quadraturen.

Brit.

/ˈkwɒdrətʃə/, U.S.

/ˈkwɑdrətʃər/,

/ˈkwɑdrətʃʊ(ə)r/

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

Etymology: < classical Latin quadrātūra division of land into squares, in post-classical Latin also a square (4th cent.), four cardinal points of the compass (5th cent. in quadratura mundi the whole world), action of squaring the circle (6th cent. in quadratura circuli squaring of the circle), squareness, quality of being square in form (from 12th cent. in British sources), (in astronomy) state that exists between two celestial bodies when they lie ninety degrees apart on the ecliptic, point at which a celestial body enters each of its four quarteres (from 13th cent. in British sources), each side of a square object (1550 in the passage translated in quot. 1553 at sense 2), (in heraldry) quartering (c1595 in a British source) < quadrāt- , past participial stem of quadrāre quadrate v. + -ūra -ure suffix¹. Compare Middle French, French quadrature process of constructing geometrically a square equal in area to that of a given figure (1404–7 in quadrature du cercle squaring of the circle), (in astronomy) type of aspect (1546), Italian quadratura (1542).With sense 3a compare earlier quarreure n., and also quadrate n.¹ 3a.

1. The quality, state, or condition of being quadrate or quadrangular; squareness; (also) †a square or rectangle (obsolete). Now rare.In quot. a1460: a square battle formation.

ΘΚΠ

the world > space > shape > angularity > specific angular shape > [noun] > quadrilateral > square > quality

squarenessc1400

quadraturea1460

quadrateness1599

a1460 Knyghthode & Bataile (Pembr. Cambr. 243) 583 (MED) Thus vs embataile..A sengil ege is first to strecch in longe..With dowbeling forwith let make it stronge..And with a woord turne hem to quadrature.

a1555 J. Philpot Let. in J. Foxe Actes & Monuments (1570) III. 2012/1 The meruelous quadrature of the same, I take to signifie the vniuersall agreement in the same.

1561 R. Eden tr. M. Cortés Arte Nauigation iii. ii. sig. H iii^v These two orders of lynes, shall deuide all the superficiall parte of the Carde into perfect squares or quadratures.

1600 P. Holland tr. Livy Rom. Hist. xxv. xxiii. 565 One of the Romans..counted the stones..and made estimate to himselfe of their quadrature and proportion.

1653 R. Saunders Physiognomie i. 60 When the Quadrangle is broad, and well-proportioned in its quadrature.

1667 J. Milton Paradise Lost x. 381 Parted by th' Empyreal bounds, His Quadrature, from thy Orbicular World.

1994 C. McCarthy Crossing 103 The spare houses of Colonia Morelos stood along the quadrature of its four streets like markers in a child's game drawn in the dust.

†2. Each of the four sides of a square or square-shaped object. Obsolete. rare.

ΘΚΠ

the world > space > shape > angularity > specific angular shape > [noun] > quadrilateral > square > side of a square

squarec1400

quadrature1553

quadrant1587

1553 R. Eden tr. S. Münster Treat. Newe India sig. Fiij Euery quadrature or syde of the wall [L. quaelibet muri quadratura], hath in it thre principal portes or gates.

a. Astronomy. The aspect of an object in the solar system when situated 90 degrees from the sun as seen from earth (formerly also †quadrature aspect); a similar aspect between any two celestial objects or zodiacal signs; frequently in in quadrature. Also: each of the two points at which the moon is 90 degrees from the sun as seen from the earth, i.e. midway between the points of conjunction and opposition. Cf. octant n. 2, syzygy n. 1b.

ΘΚΠ

the world > the universe > planet > position of planet > aspect > [noun] > quadrature

quarreurea1500

quartile1517

quadrate1555

quadrature1555

tetragona1626

quadrine1628

square1667

the world > the universe > planet > primary planet > moon > lunar orbit > [noun] > quadrature

quartile1517

quadrate1555

quadrature1555

quarter moon1601

square1667

1555 L. Digges Prognostication Right Good Effect sig. B.iv^v The quadrature, sextile, or opposition of Saturne, wyth Iuppiter in moyst signes cawsith troubled ayer.

