modulusn.

Brit.

/ˈmɒdjᵿləs/,

/ˈmɒdʒᵿləs/, U.S.

/ˈmɑdʒələs/

Inflections: Plural moduli Brit.

/ˈmɒdjᵿlʌɪ/,

/ˈmɒdʒᵿlʌɪ/,

/ˈmɒdjᵿliː/,

/ˈmɒdʒᵿliː/, U.S.

/ˈmɑdʒəˌlaɪ/, moduluses.

Origin: A borrowing from Latin. Etymon: Latin modulus.

Etymology: < classical Latin modulus (see module n.).In sense 2 < post-classical Latin modulus (1714 in sense 2a in the phrase systematis modulus (R. Cotes 1714, in Philos. Trans. Royal Soc. 29 8), compare quot. 1753 at sense 2a below; 1801 in sense 2b (C. F. Gauss Disquisitiones arithmeticae (1801) i. 1)). In sense 2e after French module (J. R. Argand 1815, in Ann. de math. 5 208).

†1. Architecture. = module n. 3b. Obsolete.

ΘΚΠ

society > leisure > the arts > visual arts > architecture > column > [noun] > unit of proportion based on column diameter

modulus1563

model1598

module1664

1563 J. Shute First Groundes Archit. sig. Ci A Modulus, or half the thicknes of the pillor.

1601 I. T. tr. J. Bluom Bk. Five Collvmnes Archit. For Scapi Cimatium, standing vpon Stilobata, whose height being one Modulus of the Piller, deuide in two parts.

2. Mathematics.

a. A number by which logarithms in one base must be multiplied in order to obtain the corresponding logarithms in another base.

ΘΚΠ

the world > relative properties > number > arithmetic or algebraic operations > logarithm > [noun] > numerical elements

characteristic1654

index1678

exponent1734

modulus1753

base1772

mantissa1846

M1890

1753 Chambers's Cycl. Suppl. at Logarithm The line oe is what Mr. Cotes calls the modulus of the system.

1798 C. Hutton Course Math. II. 284 Multiply the result by the modulus of the system of logarithms.

1897 Chambers' Math. Tables 454 Modulus of common logarithms = M = 0·4342944819.

1989 W. Gellert et al. VNR Conc. Encycl. Math. (ed. 2) ii. 58 The common logarithms..arise from the natural logarithms after multiplication by the constant 1/ln 10 = M₁₀, which is called the modulus of the logarithms to the basis 10.

b. A whole number used as a divisor in a system of arithmetic (modular arithmetic) in which integers having the same remainder when divided by this number are regarded as equivalent. Cf. congruent adj. 5, modulo prep., residue n. 3b.

ΚΠ

1808 Monthly Rev. 55 App. 529 The numbers b and c are called residues, (residus,) b the residue of c, and c the residue of b, to the modulus a.

a1831 Encycl. Metrop. (1845) I. 642/2 Numbers of the same form with respect to any modulus, are all those which can be represented by the same formula. Thus, 13, 17, 21, &c. are all of the form 4n + 1; and 19, 25, 31, &c. of the form 6n + 1; 4 and 6 being the moduli.

1888 C. Smith Treat. Algebra xxviii. 487 If two numbers a and b leave the same remainder when divided by a third number c, they are said to be congruent with respect to the modulus c.

1949 J. V. Uspensky & M. A. Heaslet Elem. Number Theory vi. 128 Two congruences with the same moduli can be added or subtracted, member by member, like equalities. In other words, from two congruences A ≡ a (mod m), B ≡ b (mod m) it follows that A ± B ≡ a ± b (mod m).

1967 J. E. Shockley Introd. Number Theory iii. 48 Corollary 6.2 furnishes the most efficient method for solving several systems of congruences when the same sets of moduli appear in each system.

1990 Sciences July 53/1 In general a number is translated with the remainder after the number is divided by the modulus.

†c. The function obtained from a given function of two variables by setting the second variable equal to the first. Obsolete. rare.

ΘΚΠ

the world > relative properties > number > mathematical number or quantity > [noun] > relationship between quantities > congruence > modulus

modulusa1832

a1832 A. De Morgan Theory Probab. in Encycl. Metrop. (1845) II. 375/1 By the modulus of α(x, y) we mean the function α(x, x) considered as of a single subject. The moduli of the sum, difference, product, &c. of two functions are the sum, difference, &c. of the moduli.

d. A constant multiplier, coefficient, or parameter involved in a given function, transformation, etc.; spec. †(a) the constant ratio of distance from a given point to distance from a given plane (or line) that defines the points of a surface (or curve) (obsolete); (b) a constant parameter occurring in simplified forms of elliptic integrals; (c) the determinant of the matrix of a linear transformation (now rare).

ΘΚΠ

the world > relative properties > number > algebra > [noun] > expression > function > value or set of values of

maximum1646

minimum1646

nullity1710

modulus1843

argument1865

zero1873

range1891

extremum1904

interpolate1920

1843 MacCullagh in Proc. Royal Irish Acad. 1840–4 (1846) 2 448 The given plane may be called a directive plane, and the constant ratio may be termed the modulus.

1846 A. Cayley Coll. Math. Papers I. 238 The square of the secant of the semi-angle of resultant rotation will be the modulus of the rotation.

1865 W. T. Brande & G. W. Cox Dict. Sci., Lit. & Art (new ed.) I. 768/1 Any trigonometrical function of ϕ is termed an elliptic function, having the argument u and modulus k.

1866 W. T. Brande & G. W. Cox Dict. Sci., Lit. & Art II. 378/1 The determinant formed from the coefficients [of the linear transformation]..is called the modulus of transformation.

1873 J. C. Maxwell Treat. Electr. & Magnetism I. i. x. 183 We may call k and k′ the two complementary moduli of the confocal system.

a1883 H. J. S. Smith Coll. Math. Papers (1894) II. 570 Geometrical construction of the transformed modulus by means of the modular curve.

1924 Circular U.S. Bureau of Standards No. 154. 2 The American Petroleum Institute, the U.S. Bureau of Mines, and the U.S. Bureau of Standards..agreed to recommend that in the future only the scale based on the modulus 141.5 be used in the petroleum-oil industry.

1956 S. Glasstone Princ. Nucl. Reactor Engin. xi. 679 For the correlation of heat-transfer data it is now appropriate to use another dimensionless modulus, namely, the Peclet number, Pe.

1989 W. Gellert et al. VNR Conc. Encycl. Math. (ed. 2) xxiii. 529 The Legendre form of an elliptic integral arises when w² = (1 − z²)(1 − k²z²)..; k is called the modulus.

e. The absolute value of a complex (or real) number; the magnitude of a complex (or real) vector.

ΘΚΠ

the world > relative properties > number > mathematical number or quantity > [noun] > particular qualities > real > absolute value of

absolute value1816

modulus1866

the world > relative properties > number > mathematical number or quantity > [noun] > particular qualities > complex > absolute value of

absolute value1816

modulus1866

1866 W. T. Brande & G. W. Cox Dict. Sci., Lit. & Art II. 551/2 The positive square root of a² + b² is often termed the modulus of the imaginary expression a + b√−1.

1891 E. W. Hobson Treat. Plane Trigonom. 255 The modulus of the sum of a number of complex quantities is less than, or equal to, the sum of their moduli.

1931 P. Dienes Taylor Series 48 We call the positive number |√a² + b²| = |a + bi| the absolute value or modulus of a + bi.

1989 D. Thouless in P. Davies New Physics vii. 225/2 The length of the vector is known as its ‘modulus’, and the angle it makes with an arbitrary direction is known as its ‘phase’.

1991 Struct. Change & Econ. Dynamics 2 47 From a mathematical stand point, stability is obtained if the moduli of all the eigenvalues of the Jacobian matrix are smaller than 1.

3. Physics and Engineering. A numerical constant representing some property of a substance, and equal to the ratio of a (usually mechanical) cause to the magnitude of its effect on the substance. modulus of elasticity n. (originally) a quantity relating the amount of extension or contraction of a substance to the amount of tension or pressure acting on it; (now) spec. the ratio of the stress acting on a substance to the strain produced; also called elastic modulus, Young's modulus. (One of the four elastic constants, the others being the shear (or rigidity) modulus, the bulk modulus, and Poisson's ratio.) modulus of rigidity n. = shear modulus n. at shear n.² Compounds 2.bulk, rigidity, shear modulus: see the first element.

ΘΚΠ

the world > matter > physics > mechanics > force > [noun] > specific constant, function, or quantity

modulus1807

potential function1828

the world > matter > constitution of matter > hardness > types of hardness > [noun] > stiffness or rigidity > measurement of

modulus of rigidity1877

shear modulus1937

the world > matter > physics > mechanics > force > stress or force exerted and tending to deform > [noun] > modules of elasticity

Young's modulus1857

modulus of elasticity1877

the world > matter > physics > mechanics > force > stress or force exerted and tending to deform > [noun] > modulus of rigidity

modulus of rigidity1877

rigidity modulus1883

shear modulus1937

1807 T. Young Course Lect. Nat. Philos. I. xiii. 137 According to this analogy, we may express the elasticity of any substance by the weight of a certain column of the same substance, which may be denominated the modulus of its elasticity.

1807 T. Young Course Lect. Nat. Philos. II. xiii. 66 Every small change of form is propagated along an extended chord with a velocity equal to that of a heavy body falling through a height equal to half the length of a portion of the chord, of which the weight is equivalent to a force producing the tension, and which may be called the modulus of the tension.

1824 T. Tredgold Pract. Ess. Strength of Cast Iron 251 The measure of the power of a body to resist impulsion, that is, the modulus of resilience.

1843 H. Moseley Mech. Princ. Engin. 162 The modulus of a machine..is the relation between the work constantly done upon it by the moving power, and that constantly yielded at the working points [etc.].

1869 W. J. M. Rankine Cycl. Machine & Hand-tools App. 9 The square of the proof stress, divided by the modulus of elasticity, is called the Modulus of Resilience.

1877 Sir W. Thomson in Encycl. Brit. VII. 804/2 Moduluses of Elasticity. A modulus of elasticity is the number obtained by dividing the number expressing a stress by the number expressing the strain which it produces... An isotropic solid has two principal moduluses—a modulus of compression and a rigidity.

1877 Encycl. Brit. VII. 805/2 The ‘modulus of rigidity’ of an isotropic solid is the amount of tangential stress divided by the deformation it produces.

1940 Physical Rev. 57 417 Measurements of the temperature variation of the adiabatic and isothermal Young's and rigidity moduli..of pressed specimens of ammonium chloride.

1971 New Scientist 8 July 70/1 Composites of [carbon] fibres in resin having the expected high tensile strength and modulus..had a low interlaminar shear strength of only 2500 lb/sq in.

1990 Fly Fisherman Dec. 16/1 Claims are made that the higher modulus fiber rods will make you a better caster.

2002 M. Vable Mech. of Materials iii. 150 Assume beam is made from elastic-perfectly plastic material that has..a modulus of elasticity E = 200 GPa.

†4. Cambridge University. A unit of payment used at Trinity College (see quot. 1882). Obsolete.

ΚΠ

1840 J. Romilly Diary 8 Dec. in Cambridge Diary (1967) 206 Modulus for Trinity Fellowship £926.7.6.

1882 Cambr. Stat., Trin. Coll. (1883) 590 The Council shall fix for the year the amount being not more than..250l. to be called a modulus. And there shall be paid to each Fellow..his proper dividend fixed as hereinafter mentioned by reference to the amount of the modulus. There shall be paid to the Master seven moduli, and to each of the Chaplains and to the Librarian one half of a modulus.

†5. Metrical structure or pattern. Cf. module n. 4. Obsolete. rare.

ΘΚΠ

the world > relative properties > order > agreement, harmony, or congruity > conformity to or with a pattern, etc. > [noun] > a standard or norm

regulaOE

standardc1475

rate1509

square1549

formular1563

squarier1581

scantling1587

the King's beam1607

referencea1627

modulea1628

norme1635

the common beam1647

normaa1676

plummet line1683

norm1821

modulus1857

normative1909

1857 C. Patmore in N. Brit. Rev. 27 131 The best poet is..[he] who, in his verse, preserves everywhere the living sense of metre, not so much by unvarying obedience to, as by innumerable small departures from, its modulus.

1864 Reader 30 Apr. 544/3 He sometimes deviates from the strict modulus of the sonnet.

This entry has been updated (OED Third Edition, September 2002; most recently modified version published online March 2022).

单词	modulus
释义	modulusn. Brit. /ˈmɒdjᵿləs/, /ˈmɒdʒᵿləs/, U.S. /ˈmɑdʒələs/ Inflections: Plural moduli Brit. /ˈmɒdjᵿlʌɪ/, /ˈmɒdʒᵿlʌɪ/, /ˈmɒdjᵿliː/, /ˈmɒdʒᵿliː/, U.S. /ˈmɑdʒəˌlaɪ/, moduluses. Origin: A borrowing from Latin. Etymon: Latin modulus. Etymology: < classical Latin modulus (see module n.).In sense 2 < post-classical Latin modulus (1714 in sense 2a in the phrase systematis modulus (R. Cotes 1714, in Philos. Trans. Royal Soc. 29 8), compare quot. 1753 at sense 2a below; 1801 in sense 2b (C. F. Gauss Disquisitiones arithmeticae (1801) i. 1)). In sense 2e after French module (J. R. Argand 1815, in Ann. de math. 5 208). †1. Architecture. = module n. 3b. Obsolete. ΘΚΠ society > leisure > the arts > visual arts > architecture > column > [noun] > unit of proportion based on column diameter modulus1563 model1598 module1664 1563 J. Shute First Groundes Archit. sig. Ci A Modulus, or half the thicknes of the pillor. 1601 I. T. tr. J. Bluom Bk. Five Collvmnes Archit. For Scapi Cimatium, standing vpon Stilobata, whose height being one Modulus of the Piller, deuide in two parts. 2. Mathematics. a. A number by which logarithms in one base must be multiplied in order to obtain the corresponding logarithms in another base. ΘΚΠ the world > relative properties > number > arithmetic or algebraic operations > logarithm > [noun] > numerical elements characteristic1654 index1678 exponent1734 modulus1753 base1772 mantissa1846 M1890 1753 Chambers's Cycl. Suppl. at Logarithm The line oe is what Mr. Cotes calls the modulus of the system. 1798 C. Hutton Course Math. II. 284 Multiply the result by the modulus of the system of logarithms. 1897 Chambers' Math. Tables 454 Modulus of common logarithms = M = 0·4342944819. 1989 W. Gellert et al. VNR Conc. Encycl. Math. (ed. 2) ii. 58 The common logarithms..arise from the natural logarithms after multiplication by the constant 1/ln 10 = M₁₀, which is called the modulus of the logarithms to the basis 10. b. A whole number used as a divisor in a system of arithmetic (modular arithmetic) in which integers having the same remainder when divided by this number are regarded as equivalent. Cf. congruent adj. 5, modulo prep., residue n. 3b. ΚΠ 1808 Monthly Rev. 55 App. 529 The numbers b and c are called residues, (residus,) b the residue of c, and c the residue of b, to the modulus a. a1831 Encycl. Metrop. (1845) I. 642/2 Numbers of the same form with respect to any modulus, are all those which can be represented by the same formula. Thus, 13, 17, 21, &c. are all of the form 4n + 1; and 19, 25, 31, &c. of the form 6n + 1; 4 and 6 being the moduli. 1888 C. Smith Treat. Algebra xxviii. 487 If two numbers a and b leave the same remainder when divided by a third number c, they are said to be congruent with respect to the modulus c. 1949 J. V. Uspensky & M. A. Heaslet Elem. Number Theory vi. 128 Two congruences with the same moduli can be added or subtracted, member by member, like equalities. In other words, from two congruences A ≡ a (mod m), B ≡ b (mod m) it follows that A ± B ≡ a ± b (mod m). 1967 J. E. Shockley Introd. Number Theory iii. 48 Corollary 6.2 furnishes the most efficient method for solving several systems of congruences when the same sets of moduli appear in each system. 1990 Sciences July 53/1 In general a number is translated with the remainder after the number is divided by the modulus. †c. The function obtained from a given function of two variables by setting the second variable equal to the first. Obsolete. rare. ΘΚΠ the world > relative properties > number > mathematical number or quantity > [noun] > relationship between quantities > congruence > modulus modulusa1832 a1832 A. De Morgan Theory Probab. in Encycl. Metrop. (1845) II. 375/1 By the modulus of α(x, y) we mean the function α(x, x) considered as of a single subject. The moduli of the sum, difference, product, &c. of two functions are the sum, difference, &c. of the moduli. d. A constant multiplier, coefficient, or parameter involved in a given function, transformation, etc.; spec. †(a) the constant ratio of distance from a given point to distance from a given plane (or line) that defines the points of a surface (or curve) (obsolete); (b) a constant parameter occurring in simplified forms of elliptic integrals; (c) the determinant of the matrix of a linear transformation (now rare). ΘΚΠ the world > relative properties > number > algebra > [noun] > expression > function > value or set of values of maximum1646 minimum1646 nullity1710 modulus1843 argument1865 zero1873 range1891 extremum1904 interpolate1920 1843 MacCullagh in Proc. Royal Irish Acad. 1840–4 (1846) 2 448 The given plane may be called a directive plane, and the constant ratio may be termed the modulus. 