Definitions

• WordNet 3.6
• n quadrature the construction of a square having the same area as some other figure
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Webster's Revised Unabridged Dictionary
• Quadrature (Math) The act of squaring; the finding of a square having the same area as some given curvilinear figure; as, the quadrature of a circle; the operation of finding an expression for the area of a figure bounded wholly or in part by a curved line, as by a curve, two ordinates, and the axis of abscissas.
• Quadrature (Integral Calculus) The integral used in obtaining the area bounded by a curve; hence, the definite integral of the product of any function of one variable into the differential of that variable.
• Quadrature (Astron) The position of one heavenly body in respect to another when distant from it 90°, or a quarter of a circle, as the moon when at an equal distance from the points of conjunction and opposition.
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Century Dictionary and Cyclopedia
• n quadrature In geometry, the act of squaring an area; the finding of a square or several squares equal in area to a given surface.
• n quadrature A quadrate; a square space.
• n quadrature The relative position of two planets, or of a planet and the sun, when the difference of their longitudes is 90°.
• n quadrature But when armillæ were employed to observe the moon in other situations … a second inequality was discovered, which was connected, not with the anomalistical, but with the synodical revolution of the moon, disappearing in conjunctions and oppositions, and coming to its greatest amount in quadratures. What was most perplexing about this second inequality was that it did not return in every quadrature, but, though in some it amounted to 2° 39′ , in other quadratures it totally disappeared.
• n quadrature A side of a square.
• n quadrature In electricity, phase difference of 90°, or one quarter period.
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Chambers's Twentieth Century Dictionary
• Quadrature a squaring: :
• Quadrature (geom.) the finding, exactly or approximately, of a square that shall be equal to a given figure of some other shape: the position of a heavenly body when 90° distant from another
• Quadrature (Milt.) a square space
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Etymology

Webster's Revised Unabridged Dictionary
Chambers's Twentieth Century Dictionary
O. Fr. quadrat—L. quadratus, pa.p. of quadrāre, to square—quatuor, four.

Usage

In literature:

Will they not seek the quadrature of the circle, even when on their wives?
"The Essays of Montaigne, Complete" by Michel de Montaigne
A solution of the secular problem of the quadrature of the circle, government premium 1,000,000 pounds sterling.
"Ulysses" by James Joyce
It is just the same with the quadrature of the circle.
"The Exemplary Novels of Cervantes" by Miguel de Cervantes Saavedra
Aboue the which stood an vnequal quadrature three foot long, two foot broad, and six foote high.
"Hypnerotomachia" by Francesco Colonna
If the moon is in quadrature, the effect will be null.
"Outlines of a Mechanical Theory of Storms" by T. Bassnett
The quadrature deserved it; but that is another point.
"A Budget of Paradoxes, Volume I (of II)" by Augustus De Morgan
IV was in quadrature.
"A Matter of Importance" by William Fitzgerald Jenkins
The moon is said to be in quadrature at the first and last quarter, when her longitude differs 90 deg.
"The Sailor's Word-Book" by William Henry Smyth
And now I have made my own age a problem of quadrature, and Mr. J. Smith may solve it.
"A Budget of Paradoxes, Volume II (of II)" by Augustus de Morgan
From the Table I., or by quadrature of the curve in fig.
"Encyclopaedia Britannica, 11th Edition, Volume 3, Part 1, Slice 2" by Various
The Moon is then a semi-circle, or in quadrature.
"The Astronomy of Milton's 'Paradise Lost'" by Thomas Orchard
All next week it is moving against the same extra pull, and so arrives at quadrature (half moon) somewhat late.
"Pioneers of Science" by Oliver Lodge
Among his mathematical investigations must not be omitted the quadrature of the parabola.
"History of the Intellectual Development of Europe, Volume I (of 2)" by John William Draper
Rectification and quadrature of the circle have thus been, since the time of Archimedes at least, practically identical problems.
"Encyclopaedia Britannica, 11th Edition, Volume 6, Slice 4" by Various
And, were it lost, the quadrature of the circle would not be more difficult than its restoration.
"The Truth About Tristrem Varick" by Edgar Saltus
Circle, the quadrature of, treated by Archimedes, i.
"History of the Intellectual Development of Europe, Volume II (of 2)" by John William Draper
Such ideas are evidently akin to the poetic notion of the quadrature.
"The Seven Follies of Science [2nd ed.]" by John Phin
QUADRATURES OF THE MOON.
"Conversations on Natural Philosophy, in which the Elements of that Science are Familiarly Explained" by Jane Haldimand Marcet and Thomas P. Jones
Even the moon, whose assistance is needed, is in the house of a friendly star, and in a favorable quadrature to Jupiter.
"The Magic of the Middle Ages" by Viktor Rydberg
When Cavalieri was printing his two treatises there was much discussion of the problem of quadratures.
"Encyclopaedia Britannica, 11th Edition, Volume 14, Slice 5" by Various
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In news:

