equationn.

/ɪˈkweɪʒən/

/iːˈkweɪʒən/

/ɪˈkweɪʃən/

/iːˈkweɪʃən/

Forms: Also Middle English equacion, equacioun, 1500s–1600s æquation.

Etymology: < Latin aequātiōn-em, < aequāre : see equant adj. and n.

The action of equalling.

I. The action of making equal.

†1. spec. in Astrology. Equal partition. equations of houses: the method of dividing the sphere equally into ‘houses’ for astrological purposes. Obsolete.

ΘΚΠ

the world > the universe > astrology > [noun] > calculation > equation

equation1393

1393 J. Gower Confessio Amantis III. 67 He loketh his equacions And eke the constellacions.

c1400 ( G. Chaucer Treat. Astrolabe (Cambr. Dd.3.53) (1872) i. §22. 14 With the smale point of the forseide label, shaltow kalcule thyne equaciouns in the bordure of thin Astrolabie.

c1405 (c1395) G. Chaucer Franklin's Tale (Hengwrt) (2003) l. 571 And hise proporcionels conuenientz For hise equacions in euery thyng.

2. gen. The action of making equal or balancing; the state of being equally balanced, equilibrium, equality. Now chiefly in phrases like equation of demand and supply, equation of trade, etc.

ΘΚΠ

the world > relative properties > relationship > equality or equivalence > [noun] > making equal

coequation1471

perequation1611

equiparation1615

pariation1623

adequation1650

equation1656

equalization1793

nivellization1947

1656 T. Blount Glossographia Equation, making equal, even or plain.

a1676 M. Hale Primitive Originat. Mankind (1677) ii. ix. 216 The very Redundance it self of Mankind seeming by a natural consecution to yield and subminister this Remedy, for its Reduction and Equation.

1718 N. Rowe tr. Lucan Pharsalia ii. (R.) Again the golden day resum'd its right, And rul'd in just equation with the night.

1726 G. Shelvocke Voy. round World iv. 140 It would be difficult to determine the different values of the dollars and the candlesticks, so as to come to a nice equation of the matter.

1848 J. S. Mill Princ. Polit. Econ. II. iii. xxi. §1. 157 An excess of imports over exports, arising from the fact that the equation of international demand is not yet established.

1850 G. Grote Hist. Greece VII. ii. lx. 481 If his personal suffering could..be..set in equation against the mischief brought by himself both on his army and his country.

1863 H. Fawcett Man. Polit. Econ. iii. vii. 398 These prices would adjust the equation of international trade.

II. Reduction to a normal value or position.

a. Astronomy. The action of adding to or subtracting from any result of observation or calculation such a quantity as will compensate for a known cause of irregularity or error. Chiefly concrete the quantity added or subtracted for this purpose.annual equation: see annual adj. and n. Compounds 2. equation of the centre: the difference between the mean and the true anomaly of a celestial object.† eccentric equation: = equation to the centre. equation of the equinoxes: the difference between the mean and apparent places of the equinoxes, arising from the phenomenon known as precession of the equinoxes. equation of time: the difference between the time shown by a clock (mean time) and that shown by a sundial.personal equation: see personal equation n. at personal adj., n., and adv. Compounds.

ΘΚΠ

the world > relative properties > relationship > equality or equivalence > [noun] > compensation

compensation1387

countervailment1594

supererogating1617

equation1666

compensating1668

upmaking1669

requital1885

weightage1906

1666 J. Evelyn Mem. (1857) II. 11 To the Royal Society, where one Mercator. produced his rare clock, and new motion to perform the equations.

1715 tr. D. Gregory Elements Astron. I. iii. §17. 421 When both these causes of the Equation of Time hold.

1812 R. Woodhouse Elem. Treat. Astron. xxxiv. 320 Corrections, or, as they are astronomically called, equations.

1834 Nat. Philos. (Libr. Useful Knowl.) III. Astron. x. 193/1 The equation of the centre [of the sun] is subject to a very slow secular variation.

1845 Penny Cycl. Suppl. I. 535/2 If A and B are severally in the habit of noting events 3-tenths of a second after and 4-tenths of a second before they take place, their personal equations may be described as being + 0^s.3 and 0^s.4.

1852 W. T. Brande Dict. Sci., Lit. & Art (ed. 2) Suppl. 1365/2 The term Personal Equation has of late been introduced into Astronomy.

