proportionalityn.

Brit.

/prəˌpɔːʃəˈnalᵻti/, U.S.

/prəˌpɔrʃəˈnælədi/,

/pərˌpɔrʃəˈnælədi/

Forms: late Middle English proporcionalitee, late Middle English–1500s proporcionalite, 1500s proportionalitie, 1500s proportionallitie, 1500s proportionalytie, 1500s– proportionality.

Origin: Of multiple origins. Partly a borrowing from French. Partly a borrowing from Latin. Etymons: French proporcionalité; Latin proportionalitat-, proportionalitas.

Etymology: < Middle French proporcionalité quality or fact of being proportional (1272 in Old French; French proportionnalité ) and its etymon post-classical Latin proportionalitat-, proportionalitas fact of being in numerical or geometrical proportion (6th cent. in Boethius), just proportion (a1200, 1686 in British sources), quality or fact of being proportional (1531 in the passage translated in quot. 1569 at sense 2) < proportionalis proportional adj. + classical Latin -tās (see -ty suffix¹; compare -ity suffix). Compare Spanish proporcionalidad (1562), Italian proporzionalità (1561).With continual proportionality (see quot. 1570 at sense 1a) compare post-classical Latin proportionalitas continua (6th cent. in Boethius). With harmonic proportionality (see quot. 1882 at sense 1b) compare post-classical Latin proportionalitas armonica (6th cent. in Boethius). Compare also post-classical Latin proportionalitas arithmetica, proportionalitas geometrica (6th cent. in Boethius).

1. Mathematics and Science.

a. The fact or an instance of being in numerical or geometrical proportion (proportion n. 9a).

ΚΠ

a1450 Musical Treat. in Speculum (1935) 10 268 (MED) As proporcion as [read is] a comparison be-twene diuerse quantites oyþir numbris, so is proporcionalitas a comparison eyþir a likenes be 2o proporcions in 3re diuerse quantiteis atte last, þe whech quan[ti]teis or numbris been callid þe termis of þat proporcionalite.

1570 H. Billingsley tr. Euclid Elements Geom. v. f. 130^v Here is to be noted that this likenes or idemptitie of proportion which is called, as before was said proportionalitie, is of two sortes: the one is continuall, the other is discontinuall.

1672 Philos. Trans. 1671 (Royal Soc.) 6 3077 This computation was founded on the Hypothesis of the proportionality of the sines of Incidence, and Refraction.

1771 Philos. Trans. 1770 (Royal Soc.) 60 244 The lines OA, AB, BC, &c. are to be taken proportional to the coefficients a, b, c, &c... To preserve the above-mentioned proportionality, [etc.].

1853 Trans. Royal Soc. Edinb. 20 89 Having assumed the proportionality of pressure to compression, he proceeds to define his coefficients.

1961 S. E. Toulmin Foresight & Understanding iii. 49 How else, then, can Aristotle's thesis be taken? In general, his practice in the Physics is to put forward, not precise equations, but at most ratios or proportionalities.

1996 S. McCall Model of Universe iv. 88 Cantor showed long ago that there exist no well-defined proportionalities among infinite sets.

b. A formula or expression stating the proportionality of two or more quantities.

ΘΚΠ

the world > relative properties > number > algebra > [noun] > expression > formula

binomial theorem1755

formula1794

Rankine's formula1868

proportionality1882

Hero's formula1886

Rutherford's law1913

Mellin transform1927

Langevin equation1943

1882 Analyst 9 50 The photodynamic vis viva at the chief centre of condensation, ½(m₃v²_λ), furnishes the following approx. harmonic proportionality:—m₀v₃v_λ:m₃v_λ²::m₃v_λ²:m₅v₃v_λ.

1954 A. Dresden tr. Van der Waerden Sci. Awakening vi. 176 The proportionality a:b::c:d means that na > mb implies nc > md, and na = mb implies nc = md, and na < mb implies nc < md, no matter how the integers m and n are chosen.

