arithmetical ration.

Brit.

/ˌarᵻθˌmɛtᵻkl ˈreɪʃɪəʊ/, U.S.

/ˌɛrɪθˌmɛdək(ə)l ˈreɪʃ(i)oʊ/

Origin: Formed within English, by compounding; modelled on a Latin lexical item. Etymons: arithmetical adj., ratio n.

Etymology: < arithmetical adj. + ratio n., after post-classical Latin arithmetica ratio (5th cent.). Compare earlier geometrical ratio n.

Mathematics.

1. The amount by which one number or magnitude exceeds another; = difference n.¹ 4a. Contrasted with geometrical ratio.

ΘΚΠ

the world > relative properties > number > arithmetic or algebraic operations > [noun] > division > result of > remainder > after subtraction

differencec1392

resolvend1667

arithmetical ratio1718

semi-difference1766

1718 A. Malcolm New Treat. Arithmetick & Bk.-keeping vi. 43 The difference is called the Arithmetical Ratio (or Relation) of the two Numbers compared; so 5 is the Arithmetical Ratio betwixt 12 and 7.

1774 W. Perry Man of Business iv. 162 Of these numbers 6 and 3; the difference, or arithmetical ratio, is 6 − 3 = 3.

1842 G. R. Perkins Treat. Algebra vi. 191 When the arithmetical ratio of any two terms is the same as the ratio of any other two terms, the four terms together form an arithmetical proportion.

1999 D. M. Jesseph Squaring Circle iii. 90 The arithmetical ratio of two quantities is formed considering the simple difference between them, while the geometrical ratio of two quantities compares them as part to whole.

2. A manner or mode of change in which successive quantities form an arithmetical progression; an arithmetical progression.Used esp. with allusion to Thomas Malthus and his work on the rate of increase of populations (cf. Malthusian adj.).

ΘΚΠ

the world > relative properties > number > mathematical number or quantity > numerical arrangement > [noun] > set > sequence > progression

progressionc1450

arithmetical progression1553

geometrical progression1557

geometric progression1696

geometric ratio1736

arithmetical ratio1798

geometrical ratio1798

arithmetic progression1886

harmonic series1964

1798 T. R. Malthus Ess. Princ. Population i. 14 Population..increases in a geometrical ratio. Subsistence increases only in an arithmetical ratio.

1845 Brit. Q. Rev. 2 434 He [sc. Malthus] asserted that the tendency of human increase was always in geometrical ratio, 1.2.4.8.16.32.64, &c., and the increase of food only in an arithmetical ratio, as 1.2.3.4.5.6.7.8, &c.

1914 C. H. Bromley & H. R. Cobleigh Math. Pract. Engineer ii. 48 A series of numbers are said to progress in an arithmetical ratio when the differences between any two numbers is the same.

1998 Toronto Star (Nexis) 18 July m6 Malthus stated his ‘law’ that human population tends to increase in a geometric ratio, while food supplies increase in an arithmetical ratio. In other words, it doesn't take long for population increase to outstrip the food supply.

This is a new entry (OED Third Edition, March 2012; most recently modified version published online December 2021).

单词	arithmetical ratio
释义	arithmetical ration. Brit. /ˌarᵻθˌmɛtᵻkl ˈreɪʃɪəʊ/, U.S. /ˌɛrɪθˌmɛdək(ə)l ˈreɪʃ(i)oʊ/ Origin: Formed within English, by compounding; modelled on a Latin lexical item. Etymons: arithmetical adj., ratio n. Etymology: < arithmetical adj. + ratio n., after post-classical Latin arithmetica ratio (5th cent.). Compare earlier geometrical ratio n. Mathematics. 1. The amount by which one number or magnitude exceeds another; = difference n.¹ 4a. Contrasted with geometrical ratio. ΘΚΠ the world > relative properties > number > arithmetic or algebraic operations > [noun] > division > result of > remainder > after subtraction differencec1392 resolvend1667 arithmetical ratio1718 semi-difference1766 1718 A. Malcolm New Treat. Arithmetick & Bk.-keeping vi. 43 The difference is called the Arithmetical Ratio (or Relation) of the two Numbers compared; so 5 is the Arithmetical Ratio betwixt 12 and 7. 1774 W. Perry Man of Business iv. 162 Of these numbers 6 and 3; the difference, or arithmetical ratio, is 6 − 3 = 3. 1842 G. R. Perkins Treat. Algebra vi. 191 When the arithmetical ratio of any two terms is the same as the ratio of any other two terms, the four terms together form an arithmetical proportion. 1999 D. M. Jesseph Squaring Circle iii. 90 The arithmetical ratio of two quantities is formed considering the simple difference between them, while the geometrical ratio of two quantities compares them as part to whole. 2. A manner or mode of change in which successive quantities form an arithmetical progression; an arithmetical progression.Used esp. with allusion to Thomas Malthus and his work on the rate of increase of populations (cf. Malthusian adj.). ΘΚΠ the world > relative properties > number > mathematical number or quantity > numerical arrangement > [noun] > set > sequence > progression progressionc1450 arithmetical progression1553 geometrical progression1557 geometric progression1696 geometric ratio1736 arithmetical ratio1798 geometrical ratio1798 arithmetic progression1886 harmonic series1964 1798 T. R. Malthus Ess. Princ. Population i. 14 Population..increases in a geometrical ratio. Subsistence increases only in an arithmetical ratio. 1845 Brit. Q. Rev. 2 434 He [sc. Malthus] asserted that the tendency of human increase was always in geometrical ratio, 1.2.4.8.16.32.64, &c., and the increase of food only in an arithmetical ratio, as 1.2.3.4.5.6.7.8, &c. 1914 C. H. Bromley & H. R. Cobleigh Math. Pract. Engineer ii. 48 A series of numbers are said to progress in an arithmetical ratio when the differences between any two numbers is the same. 1998 Toronto Star (Nexis) 18 July m6 Malthus stated his ‘law’ that human population tends to increase in a geometric ratio, while food supplies increase in an arithmetical ratio. In other words, it doesn't take long for population increase to outstrip the food supply. This is a new entry (OED Third Edition, March 2012; most recently modified version published online December 2021). < n.1718
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