binomiall line..applyed unto a rationall line. 1706 W. JONES Syn. Palmar. Matheseos 116 Rational Quantities may be reduced to the Form of any assign'd Root. 1798 HUTTON Course Math. (1827) I. 82 The square root of 3 is a surd root; but the square root of 4 is a rational root, being equal to 2. 1823 J. MITCHELL Dict. Math. Sci., Rational Fractions is the term commonly used to express those fractions which may be decomposed into other fractions, the sum of which is equal to the given fraction. 1885 WATSON & BURBURY Math. Th. Electr. & Magn. I. 41 Yi is a rational and integral function of cos {theta}. 1901 H. B. FINE College Algebra II. i. 86 An expression is called rational if it does not involve an indicated root of an expression in which a variable letter occurs. 1917 T. M. MACROBERT Functions of Complex Variable v. 89 The ratio of two polynomials is called a Rational Function. 1940 C. C. MACDUFFEE Introd. Abstract Algebra iii. 82 A quadratic equation with rational coefficients which does not have a rational root. 1946 A. A. ALBERT College Algebra iv. 111 A rational function of several symbols is any algebraic expression obtainable by formally applying a finite number of the rational operations of addition, subtraction, multiplication, and division to the symbols and numbers. 1966 R. E. JOHNSON University Algebra i. 20 There exist consecutive integers n and n + 1, but there do not exist consecutive rational numbers.
b. rational horizon: see HORIZON 3.
1625 N. CARPENTER Geog. Del. I. vi. (1635) 149 The rationall Horizon diuides the whole spheare into two equall parts. 1642 MILTON Apol. Smect. Wks. (1851) 310 The rationall horizon in heav'n is but one, and the sensible horizons on earth are innumerable. 1704 [see HORIZON 3]. 1833 HERSCHEL Astron. i. 52 If we suppose a spectator..to have his view bounded by the rational horizon.
c. (With admixture of sense 4a.) Physics. The epithet given by O. Heaviside to electrical units and equations now described as RATIONALIZED.
1882 O. HEAVISIDE in Nature 24 Aug. 391/1 If..electricity stands foremost amongst the exact sciences, it follows that its unit measures should be determined with the utmost accuracy. Yet, twenty years ago very little advance had been made toward the adoption of a rational system. 1892 Ibid. 28 July 293/1 If we let the rational practical units be the same multiples of the 'absolute' rational units as the present practical units are of their absolute progenitors, then [etc.]. 1905 Proc. R. Soc. A. LXXVI. 551 The calculations would have been the same if e had been measured in 'rational' electric units instead of those in common use, but we should then have had an experimental value equal to 4{pi} times that mentioned above. 1905 [see GIORGI]. 1911 Encycl. Brit. XXVII. 744/2 If the filament is an endless or poleless iron filament magnetized uniformly by a resultant external magnetic force H, the flux density will be expressed in rational units by the equation B = I + H. 1925 W. H. TIMBIE Elements of Electricity (ed. 2) vi. 171 In order to have Ohm's Law hold with these units, the rational oersted must be equal to 1·26 C.G.S. units. 1942 Phil. Mag. XXXIII. 487 All the above formulæ, whether those of the rational system or of the ordinary system, are entirely independent of any choice of units.
{dag}6. Gram. Of a conjunction: That indicates a reason. Obs. rare.
1678 GALE Crt. Gentiles IV. III. iii. 84 Those words..are immediately subjoined to vers 16, and are connected therewith by the rational Particle {gamma}{gagrave}{rho}, which points out the reason of that which next follows.
7. Descriptive of methods of analysis and planning that make use of calculation to bring about a projected result, esp. in economic or social organization.