1853 D. Lardner Handbk. Astron. §3200 If we suppose an imaginary moon to move from perihelion through aphelion back to perihelion, with a uniform angular velocity..the distance between this imaginary moon and the true moon is called the equation of the centre.

1854 H. Moseley Lect. Astron. (ed. 4) xxi. 96 The difference between true and mean solar time..is called the equation of time.

1881 Lockyer in Nature No. 614. 318 Photography has no personal equation.

1881 New York Nation XXXII. 430 The scientific genealogists of the more advanced school, who settle the problem off-hand, often in accordance with their personal equation.

b. human equation: transferred sense from personal equation.

ΚΠ

1938 Reader's Digest Apr. 77/2 The Oakland Bridge suffers from such a simple, unpredictable human equation as the preference of truck drivers to loaf on a ferry.

1964 F. Bowers Bibliogr. & Textual Crit. iii. ii. 71 We must throw out the human equation as much as we can in our search to find an explanation for seeming aberrancies.

4. equation of payments n. the process of finding a mean time for the equitable payment in one amount of several sums due at different times.

ΘΚΠ

society > trade and finance > payment > [noun] > hastening or delaying payment > due date for payment > finding mean time for payment

equation of payments1678

1678 J. Hawkins Cocker's Arithm. xxix. 309 Equation of payments is that Rule..whereby to reduce the times for payment of several sums of money to an equated time for payment of the whole debt without dammage to Debtor or Creditor.

III. Statement of equality.

†5. Mathematics. The action of stating the identity in value of two quantities or expressions. Obsolete.

ΘΚΠ

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

equation1570

1570 J. Dee in H. Billingsley tr. Euclid Elements Geom. Math. Præf. sig. *ij^v That great Arithmeticall Arte of Æquation: commonly called..Algebra.

1579 L. Digges & T. Digges Stratioticos 44 Æquation is nothing else but a certain conference of two numbers being in value Equal, and yet in multitude and Denomination different.

1664 H. Power Exper. Philos. Concl. 187 Thus came they to upbraid..Algebra with the Æquation of three discontinued Numbers.

1673 J. Kersey Elem. Algebra I. i. xi. 51 An Equation in the Algebraical Art is a mutual Comparing of two Equal quantities or things of different Denominations.

a. concrete. A formula affirming the equivalence of two quantitative expressions, which are for this purpose connected by the sign =.The two chief kinds of equations are: (1) Those which contain symbols denoting one or more unknown quantities; to discover the numerical values of these is called ‘solving’ the equation; the numbers which will ‘satisfy’ an equation, i.e. which may be substituted for the symbol of unknown quantity without rendering the statement incorrect, are called its ‘roots’. (2) Those which indicate a constant relation existing between variables; as equation to a curve, an equation expressing a relation between coordinates or the like, which is constant for every point in the curve; equation of motions, etc. Equations are distinguished as simple, quadratic, cubic, biquadratic, etc. (or as of the 1st, 2nd, 3rd, 4th, etc. degree) according to the highest power which they contain of any unknown or variable.

ΘΚΠ

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

equation1570

cardanic equation1684

binomial equation1814

simultaneous equation1816

characteristic equation1828

characteristic equation1841

characteristic equation1849

intrinsic equation of a curve1849

complete primitive1859

primitive1862

Poisson's equation1873

Jacobi equation1882

formulaic equation1884

adjoint1889

recursion formula1895

characteristic equation1899

characteristic equation1900

Pell equation1910

Lotka–Volterra equations1937

Langevin equation1943

1570 H. Billingsley tr. Euclid Elements Geom. ii. f. 60 Many rules..of Algebra, with the equations therein vsed.

1657 T. Hobbes Στιγμαι in Wks. (1845) VII. 366 You mean that..the lowermost to the lowermost in the first equation are equal.

1753 Philos. Trans. 1751–2 (Royal Soc.) 47 62 Mr. de Buffon mention'd..we should..resolve the equation.

1807 C. Hutton Course Math. (ed. 5) II. 322 The equation to the curve being ax = y².

1814 J. Playfair Outl. Nat. Philos. II. i. App. 227 This method of determining the coefficients of a given function, or correcting them from observation, by means of what are called Equations of Condition, is said to have been invented by Tobias Mayer of Göttingen.

