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Q, the sixteenth letter of the alphabet, borrowed from, the Latin or French, and for which the Saxons generally used cp, cw. The name of this letter is derived from Fr. queue, tail; its form being that of an O with a tail. The Q has this peculiar to it, that it is always followed by a U, and is therefore reckoned among the mutes. It is formed from the Hebrew p, koph; which most other languages have borrowed; though some of them have rejected it again, particularly the Greeks.

In effect, there is that resemblance between the Q and the C in some languages, and the K in others, that many grammarians, in imitation of the Greeks, banish the Q as a superfluous letter. Papias even affirms that all the Latin words now written with a Q were written among the ancient Romans with a C; but we want better authority for this. For though, in many cases, some write indifferently quur, or cur; cum, or quum; quotidie, or cotidie, &c., yet it does not thence follow that they ever wrote cis, cæ, cid, for quis, quæ, quid. Far from this, the ancients sometimes substituted Q for C; and wrote quojus, quoi, for cujus, cui, &c.

Varro, however, and some other grammarians, as we are told by Censorinus, &c., would never use the Q. The truth is, its use or disuse seems to have been so little settled and agreed on that the poets used the Q or C indifferently, as best suited their measures; it being a rule that the Q joined the two following vowels into one syllable; and that the C imported them to be divided. Hence it is that Lucretius uses cuiret for three syllables, in lieu of quiret; acua for aqua; and that Plautus uses relicuum for reliquum; as in Quod dedi, datum non vellem relicuum non ; where the cuum must be two syllables, otherwise the trochiac verse will be lame of a foot. In the French the sound of the Q and K are so near akin, that some of their nicest authors think the former might be spared. Ramus adds that till the establishment of royal professors in the university of Paris, under Francis I., they always used Q in the Latin the same as in the French; pronouncing kis, kalis, kantus, &c., for quis, qualis, quantus.

Some very learned men make Q a double letter as well as K and X. According to them, Q is evidently a C and U joined together, and they see the traces of the C U in the figure of the Q; the V being only laid obliquely, so as to come within the cavity of the C; as C <!

Q, among the ancients, was a numeral letter, signifying 500; as in the verse,

Q velut A cum D quingentus vult numerare. A dash over it, as Q, denoted it to signify 500,000.

Q is also used as an abbreviation in several arts. Q. pl. in physicians' bills, stands for quantum placet, as much as you please; q- s. for quantum sufficit, or as much as is necessary. See ABBREVIATION.

Q.

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King.

At the first appearance that a French quack made in Paris, a boy walked before him, publishing with a shrill voice, My father cures all sorts of distempers;' to which the doctor added in a grave manner, The child says true.' Addison.

Some quacks in the art of teaching pretend to make young gentlemen masters of the languages, before they can be masters of common sense.

Felton on the Classicks. Despairing quacks with curses fled the place, And vile attorneys, now an useless race. Pope.

QUADI, an ancient people of Germany, situated on the south-east of the mountains of Bohemia, on the banks of the Danube, and extending as far as the river Marus, or March, running by Moravia, which country they occupied.

QUADRA AND VANCOUVER'S ISLAND, an island on the north-west coast of North America, between Queen Charlotte's Sound and De Fuca's Straits. Nootka Sound lies not far from its south-west side. It was so named by Vancouver in honor of his meeting with signior Quadra, the officer who was commissioned by the court of Spain to cede, in the name of his court, the disputed territory of Nootka.

QUADRAGESIMAL, adj. