geometrical ration.
/ˌdʒiːəˌmɛtrᵻkl ˈreɪʃɪəʊ/, /dʒɪəˌmɛtrᵻkl ˈreɪʃɪəʊ/, U.S. /ˌdʒiəˌmɛtrək(ə)l ˈreɪʃ(i)oʊ/ Mathematics.
1. The relation between two magnitudes as determined by the number of times that one contains the other. Contrasted with arithmetical ratio.Now usually called simply ratio (ratio n. 3a).
ΚΠ
1708 G. Vaux tr. J. C. Sturm Mathesis Juvenilis III. 345 The Geometrical Ratio [L. geometrica ratio] of them all..is very intricate for Tyro's; and therefore he hath reduced their Praxis into an universal Horography.
1806 C. Hutton Course Math. (ed. 5) I. 110 Of these two numbers 6 and 3, the difference, or arithmetical ratio, is 6−3 or 3, but the geometrical ratio is 6/ 3 or 2.
1906 O. A. Kenyon tr. J. Claudel Handbk. Math. i. v. 114 When the word ratio is used alone, a geometrical ratio is always understood.
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 a geometric progression; a geometric progression.Used esp. with allusion to Thomas Malthus and his work on the rate of increase of populations (see 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.
1824 Lancet 17 Apr. 88/1 Steam increases or expands in a geometrical ratio.
1859 C. Darwin Origin of Species iii. 65 All plants and animals are tending to increase at a geometrical ratio.
1910 Bull. Amer. Inst. Mining Engineers Oct. 791 It is assumed that further dilution would not decrease the solvent action of cupric salt in a geometrical ratio.
1995 Foreign Policy No. 100. 70 Malthus asserted that poverty and disease are unavoidable, since population increases by geometrical ratio and the means of subsistence by arithmetical ratio.
This entry has been updated (OED Third Edition, March 2012; most recently modified version published online March 2022).
<
n.1708