1816 H. Douglas Ess. Mil. Bridges i. 16 The equation V = ^√mg/ _√b becomes V = ^306.7√r/ _√b.

1838 A. De Morgan Ess. Probabilities 29 An investigation of the method of solving an equation.

1871 B. Stewart Heat (ed. 2) §62 From this equation we derive at once the relation between the temperature and the density of air.

1879 W. Thomson & P. G. Tait Treat. Nat. Philos. (new ed.) I: Pt. i. §191 What is called the ‘equation of continuity’ [for fluids], an unhappily chosen expression.

b. transferred.

ΚΠ

1860 W. Thomson Outl. Laws of Thought (ed. 5) §68. 110 Every affirmative judgment may be regarded as an equation of subject and predicate.

c. A formula which represents a chemical reaction by stating the equality between the symbols representing the original and those which represent the resulting substances.

ΚΠ

1807 T. Thomson Syst. Chem. (ed. 3) II. 132 We have therefore this equation, Carbon 28 + Oxygen 72 = Carb. Ox. 69 + Oxygen 31.

1853 W. Gregory Inorg. Chem. (ed. 3) 90 The following equation explains the change. (KO,NO₅) + 2 (HO,SO₃) = (KO,HO,₂SO₃) + (HO,NO₅).

1857 E. L. Birkett Bird's Urinary Deposits (ed. 5) 245 In the following equation this decomposition of the allantoin is assumed to have occurred.

Compounds

equation box n. = equational box at equational adj. 2.

ΚΠ

1893 I. K. Funk et al. Standard Dict. Eng. Lang. I. at Equational Equation box.

equation table n. a table showing the time a clock should indicate when the sun is on the meridian.

ΚΠ

1731 (title) An explanation of the nature of equation of time, and use of the equation table for adjusting watches and clocks to the motion of the sun.

1850 E. B. Denison Rudimentary Treat. Clock & Watch Making viii. 19 This [sundial]..with the equation-table will give the means of correcting a clock on any fine day.

This entry has not yet been fully updated (first published 1891; most recently modified version published online December 2020).