1666 J. Wallis Let. 25 Apr. in R. Boyle Corr. (2001) III. 144 About the Full-moon and New-moon the Tides are at the Highest, at the Quadratures the Tides are at the Lowest.

1670 J. Flamsteed Let. 16 July in Corr. (1995) I. 48 He teaches how to corect the apparent time of the Quadrature as if the parallax caused the Moone to be really cave when shee was apparently semi illuminated but this correction is needlesse.

1715 tr. D. Gregory Elements Astron. I. i. §61. 125 The passage of the Body L from the Quadratures to the Syzygies.

1774 O. Goldsmith Hist. Earth I. 255 The tides are greatest in the syzigies, and least in the quadratures.

1854 D. Brewster More Worlds xvi. 236 The rays reflected from them when the planets are in quadrature.

1877 G. F. Chambers Handbk. Descr. Astron. (ed. 3) i. ii. 39 After starting from conjunction with the Sun it successively reaches its Eastern quadrature, [etc.].

1926 H. N. Russell et al. Astron. I. ix. 238 A planet when in opposition is on the meridian about midnight; when in quadrature, about 6 a.m. or 6 p.m.

1994 J. North Fontana Hist. Astron. & Cosmol. xii. 306 He settled on the octants, mid-way between syzygies and quadratures, and observed the Moon carefully through these points.

1999 J. Raban Passage to Juneau vii. 399 I found a note in the pilot: when the moon was in quadrature, a continuous ebb sometimes ran in Stephens Passage.

†b. Heraldry. in quadrature: at intervals of a quarter-circle. Obsolete.

ΚΠ

1765 ‘M. A. Porny’ Elements Heraldry v. 154 A circular Wreath Pearl and Diamond [equating to Argent and Sable], with four Hawk's Bells joined thereto in quadrature Topaz [equating to Or].

1894 H. Gough & J. Parker Gloss. Terms Heraldry (new ed.) 480 Four charges placed in a square have been described as in quadrature, or in quadrangle, instead of two and two, which is more correct; but this is seldom necessary, as four charges would naturally so be placed.

c. An electrical phase difference of 90 degrees. Usually attributive (esp. designating devices that produce such a phase difference) or in in quadrature (with).

ΘΚΠ

the world > matter > physics > electromagnetic radiation > electricity > electrical engineering > phase > [adjective] > working in phase

in quadrature (with)1889

synchronous1897

phased1929

the world > matter > physics > electromagnetic radiation > electricity > electrical engineering > phase > [noun] > difference in phase > of 90 degrees

quadrature1889

the world > matter > physics > electromagnetic radiation > electronics > electronic phenomena > [adjective] > in or out of phase > specific difference

quadrature1992

1889 T. H. Blakesley Alternating Currents of Electr. (ed. 2) xiii. 117 The only induction in the secondary coil is derived from the core, and is, therefore, as regards phase, in quadrature with the magnetization.

1902 C. P. Stienmetz Theoret. Elem. Electr. Engin. 296 The quadrature component of the main flux induces E.M.F. in the auxiliary circuit of the starting device.

1908 Proc. Royal Soc. 80 345 No reference is made to the conditions for accuracy of a quadrature transformer containing iron in its core.

1967 Electronics 6 Mar. 120/2 The current in these resistors is in quadrature with the current in A₃'s input resistor.

1974 P. K. Harvey & K. J. Bohlman Stereo F.M. Radio Handbk. iv. 65 The normal signal is again divided by 2 to give a 19kHz quadrature signal for feeding back along the phase-lock loop.

1992 V. Capel Public Addr. Syst. xi. 163 A quadrature sine-wave oscilator running at a frequency of 5 Hz has two ouputs..90° out of phase.

1995 P. Woodward My Own Right Time 156 Two vibrations are in quadrature if they have the same frequency but their phase angles differ by 90°.