1846 A. Cayley Coll. Math. Papers I. 238 The square of the secant of the semi-angle of resultant rotation will be the modulus of the rotation. 1865 W. T. Brande & G. W. Cox Dict. Sci., Lit. & Art (new ed.) I. 768/1 Any trigonometrical function of ϕ is termed an elliptic function, having the argument u and modulus k. 1866 W. T. Brande & G. W. Cox Dict. Sci., Lit. & Art II. 378/1 The determinant formed from the coefficients [of the linear transformation]..is called the modulus of transformation. 1873 J. C. Maxwell Treat. Electr. & Magnetism I. i. x. 183 We may call k and k′ the two complementary moduli of the confocal system. a1883 H. J. S. Smith Coll. Math. Papers (1894) II. 570 Geometrical construction of the transformed modulus by means of the modular curve. 1924 Circular U.S. Bureau of Standards No. 154. 2 The American Petroleum Institute, the U.S. Bureau of Mines, and the U.S. Bureau of Standards..agreed to recommend that in the future only the scale based on the modulus 141.5 be used in the petroleum-oil industry. 1956 S. Glasstone Princ. Nucl. Reactor Engin. xi. 679 For the correlation of heat-transfer data it is now appropriate to use another dimensionless modulus, namely, the Peclet number, Pe. 1989 W. Gellert et al. VNR Conc. Encycl. Math. (ed. 2) xxiii. 529 The Legendre form of an elliptic integral arises when w² = (1 − z²)(1 − k²z²)..; k is called the modulus. e. The absolute value of a complex (or real) number; the magnitude of a complex (or real) vector. ΘΚΠ the world > relative properties > number > mathematical number or quantity > [noun] > particular qualities > real > absolute value of absolute value1816 modulus1866 the world > relative properties > number > mathematical number or quantity > [noun] > particular qualities > complex > absolute value of absolute value1816 modulus1866 1866 W. T. Brande & G. W. Cox Dict. Sci., Lit. & Art II. 551/2 The positive square root of a² + b² is often termed the modulus of the imaginary expression a + b√−1. 1891 E. W. Hobson Treat. Plane Trigonom. 255 The modulus of the sum of a number of complex quantities is less than, or equal to, the sum of their moduli. 1931 P. Dienes Taylor Series 48 We call the positive number \|√a² + b²\| = \|a + bi\| the absolute value or modulus of a + bi. 1989 D. Thouless in P. Davies New Physics vii. 225/2 The length of the vector is known as its ‘modulus’, and the angle it makes with an arbitrary direction is known as its ‘phase’. 1991 Struct. Change & Econ. Dynamics 2 47 From a mathematical stand point, stability is obtained if the moduli of all the eigenvalues of the Jacobian matrix are smaller than 1. 3. Physics and Engineering. A numerical constant representing some property of a substance, and equal to the ratio of a (usually mechanical) cause to the magnitude of its effect on the substance. modulus of elasticity n. (originally) a quantity relating the amount of extension or contraction of a substance to the amount of tension or pressure acting on it; (now) spec. the ratio of the stress acting on a substance to the strain produced; also called elastic modulus, Young's modulus. (One of the four elastic constants, the others being the shear (or rigidity) modulus, the bulk modulus, and Poisson's ratio.) modulus of rigidity n. = shear modulus n. at shear n.