1915 M. EPSTEIN tr. Sombart's Quintessence of Capitalism xii. 182 He is ever ready to adopt a newer method if it is more rational, whether in the sphere of organization, of production, or of calculation. 1926 E. GROSSMANN Methods Econ. Rapprochement 30 The most important economies will follow not from the simplification of the machinery of distribution but from a rational organization of production itself. 1930 T. PARSONS tr. Weber's Protestant Ethic 21 But in modern times the Occident has developed..a very different form of capitalism which has appeared nowhere else: the rational capitalistic organization of (formally) free labour. Ibid., Rational industrial organization, attuned to a regular market..is not, however, the only peculiarity of Western capitalism. 1943 J. A. SCHUMPETER Capitalism, Socialism & Democracy xi. 122 The rational attitude presumably forced itself on the human mind primarily from economic necessity. Ibid., When the habit of rational analysis of..the daily tasks of life has gone far enough, it turns back upon the mass of collective ideas and criticizes..them by way of such questions as why there should be kings..or tithes or property. Ibid. 123 Capitalist practice turns the unit of money into a tool of rational cost-profit calculations, of which the towering monument is double-entry book~keeping. 1969 SIMON & STEDRY in Lindzey & Aronson Handbk. Social Psychol. (ed. 2) V. xl. 272 The classical economic theory of markets with rational agents and perfect competition is a deductive theory that requires almost no contact with empirical data..to establish its propositions. 1977 A. GIDDENS Stud. in Social & Polit. Theory v. 206 Weber's characterization of modern capitalism as involving above all the 'rational' organization of resources geared to the accumulation of profit is unsatisfactory.
{dag}B. adv. Rationally. Obs. rare.
1690 LOCKE Hum. Und. III. vi. §29 If Baalam's Ass had, all his life, discours'd as rational as he did once.
C. n.1 Absol. uses of the adj.
1. a. A rational being. Chiefly in pl. = human beings. Now Obs. or rare.
1606 WARNER Alb. Eng. XIV. lxxxii. (1612) 343 Beasts silent, that with Rationales was all a-mort suppose. 1663 GERBIER Counsel 6b, Love to Art..infers the party to be a true Rational. 1688 Lond. Gaz. No. 2357/1 We must deprive our selves of our selves, as Rationals, and become more stupid then Brutes. 1755 YOUNG Centaur 103 He is a Rational, dethroning Reason; and an Animal, transgressing Appetite. 1791 PAINE Rights of Man II. iii. (1792) 21, Kings succeed each other, not as rationals, but as animals. 1828 R. CRAIG in Memorials vi. (1862) 129 Something which might exercise the mind as well as limbs of the rationals assembled there.
b. An advocate of something 'rational'.
1756 in D'Israeli Calam. Auth. (1863) 65 He [Henley] called himself 'a Rationalist', and on his death-bed repeatedly cried out, 'Let my notorious enemies know I die a Rational'. 1896 Westm. Gaz. 28 Nov. 3/2 As a 'rational',..she thought that members should be free to adopt any costume that they liked.
{dag}2. Gram. A conjunction indicating a reason.
1612 BRINSLEY Lud. Lit. 97 Coniunctions, Copulatiues, Rationals, Aduersitiues,..Expletiues, and certaine others.
3. Math. A rational quantity.
1685 J. WALLIS Alg. xcix. 373 A Fraction (in Rationals) less than the proposed (Irrational) p. 1797 STOKES in Trans. Royal Irish Acad. VI. 222 Four quadratics and a rational may be reduced at least with the same ease. 1958 D. E. LITTLEWOOD University Algebra (ed. 2) ix. 150 The set of integers K can be embedded in a field of quotients. This field of quotients is defined as the rationals. 1971 D. G. H. B. LLOYD Mod. Syllabus Algebra vi. 110 Between any two rationals a third rational can be inserted. In this respect the set of rationals differs completely from the set of naturals or the set of integers.
4. {dag}a. The rational part of man. Obs. rare{em}1. b. That which is rational or reasonable. c. A rational concept.
1698 FARQUHAR Love & Bottle II. ii, Your rational's reversed, carrying your understandings in your legs. 1874 H. SIDGWICK Meth. Ethics III. xiii. 362 This absolute end,..can be nothing but Reason itself, or the Universe of Rationals. 1898 G. MEREDITH Odes Fr. Hist. 86 They not the less were mated, and proclaimed the rational their issue.
5. pl. 'Rational' dress; knickerbockers for women.
1889 Pall Mall G. 26 Dec. 6/2 Small shoes and latter-day 'rationals'. 1895 Westm. Gaz. 2 Sept. 8/1 A mild plot amongst lady cyclists to persuade her ladyship..to adopt 'rationals'.