4. Mathematics. The process of constructing geometrically a square equal in area to that of a given figure, esp. a circle. More widely: the calculation of the area bounded by, or lying under, a curve; the calculation of a definite integral, esp. by numerical methods.Quot. 1728 refers to markings on an instrument that can be used in the construction of polygons of four or more sides.

ΘΚΠ

the world > relative properties > number > geometry > [noun] > action or process > finding square equivalent

quadrature1569

squaring1704

tetragonism1704

quadrability1743

the world > relative properties > number > geometry > [noun] > action or process

effectiona1652

retrogression1704

genesis1706

construction of equations1728

trace1834

tortuosity1867

quadrature1911

surgery1961

1569 J. Sanford tr. H. C. Agrippa Of Vanitie Artes & Sci. xxii. f. 33 Yet no Geometrician hath founde out the true Quadrature [L. quadraturam] of the Circle.

1596 T. Nashe Haue with you to Saffron-Walden To Rdr. sig. C4^v As much time..as a man might haue found out the quadrature of the Circle in.

1652 E. Benlowes Theophila xi. xxxvii. 198 As hard to finde thy Cure, As Circles puzling Quadrature.

1665 Philos. Trans. (Royal Soc.) 1 15 A method for the Quadrature of Parabola's of all degrees.

1728 E. Chambers Cycl. (at cited word) Quadrature-Lines, or Lines of Quadrature, are two Lines frequently placed on Gunter's Sector. [Description follows.]

1743 W. Emerson Doctr. Fluxions p. iii Drawing Tangents to Curves, finding their Curvatures, their Lengths, and Quadratures.

1829 Marquis of Anglesea Let. 28 Feb. in Lady Morgan Memoirs (1862) II. xviii. 278 I am as incapable of making a rhyme as of effecting the quadrature of the circle.

1881 R. Routledge Pop. Hist. Sci. ii. 36 The attention which the problem of the quadrature of the circle has attracted.

1911 E. B. Wilson Adv. Calculus xi. 313 It is therefore customary to restrict the application of the term ‘area’ to such simple closed curves as have mal_u = 0, and to say that the quadrature of such curves is possible, but that the quadrature of curves for which l_u ≠ 0 is impossible.

1942 H. M. Bacon Differential & Integral Calculus xiv. 410 The definite integral, which solves the problem of quadrature mentioned in Chap. I, suggests the notation for integrals, the ∫ being a conventionalized form of ‘S’ for ‘sum’.

1968 L. Fox & D. F. Mayers Computing Methods for Scientists & Engineers ix. 170 Apart from the rare possibility of being able to perform the quadrature by expressing the indefinite integral in closed form.., we have various general methods and some special methods.

2002 Biometrika 89 732 Further suppose that this integral cannot be evaluated analytically nor by standard quadrature methods.

†5. A division into four parts. Cf. quadrated adj. 2. Obsolete. rare.

ΘΚΠ

the world > relative properties > number > specific numbers > four > [noun] > division into four

quadrature1578

quadripartitiona1661

quadrisection1673

quadripartiting1702

tetrachotomy1858

tetramerism1888

1578 H. Lyte tr. R. Dodoens Niewe Herball vi. lxxix. 759 Foure straight lines running alongst the young shutes or branches, the which do make a quadrature [Fr. qui sont comme vne quadrature], or a diuision of the said young branches into foure square partes or cliftes.

†6. Each of the four cardinal points of the compass, as projected on to the celestial sphere. Obsolete. rare. Cf. the note at quadrate adj. 2.

ΘΚΠ

the world > the earth > direction > cardinal points > [noun] > one of

plagea1425

quartera1450

quadrature1601

society > travel > travel by water > vessel, ship, or boat > equipment of vessel > navigational aids > [noun] > compass > card of > point(s) of compass > principal points > one of

quartera1450

rhumb1594

quadrature1601

1601 P. Holland tr. Pliny Hist. World I. 37 When this concurrence [of the planets with the sun] is about the quadratures of the heaven. [Fr. en un des quatre angles du ciel, L. circa quadrata mundi.]