The LTC5585 quadrature demodulator is capable of baseband output demodulation bandwidth of greater than 530 MHz.
Compared tosuperheterodyne architectures, a monolithic, high-linearity quadrature demodulator is vowing to reduce the component count of the receive signal chain in third-generation (3G) base stations by at least 75 percent.
The 90000X-Series real-time oscilloscopes from Agilent Technologies provide the capability to capture and analyze multiple signals or in-phase (I) and quadrature (Q) signal components at extremely high frequencies.
The circuit uses two transformers to convert three- phase power to two- phase for hum-free operation of the filaments of the final pair of tubes operating in phase quadrature.
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In science:

The function A(t), on the other hand, is then obtained by the quadrature from (6).
Exact Inflationary Solutions from a Superpotential
Here E is the particle energy in GeV, and the symbol ⊕ implies that the stochastic and constant terms in the resolution are combined in quadrature.
Studies of the Response of the Prototype CMS Hadron Calorimeter, Including Magnetic Field Effects, to Pion, Electron, and Muon Beams
This prediction uncertainty is subtracted in quadrature from the measured spatial resolution in the results shown below.
Performance of prototype BTeV silicon pixel detectors in a high energy pion beam
It is evident that the no-energy-transfer regime is not useful for the quadrature squeezing generation.
Quantum, classical and semiclassical analyses of photon statistics in harmonic generation
This is a Bernoulli equation and, unlike the Riccati equation, it is readily soluble in quadratures.
Static charged perfect fluid spheres in general relativity
Direct quadrature of the Feynman-Ka¸c formula.
Random Series and Discrete Path Integral methods: The Levy-Ciesielski implementation
Replacing the monodimensional integral in the FeynmanKa¸c formula (9) by its quadrature form, we obtain an approximation to the density matrix of the form x,x′ (ui )idu) .
Random Series and Discrete Path Integral methods: The Levy-Ciesielski implementation
Given a quadrature scheme, one diagonalizes the tridiagonal matrix A and tabulates the values of Si,j and λi .
Random Series and Discrete Path Integral methods: The Levy-Ciesielski implementation
However, as we have shown in Section II, the discrete methods can be directly derived from the Feynman-Ka¸c formula by simply replacing the integrals given by Eq. (43) with appropriate quadrature sums.
Random Series and Discrete Path Integral methods: The Levy-Ciesielski implementation
An interesting property of the metric (4.20) is that if the function v (ρ) is known, then z(ρ) can be obtained from equation (4.12) by performing two quadratures.
Ellipsoidal shapes in general relativity: general definitions and an application
The quadratures play the role of the real and the imaginary parts of the mode amplitudes.
Quantum Physics of Simple Optical Instruments
The q quadrature appears as the position and the p quadrature as the momentum of the electromagnetic oscillator represented in a single mode of light.
Quantum Physics of Simple Optical Instruments
However, since the quadrature operators ˆq and ˆp do not commute, since ˆq and ˆp cannot be measured simultaneously and precisely, the quasiprobability distributions must not represent perfect phase-space densities.
Quantum Physics of Simple Optical Instruments
The marginal distributions of the Wigner function agree with the correct quadrature histograms with respect to an arbitrary phase shift.
Quantum Physics of Simple Optical Instruments
The Wigner function (4.14) describes the quantumstatistical ﬂuctuations of the amplitude components q and p, the quadratures .
Quantum Physics of Simple Optical Instruments
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