单词	equation
释义	equationn. /ɪˈkweɪʒən//iːˈkweɪʒən//ɪˈkweɪʃən//iːˈkweɪʃən/ Forms: Also Middle English equacion, equacioun, 1500s–1600s æquation. Etymology: < Latin aequātiōn-em, < aequāre : see equant adj. and n. The action of equalling. I. The action of making equal. †1. spec. in Astrology. Equal partition. equations of houses: the method of dividing the sphere equally into ‘houses’ for astrological purposes. Obsolete. ΘΚΠ the world > the universe > astrology > [noun] > calculation > equation equation1393 1393 J. Gower Confessio Amantis III. 67 He loketh his equacions And eke the constellacions. c1400 ( G. Chaucer Treat. Astrolabe (Cambr. Dd.3.53) (1872) i. §22. 14 With the smale point of the forseide label, shaltow kalcule thyne equaciouns in the bordure of thin Astrolabie. c1405 (c1395) G. Chaucer Franklin's Tale (Hengwrt) (2003) l. 571 And hise proporcionels conuenientz For hise equacions in euery thyng. 2. gen. The action of making equal or balancing; the state of being equally balanced, equilibrium, equality. Now chiefly in phrases like equation of demand and supply, equation of trade, etc. ΘΚΠ the world > relative properties > relationship > equality or equivalence > [noun] > making equal coequation1471 perequation1611 equiparation1615 pariation1623 adequation1650 equation1656 equalization1793 nivellization1947 1656 T. Blount Glossographia Equation, making equal, even or plain. a1676 M. Hale Primitive Originat. Mankind (1677) ii. ix. 216 The very Redundance it self of Mankind seeming by a natural consecution to yield and subminister this Remedy, for its Reduction and Equation. 1718 N. Rowe tr. Lucan Pharsalia ii. (R.) Again the golden day resum'd its right, And rul'd in just equation with the night. 1726 G. Shelvocke Voy. round World iv. 140 It would be difficult to determine the different values of the dollars and the candlesticks, so as to come to a nice equation of the matter. 1848 J. S. Mill Princ. Polit. Econ. II. iii. xxi. §1. 157 An excess of imports over exports, arising from the fact that the equation of international demand is not yet established. 1850 G. Grote Hist. Greece VII. ii. lx. 481 If his personal suffering could..be..set in equation against the mischief brought by himself both on his army and his country. 1863 H. Fawcett Man. Polit. Econ. iii. vii. 398 These prices would adjust the equation of international trade. II. Reduction to a normal value or position. 3. a. Astronomy. The action of adding to or subtracting from any result of observation or calculation such a quantity as will compensate for a known cause of irregularity or error. Chiefly concrete the quantity added or subtracted for this purpose.annual equation: see annual adj. and n. Compounds 2. equation of the centre: the difference between the mean and the true anomaly of a celestial object.† eccentric equation: = equation to the centre. equation of the equinoxes: the difference between the mean and apparent places of the equinoxes, arising from the phenomenon known as precession of the equinoxes. equation of time: the difference between the time shown by a clock (mean time) and that shown by a sundial.personal equation: see personal equation n. at personal adj., n., and adv. Compounds. ΘΚΠ the world > relative properties > relationship > equality or equivalence > [noun] > compensation compensation1387 countervailment1594 supererogating1617 equation1666 compensating1668 upmaking1669 requital1885 weightage1906 1666 J. Evelyn Mem. (1857) II. 11 To the Royal Society, where one Mercator. produced his rare clock, and new motion to perform the equations. 1715 tr. D. Gregory Elements Astron. I. iii. §17. 421 When both these causes of the Equation of Time hold. 1812 R. Woodhouse Elem. Treat. Astron. xxxiv. 320 Corrections, or, as they are astronomically called, equations. 1834 Nat. Philos. (Libr. Useful Knowl.) III. Astron. x. 193/1 The equation of the centre [of the sun] is subject to a very slow secular variation. 1845 Penny Cycl. Suppl. I. 535/2 If A and B are severally in the habit of noting events 3-tenths of a second after and 4-tenths of a second before they take place, their personal equations may be described as being + 0^s.3 and 0^s.4. 1852 W. T. Brande Dict. Sci., Lit. & Art (ed. 2) Suppl. 1365/2 The term Personal Equation has of late been introduced into Astronomy. 1853 D. Lardner Handbk. Astron. §3200 If we suppose an imaginary moon to move from perihelion through aphelion back to perihelion, with a uniform angular velocity..the distance between this imaginary moon and the true moon is called the equation of the centre. 1854 H. Moseley Lect. Astron. (ed. 4) xxi. 96 The difference between true and mean solar time..is called the equation of time. 1881 Lockyer in Nature No. 614. 318 Photography has no personal equation. 1881 New York Nation XXXII. 430 The scientific genealogists of the more advanced school, who settle the problem off-hand, often in accordance with their personal equation. b. human equation: transferred sense from personal equation. ΚΠ 1938 Reader's Digest Apr. 77/2 The Oakland Bridge suffers from such a simple, unpredictable human equation as the preference of truck drivers to loaf on a ferry. 1964 F. Bowers Bibliogr. & Textual Crit. iii. ii. 71 We must throw out the human equation as much as we can in our search to find an explanation for seeming aberrancies. 