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

单词	quadrature
释义	quadraturen. Brit. /ˈkwɒdrətʃə/, U.S. /ˈkwɑdrətʃər/, /ˈkwɑdrətʃʊ(ə)r/ Origin: A borrowing from Latin. Etymon: Latin quadrātūra. Etymology: < classical Latin quadrātūra division of land into squares, in post-classical Latin also a square (4th cent.), four cardinal points of the compass (5th cent. in quadratura mundi the whole world), action of squaring the circle (6th cent. in quadratura circuli squaring of the circle), squareness, quality of being square in form (from 12th cent. in British sources), (in astronomy) state that exists between two celestial bodies when they lie ninety degrees apart on the ecliptic, point at which a celestial body enters each of its four quarteres (from 13th cent. in British sources), each side of a square object (1550 in the passage translated in quot. 1553 at sense 2), (in heraldry) quartering (c1595 in a British source) < quadrāt- , past participial stem of quadrāre quadrate v. + -ūra -ure suffix¹. Compare Middle French, French quadrature process of constructing geometrically a square equal in area to that of a given figure (1404–7 in quadrature du cercle squaring of the circle), (in astronomy) type of aspect (1546), Italian quadratura (1542).With sense 3a compare earlier quarreure n., and also quadrate n.¹ 3a. 1. The quality, state, or condition of being quadrate or quadrangular; squareness; (also) †a square or rectangle (obsolete). Now rare.In quot. a1460: a square battle formation. ΘΚΠ the world > space > shape > angularity > specific angular shape > [noun] > quadrilateral > square > quality squarenessc1400 quadraturea1460 quadrateness1599 a1460 Knyghthode & Bataile (Pembr. Cambr. 243) 583 (MED) Thus vs embataile..A sengil ege is first to strecch in longe..With dowbeling forwith let make it stronge..And with a woord turne hem to quadrature. a1555 J. Philpot Let. in J. Foxe Actes & Monuments (1570) III. 2012/1 The meruelous quadrature of the same, I take to signifie the vniuersall agreement in the same. 1561 R. Eden tr. M. Cortés Arte Nauigation iii. ii. sig. H iii^v These two orders of lynes, shall deuide all the superficiall parte of the Carde into perfect squares or quadratures. 1600 P. Holland tr. Livy Rom. Hist. xxv. xxiii. 565 One of the Romans..counted the stones..and made estimate to himselfe of their quadrature and proportion. 1653 R. Saunders Physiognomie i. 60 When the Quadrangle is broad, and well-proportioned in its quadrature. 1667 J. Milton Paradise Lost x. 381 Parted by th' Empyreal bounds, His Quadrature, from thy Orbicular World. View more context for this quotation 1994 C. McCarthy Crossing 103 The spare houses of Colonia Morelos stood along the quadrature of its four streets like markers in a child's game drawn in the dust. †2. Each of the four sides of a square or square-shaped object. Obsolete. rare. ΘΚΠ the world > space > shape > angularity > specific angular shape > [noun] > quadrilateral > square > side of a square squarec1400 quadrature1553 quadrant1587 1553 R. Eden tr. S. Münster Treat. Newe India sig. Fiij Euery quadrature or syde of the wall [L. quaelibet muri quadratura], hath in it thre principal portes or gates. 3. a. Astronomy. The aspect of an object in the solar system when situated 90 degrees from the sun as seen from earth (formerly also †quadrature aspect); a similar aspect between any two celestial objects or zodiacal signs; frequently in in quadrature. Also: each of the two points at which the moon is 90 degrees from the sun as seen from the earth, i.e. midway between the points of conjunction and opposition. Cf. octant n. 2, syzygy n. 1b. ΘΚΠ the world > the universe > planet > position of planet > aspect > [noun] > quadrature quarreurea1500 quartile1517 quadrate1555 quadrature1555 tetragona1626 quadrine1628 square1667 the world > the universe > planet > primary planet > moon > lunar orbit > [noun] > quadrature quartile1517 quadrate1555 quadrature1555 quarter moon1601 square1667 1555 L. Digges Prognostication Right Good Effect sig. B.iv^v The quadrature, sextile, or opposition of Saturne, wyth Iuppiter in moyst signes cawsith troubled ayer. 1666 J. Wallis Let. 25 Apr. in R. Boyle Corr. (2001) III. 144 About the Full-moon and New-moon the Tides are at the Highest, at the Quadratures the Tides are at the Lowest. 