1976 Nature 27 May 301/2 The luminosity of a star of solar mass satisfies the approximate proportionality L ∝ G⁷M⁵ ∝ t³.

1986 M. Rigby et al. Forces between Molecules v. 113 In fact, our simple model leads to the conclusion that there is a proportionality between the viscosity and thermal conductivity coefficients of a rigid sphere gas, namely λ = ηc_v/m.

2. gen. The quality, character, or fact of being proportional. Formerly also occasionally in plural: †proportions (obsolete).

ΘΚΠ

the world > relative properties > order > agreement, harmony, or congruity > suitability or appropriateness > [noun] > due proportion or proportionateness

proportiona1382

equality1447

proportioningc1450

temperance1471

temperancy1526

proportionality1545

commensurability1570

equability1576

proportionableness1606

apportionateness1645

proportionateness1658

commensurateness1661

proportionability1697

1545 J. Bale Mysterye Inyquyte P. Pantolabus f. 34 After that came in ydemptyte, realyte, formalyte..potencialite, personalyte, presencialyte, proporcionalite, perticipalite [etc.].

1569 J. Sanford tr. H. C. Agrippa Of Vanitie Artes & Sci. xii. f. 25^v In like manner of proportion and proportionallitie [L. proportionalitate], and of their species.

1642 H. More Ψυχωδια Platonica sig. K6 The vast extent Of their round bodies, without outward eyes Hath view'd, told their proportionalities.

1701 N. Grew Cosmol. Sacra ii. ii. §5 All Sense, so far as Grateful, dependeth upon the Equality, or the Proportionality, of the Motion or Impression which is made.

1789 J. Bentham Introd. Princ. Morals & Legisl. xiv. 184 The necessity of making small sacrifices, in point of proportionality, for the sake of simplicity.

1830 J. F. W. Herschel Prelim. Disc. Study Nat. Philos. 152 Proportionality of the effect to its cause.

1891 M. E. Lowndes tr. H. Höffding Outl. Psychol. ii. 64 Both the parallelism and the proportionality between the activity of consciousness and cerebral activity point to an identity at bottom.

1965 B. Pearce tr. E. Preobrazhensky New Econ. 74 The confusion made between proportionality in the economy, which is objectively necessary..and the historically-transient method of achieving this proportionality on the basis of the law of value.

1992 New Republic 30 Nov. 20/2 No judge has ruled that jury lists must match census data..but from the standpoint of a court administrator it's impossible to err on the side of proportionality.

Compounds

proportionality constant n. (also constant of proportionality) Mathematics and Science the constant ratio of one variable quantity to a second to which it is proportional.

ΚΠ

1908 Proc. Royal Soc. A. 81 p. xxiii To Helmholtz belongs the merit of determining theoretically the constant of proportionality in Faraday's law of induction.

1911 Proc. Amer. Philos. Soc. 50 327 This added mass, he found would be proportional to the amount of energy present. My proportionality constant agrees with his.

1955 J. Lindhard in W. Pauli Niels Bohr & Devel. Physics 188 Accordingly, ω and the average excitation potential become proportional to Z, i.e. ℏω = I = Z.I₀. However, it was found difficult to calculate the proportionality constant I₀.

1994 Sci. News 8 Oct. 232/2 The constant of proportionality between the distance of a galaxy and its speed is now known as H₀, the Hubble constant.

proportionality factor n. (also factor of proportionality) Mathematics and Science = proportionality constant n.

ΚΠ

1892 Amer. Jrnl. Math. 14 280 There are therefore in all eight parameters to be fixed—exactly the number of coefficients, barring the factor of proportionality, that occur in the given linear transformation.

1915 Science 4 June 826/1 It will be necessary to modify most of the equations slightly by introducing a proportionality factor.

1948 P. A. Samuelson Economics xiii. 291 According to the simplified quantity theory M = kP or P = ¹/ _kM where k is a factor of proportionality.

2001 Rev. Financial Stud. 14 995 The proportionality factor by which the rate of daytime information flow exceeds that of overnight information flow.

This entry has been updated (OED Third Edition, June 2007; most recently modified version published online March 2022).