² Compounds 2.bulk, rigidity, shear modulus: see the first element. ΘΚΠ the world > matter > physics > mechanics > force > [noun] > specific constant, function, or quantity modulus1807 potential function1828 the world > matter > constitution of matter > hardness > types of hardness > [noun] > stiffness or rigidity > measurement of modulus of rigidity1877 shear modulus1937 the world > matter > physics > mechanics > force > stress or force exerted and tending to deform > [noun] > modules of elasticity Young's modulus1857 modulus of elasticity1877 the world > matter > physics > mechanics > force > stress or force exerted and tending to deform > [noun] > modulus of rigidity modulus of rigidity1877 rigidity modulus1883 shear modulus1937 1807 T. Young Course Lect. Nat. Philos. I. xiii. 137 According to this analogy, we may express the elasticity of any substance by the weight of a certain column of the same substance, which may be denominated the modulus of its elasticity. 1807 T. Young Course Lect. Nat. Philos. II. xiii. 66 Every small change of form is propagated along an extended chord with a velocity equal to that of a heavy body falling through a height equal to half the length of a portion of the chord, of which the weight is equivalent to a force producing the tension, and which may be called the modulus of the tension. 1824 T. Tredgold Pract. Ess. Strength of Cast Iron 251 The measure of the power of a body to resist impulsion, that is, the modulus of resilience. 1843 H. Moseley Mech. Princ. Engin. 162 The modulus of a machine..is the relation between the work constantly done upon it by the moving power, and that constantly yielded at the working points [etc.]. 1869 W. J. M. Rankine Cycl. Machine & Hand-tools App. 9 The square of the proof stress, divided by the modulus of elasticity, is called the Modulus of Resilience. 1877 Sir W. Thomson in Encycl. Brit. VII. 804/2 Moduluses of Elasticity. A modulus of elasticity is the number obtained by dividing the number expressing a stress by the number expressing the strain which it produces... An isotropic solid has two principal moduluses—a modulus of compression and a rigidity. 1877 Encycl. Brit. VII. 805/2 The ‘modulus of rigidity’ of an isotropic solid is the amount of tangential stress divided by the deformation it produces. 1940 Physical Rev. 57 417 Measurements of the temperature variation of the adiabatic and isothermal Young's and rigidity moduli..of pressed specimens of ammonium chloride. 1971 New Scientist 8 July 70/1 Composites of [carbon] fibres in resin having the expected high tensile strength and modulus..had a low interlaminar shear strength of only 2500 lb/sq in. 1990 Fly Fisherman Dec. 16/1 Claims are made that the higher modulus fiber rods will make you a better caster. 2002 M. Vable Mech. of Materials iii. 150 Assume beam is made from elastic-perfectly plastic material that has..a modulus of elasticity E = 200 GPa. †4. Cambridge University. A unit of payment used at Trinity College (see quot. 1882). Obsolete. ΚΠ 1840 J. Romilly Diary 8 Dec. in Cambridge Diary (1967) 206 Modulus for Trinity Fellowship £926.7.6. 1882 Cambr. Stat., Trin. Coll. (1883) 590 The Council shall fix for the year the amount being not more than..250l. to be called a modulus. And there shall be paid to each Fellow..his proper dividend fixed as hereinafter mentioned by reference to the amount of the modulus. There shall be paid to the Master seven moduli, and to each of the Chaplains and to the Librarian one half of a modulus. †5. Metrical structure or pattern. Cf. module n. 4. Obsolete. rare. ΘΚΠ the world > relative properties > order > agreement, harmony, or congruity > conformity to or with a pattern, etc. > [noun] > a standard or norm regulaOE standardc1475 rate1509 square1549 formular1563 squarier1581 scantling1587 the King's beam1607 referencea1627 modulea1628 norme1635 the common beam1647 normaa1676 plummet line1683 norm1821 modulus1857 normative1909 1857 C. Patmore in N. Brit. Rev. 27 131 The best poet is..[he] who, in his verse, preserves everywhere the living sense of metre, not so much by unvarying obedience to, as by innumerable small departures from, its modulus. 1864 Reader 30 Apr. 544/3 He sometimes deviates from the strict modulus of the sonnet. This entry has been updated (OED Third Edition, September 2002; most recently modified version published online March 2022). < n.1563
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