1670 J. Flamsteed Let. 16 July in Corr. (1995) I. 48 He teaches how to corect the apparent time of the Quadrature as if the parallax caused the Moone to be really cave when shee was apparently semi illuminated but this correction is needlesse. 1715 tr. D. Gregory Elements Astron. I. i. §61. 125 The passage of the Body L from the Quadratures to the Syzygies. 1774 O. Goldsmith Hist. Earth I. 255 The tides are greatest in the syzigies, and least in the quadratures. 1854 D. Brewster More Worlds xvi. 236 The rays reflected from them when the planets are in quadrature. 1877 G. F. Chambers Handbk. Descr. Astron. (ed. 3) i. ii. 39 After starting from conjunction with the Sun it successively reaches its Eastern quadrature, [etc.]. 1926 H. N. Russell et al. Astron. I. ix. 238 A planet when in opposition is on the meridian about midnight; when in quadrature, about 6 a.m. or 6 p.m. 1994 J. North Fontana Hist. Astron. & Cosmol. xii. 306 He settled on the octants, mid-way between syzygies and quadratures, and observed the Moon carefully through these points. 1999 J. Raban Passage to Juneau vii. 399 I found a note in the pilot: when the moon was in quadrature, a continuous ebb sometimes ran in Stephens Passage. †b. Heraldry. in quadrature: at intervals of a quarter-circle. Obsolete. ΚΠ 1765 ‘M. A. Porny’ Elements Heraldry v. 154 A circular Wreath Pearl and Diamond [equating to Argent and Sable], with four Hawk's Bells joined thereto in quadrature Topaz [equating to Or]. 1894 H. Gough & J. Parker Gloss. Terms Heraldry (new ed.) 480 Four charges placed in a square have been described as in quadrature, or in quadrangle, instead of two and two, which is more correct; but this is seldom necessary, as four charges would naturally so be placed. c. An electrical phase difference of 90 degrees. Usually attributive (esp. designating devices that produce such a phase difference) or in in quadrature (with). ΘΚΠ the world > matter > physics > electromagnetic radiation > electricity > electrical engineering > phase > [adjective] > working in phase in quadrature (with)1889 synchronous1897 phased1929 the world > matter > physics > electromagnetic radiation > electricity > electrical engineering > phase > [noun] > difference in phase > of 90 degrees quadrature1889 the world > matter > physics > electromagnetic radiation > electronics > electronic phenomena > [adjective] > in or out of phase > specific difference quadrature1992 1889 T. H. Blakesley Alternating Currents of Electr. (ed. 2) xiii. 117 The only induction in the secondary coil is derived from the core, and is, therefore, as regards phase, in quadrature with the magnetization. 1902 C. P. Stienmetz Theoret. Elem. Electr. Engin. 296 The quadrature component of the main flux induces E.M.F. in the auxiliary circuit of the starting device. 1908 Proc. Royal Soc. 80 345 No reference is made to the conditions for accuracy of a quadrature transformer containing iron in its core. 1967 Electronics 6 Mar. 120/2 The current in these resistors is in quadrature with the current in A₃'s input resistor. 1974 P. K. Harvey & K. J. Bohlman Stereo F.M. Radio Handbk. iv. 65 The normal signal is again divided by 2 to give a 19kHz quadrature signal for feeding back along the phase-lock loop. 1992 V. Capel Public Addr. Syst. xi. 163 A quadrature sine-wave oscilator running at a frequency of 5 Hz has two ouputs..90° out of phase. 1995 P. Woodward My Own Right Time 156 Two vibrations are in quadrature if they have the same frequency but their phase angles differ by 90°. 