单词	proportionality
释义	proportionalityn. Brit. /prəˌpɔːʃəˈnalᵻti/, U.S. /prəˌpɔrʃəˈnælədi/, /pərˌpɔrʃəˈnælədi/ Forms: late Middle English proporcionalitee, late Middle English–1500s proporcionalite, 1500s proportionalitie, 1500s proportionallitie, 1500s proportionalytie, 1500s– proportionality. Origin: Of multiple origins. Partly a borrowing from French. Partly a borrowing from Latin. Etymons: French proporcionalité; Latin proportionalitat-, proportionalitas. Etymology: < Middle French proporcionalité quality or fact of being proportional (1272 in Old French; French proportionnalité ) and its etymon post-classical Latin proportionalitat-, proportionalitas fact of being in numerical or geometrical proportion (6th cent. in Boethius), just proportion (a1200, 1686 in British sources), quality or fact of being proportional (1531 in the passage translated in quot. 1569 at sense 2) < proportionalis proportional adj. + classical Latin -tās (see -ty suffix¹; compare -ity suffix). Compare Spanish proporcionalidad (1562), Italian proporzionalità (1561).With continual proportionality (see quot. 1570 at sense 1a) compare post-classical Latin proportionalitas continua (6th cent. in Boethius). With harmonic proportionality (see quot. 1882 at sense 1b) compare post-classical Latin proportionalitas armonica (6th cent. in Boethius). Compare also post-classical Latin proportionalitas arithmetica, proportionalitas geometrica (6th cent. in Boethius). 1. Mathematics and Science. a. The fact or an instance of being in numerical or geometrical proportion (proportion n. 9a). ΚΠ a1450 Musical Treat. in Speculum (1935) 10 268 (MED) As proporcion as [read is] a comparison be-twene diuerse quantites oyþir numbris, so is proporcionalitas a comparison eyþir a likenes be 2o proporcions in 3re diuerse quantiteis atte last, þe whech quan[ti]teis or numbris been callid þe termis of þat proporcionalite. 1570 H. Billingsley tr. Euclid Elements Geom. v. f. 130^v Here is to be noted that this likenes or idemptitie of proportion which is called, as before was said proportionalitie, is of two sortes: the one is continuall, the other is discontinuall. 1672 Philos. Trans. 1671 (Royal Soc.) 6 3077 This computation was founded on the Hypothesis of the proportionality of the sines of Incidence, and Refraction. 1771 Philos. Trans. 1770 (Royal Soc.) 60 244 The lines OA, AB, BC, &c. are to be taken proportional to the coefficients a, b, c, &c... To preserve the above-mentioned proportionality, [etc.]. 1853 Trans. Royal Soc. Edinb. 20 89 Having assumed the proportionality of pressure to compression, he proceeds to define his coefficients. 1961 S. E. Toulmin Foresight & Understanding iii. 49 How else, then, can Aristotle's thesis be taken? In general, his practice in the Physics is to put forward, not precise equations, but at most ratios or proportionalities. 1996 S. McCall Model of Universe iv. 88 Cantor showed long ago that there exist no well-defined proportionalities among infinite sets. b. A formula or expression stating the proportionality of two or more quantities. ΘΚΠ the world > relative properties > number > algebra > [noun] > expression > formula binomial theorem1755 formula1794 Rankine's formula1868 proportionality1882 Hero's formula1886 Rutherford's law1913 Mellin transform1927 Langevin equation1943 1882 Analyst 9 50 The photodynamic vis viva at the chief centre of condensation, ½(m₃v²_λ), furnishes the following approx. harmonic proportionality:—m₀v₃v_λ:m₃v_λ²::m₃v_λ²:m₅v₃v_λ. 1954 A. Dresden tr. Van der Waerden Sci. Awakening vi. 176 The proportionality a:b::c:d means that na > mb implies nc > md, and na = mb implies nc = md, and na < mb implies nc < md, no matter how the integers m and n are chosen. 