4. equation of payments n. the process of finding a mean time for the equitable payment in one amount of several sums due at different times. ΘΚΠ society > trade and finance > payment > [noun] > hastening or delaying payment > due date for payment > finding mean time for payment equation of payments1678 1678 J. Hawkins Cocker's Arithm. xxix. 309 Equation of payments is that Rule..whereby to reduce the times for payment of several sums of money to an equated time for payment of the whole debt without dammage to Debtor or Creditor. III. Statement of equality. †5. Mathematics. The action of stating the identity in value of two quantities or expressions. Obsolete. ΘΚΠ the world > relative properties > number > mathematical number or quantity > [noun] > relationship between quantities equation1570 1570 J. Dee in H. Billingsley tr. Euclid Elements Geom. Math. Præf. sig. ij^v That great Arithmeticall Arte of Æquation: commonly called..Algebra. 1579 L. Digges & T. Digges Stratioticos* 44 Æquation is nothing else but a certain conference of two numbers being in value Equal, and yet in multitude and Denomination different. 1664 H. Power Exper. Philos. Concl. 187 Thus came they to upbraid..Algebra with the Æquation of three discontinued Numbers. 1673 J. Kersey Elem. Algebra I. i. xi. 51 An Equation in the Algebraical Art is a mutual Comparing of two Equal quantities or things of different Denominations. 6. a. concrete. A formula affirming the equivalence of two quantitative expressions, which are for this purpose connected by the sign =.The two chief kinds of equations are: (1) Those which contain symbols denoting one or more unknown quantities; to discover the numerical values of these is called ‘solving’ the equation; the numbers which will ‘satisfy’ an equation, i.e. which may be substituted for the symbol of unknown quantity without rendering the statement incorrect, are called its ‘roots’. (2) Those which indicate a constant relation existing between variables; as equation to a curve, an equation expressing a relation between coordinates or the like, which is constant for every point in the curve; equation of motions, etc. Equations are distinguished as simple, quadratic, cubic, biquadratic, etc. (or as of the 1st, 2nd, 3rd, 4th, etc. degree) according to the highest power which they contain of any unknown or variable. ΘΚΠ the world > relative properties > number > algebra > [noun] > expression > equation equation1570 cardanic equation1684 binomial equation1814 simultaneous equation1816 characteristic equation1828 characteristic equation1841 characteristic equation1849 intrinsic equation of a curve1849 complete primitive1859 primitive1862 Poisson's equation1873 Jacobi equation1882 formulaic equation1884 adjoint1889 recursion formula1895 characteristic equation1899 characteristic equation1900 Pell equation1910 Lotka–Volterra equations1937 Langevin equation1943 1570 H. Billingsley tr. Euclid Elements Geom. ii. f. 60 Many rules..of Algebra, with the equations therein vsed. 1657 T. Hobbes Στιγμαι in Wks. (1845) VII. 366 You mean that..the lowermost to the lowermost in the first equation are equal. 1753 Philos. Trans. 1751–2 (Royal Soc.) 47 62 Mr. de Buffon mention'd..we should..resolve the equation. 1807 C. Hutton Course Math. (ed. 5) II. 322 The equation to the curve being ax = y². 1814 J. Playfair Outl. Nat. Philos. II. i. App. 227 This method of determining the coefficients of a given function, or correcting them from observation, by means of what are called Equations of Condition, is said to have been invented by Tobias Mayer of Göttingen. 1816 H. Douglas Ess. Mil. Bridges i. 16 The equation V = ^√mg/ _√b becomes V = ^306.7√r/ _√b. 1838 A. De Morgan Ess. Probabilities 29 An investigation of the method of solving an equation. 1871 B. Stewart Heat (ed. 2) §62 From this equation we derive at once the relation between the temperature and the density of air. 1879 W. Thomson & P. G. Tait Treat. Nat. Philos. (new ed.) I: Pt. i. §191 What is called the ‘equation of continuity’ [for fluids], an unhappily chosen expression. b. transferred. ΚΠ 1860 W. Thomson Outl. Laws of Thought (ed. 5) §68. 110 Every affirmative judgment may be regarded as an equation of subject and predicate. c. A formula which represents a chemical reaction by stating the equality between the symbols representing the original and those which represent the resulting substances. ΚΠ 1807 T. Thomson Syst. Chem. (ed. 3) II. 132 We have therefore this equation, Carbon 28 + Oxygen 72 = Carb. Ox. 69 + Oxygen 31. 1853 W. Gregory Inorg. Chem. (ed. 3) 90 The following equation explains the change. (KO,NO₅) + 2 (HO,SO₃) = (KO,HO,₂SO₃) + (HO,NO₅). 1857 E. L. Birkett Bird's Urinary Deposits (ed. 5) 245 In the following equation this decomposition of the allantoin is assumed to have occurred. Compounds equation box n. = equational box at equational adj. 2. ΚΠ 1893 I. K. Funk et al. Standard Dict. Eng. Lang. I. at Equational Equation box. equation table n. a table showing the time a clock should indicate when the sun is on the meridian. ΚΠ 1731 (title) An explanation of the nature of equation of time, and use of the equation table for adjusting watches and clocks to the motion of the sun. 1850 E. B. Denison Rudimentary Treat. Clock & Watch Making viii. 19 This [sundial]..with the equation-table will give the means of correcting a clock on any fine day. This entry has not yet been fully updated (first published 1891; most recently modified version published online December 2020). < n.1393
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