4. Mathematics. The process of constructing geometrically a square equal in area to that of a given figure, esp. a circle. More widely: the calculation of the area bounded by, or lying under, a curve; the calculation of a definite integral, esp. by numerical methods.Quot. 1728 refers to markings on an instrument that can be used in the construction of polygons of four or more sides. ΘΚΠ the world > relative properties > number > geometry > [noun] > action or process > finding square equivalent quadrature1569 squaring1704 tetragonism1704 quadrability1743 the world > relative properties > number > geometry > [noun] > action or process effectiona1652 retrogression1704 genesis1706 construction of equations1728 trace1834 tortuosity1867 quadrature1911 surgery1961 1569 J. Sanford tr. H. C. Agrippa Of Vanitie Artes & Sci. xxii. f. 33 Yet no Geometrician hath founde out the true Quadrature [L. quadraturam] of the Circle. 1596 T. Nashe Haue with you to Saffron-Walden To Rdr. sig. C4^v As much time..as a man might haue found out the quadrature of the Circle in. 1652 E. Benlowes Theophila xi. xxxvii. 198 As hard to finde thy Cure, As Circles puzling Quadrature. 1665 Philos. Trans. (Royal Soc.) 1 15 A method for the Quadrature of Parabola's of all degrees. 1728 E. Chambers Cycl. (at cited word) Quadrature-Lines, or Lines of Quadrature, are two Lines frequently placed on Gunter's Sector. [Description follows.] 1743 W. Emerson Doctr. Fluxions p. iii Drawing Tangents to Curves, finding their Curvatures, their Lengths, and Quadratures. 1829 Marquis of Anglesea Let. 28 Feb. in Lady Morgan Memoirs (1862) II. xviii. 278 I am as incapable of making a rhyme as of effecting the quadrature of the circle. 1881 R. Routledge Pop. Hist. Sci. ii. 36 The attention which the problem of the quadrature of the circle has attracted. 1911 E. B. Wilson Adv. Calculus xi. 313 It is therefore customary to restrict the application of the term ‘area’ to such simple closed curves as have mal_u = 0, and to say that the quadrature of such curves is possible, but that the quadrature of curves for which l_u ≠ 0 is impossible. 1942 H. M. Bacon Differential & Integral Calculus xiv. 410 The definite integral, which solves the problem of quadrature mentioned in Chap. I, suggests the notation for integrals, the ∫ being a conventionalized form of ‘S’ for ‘sum’. 1968 L. Fox & D. F. Mayers Computing Methods for Scientists & Engineers ix. 170 Apart from the rare possibility of being able to perform the quadrature by expressing the indefinite integral in closed form.., we have various general methods and some special methods. 2002 Biometrika 89 732 Further suppose that this integral cannot be evaluated analytically nor by standard quadrature methods. †5. A division into four parts. Cf. quadrated adj. 2. Obsolete. rare. ΘΚΠ the world > relative properties > number > specific numbers > four > [noun] > division into four quadrature1578 quadripartitiona1661 quadrisection1673 quadripartiting1702 tetrachotomy1858 tetramerism1888 1578 H. Lyte tr. R. Dodoens Niewe Herball vi. lxxix. 759 Foure straight lines running alongst the young shutes or branches, the which do make a quadrature [Fr. qui sont comme vne quadrature], or a diuision of the said young branches into foure square partes or cliftes. †6. Each of the four cardinal points of the compass, as projected on to the celestial sphere. Obsolete. rare. Cf. the note at quadrate adj. 2. ΘΚΠ the world > the earth > direction > cardinal points > [noun] > one of plagea1425 quartera1450 quadrature1601 society > travel > travel by water > vessel, ship, or boat > equipment of vessel > navigational aids > [noun] > compass > card of > point(s) of compass > principal points > one of quartera1450 rhumb1594 quadrature1601 1601 P. Holland tr. Pliny Hist. World I. 37 When this concurrence [of the planets with the sun] is about the quadratures of the heaven. [Fr. en un des quatre angles du ciel, L. circa quadrata mundi.] This entry has been updated (OED Third Edition, December 2007; most recently modified version published online March 2022). < n.a1460
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