1976 Nature 27 May 301/2 The luminosity of a star of solar mass satisfies the approximate proportionality L ∝ G⁷M⁵ ∝ t³. 1986 M. Rigby et al. Forces between Molecules v. 113 In fact, our simple model leads to the conclusion that there is a proportionality between the viscosity and thermal conductivity coefficients of a rigid sphere gas, namely λ = ηc_v/m. 2. gen. The quality, character, or fact of being proportional. Formerly also occasionally in plural: †proportions (obsolete). ΘΚΠ the world > relative properties > order > agreement, harmony, or congruity > suitability or appropriateness > [noun] > due proportion or proportionateness proportiona1382 equality1447 proportioningc1450 temperance1471 temperancy1526 proportionality1545 commensurability1570 equability1576 proportionableness1606 apportionateness1645 proportionateness1658 commensurateness1661 proportionability1697 1545 J. Bale Mysterye Inyquyte P. Pantolabus f. 34 After that came in ydemptyte, realyte, formalyte..potencialite, personalyte, presencialyte, proporcionalite, perticipalite [etc.]. 1569 J. Sanford tr. H. C. Agrippa Of Vanitie Artes & Sci. xii. f. 25^v In like manner of proportion and proportionallitie [L. proportionalitate], and of their species. 1642 H. More Ψυχωδια Platonica sig. K6 The vast extent Of their round bodies, without outward eyes Hath view'd, told their proportionalities. 1701 N. Grew Cosmol. Sacra ii. ii. §5 All Sense, so far as Grateful, dependeth upon the Equality, or the Proportionality, of the Motion or Impression which is made. 1789 J. Bentham Introd. Princ. Morals & Legisl. xiv. 184 The necessity of making small sacrifices, in point of proportionality, for the sake of simplicity. 1830 J. F. W. Herschel Prelim. Disc. Study Nat. Philos. 152 Proportionality of the effect to its cause. 1891 M. E. Lowndes tr. H. Höffding Outl. Psychol. ii. 64 Both the parallelism and the proportionality between the activity of consciousness and cerebral activity point to an identity at bottom. 1965 B. Pearce tr. E. Preobrazhensky New Econ. 74 The confusion made between proportionality in the economy, which is objectively necessary..and the historically-transient method of achieving this proportionality on the basis of the law of value. 1992 New Republic 30 Nov. 20/2 No judge has ruled that jury lists must match census data..but from the standpoint of a court administrator it's impossible to err on the side of proportionality. Compounds proportionality constant n. (also constant of proportionality) Mathematics and Science the constant ratio of one variable quantity to a second to which it is proportional. ΚΠ 1908 Proc. Royal Soc. A. 81 p. xxiii To Helmholtz belongs the merit of determining theoretically the constant of proportionality in Faraday's law of induction. 1911 Proc. Amer. Philos. Soc. 50 327 This added mass, he found would be proportional to the amount of energy present. My proportionality constant agrees with his. 1955 J. Lindhard in W. Pauli Niels Bohr & Devel. Physics 188 Accordingly, ω and the average excitation potential become proportional to Z, i.e. ℏω = I = Z.I₀. However, it was found difficult to calculate the proportionality constant I₀. 1994 Sci. News 8 Oct. 232/2 The constant of proportionality between the distance of a galaxy and its speed is now known as H₀, the Hubble constant. proportionality factor n. (also factor of proportionality) Mathematics and Science = proportionality constant n. ΚΠ 1892 Amer. Jrnl. Math. 14 280 There are therefore in all eight parameters to be fixed—exactly the number of coefficients, barring the factor of proportionality, that occur in the given linear transformation. 1915 Science 4 June 826/1 It will be necessary to modify most of the equations slightly by introducing a proportionality factor. 1948 P. A. Samuelson Economics xiii. 291 According to the simplified quantity theory M = kP or P = ¹/ _kM where k is a factor of proportionality. 2001 Rev. Financial Stud. 14 995 The proportionality factor by which the rate of daytime information flow exceeds that of overnight information flow. This entry has been updated (OED Third Edition, June 2007; most recently modified version published online March 2022). < n.a1450
随便看	beyond memory of beyond one's depth beyond one's grasp beyond one's remit beyond or out of one's depth beyond past compare beyond peradventure beyond price beyond question beyond reach beyond reach of beyond reasonable doubt beyond recall beyond reclaim beyond recovery beyond redemption beyond repair beyond reproach beyond retrieval beyond retrieve beyond revoke beyond sea beyond seas beyond sundown beyond the beltway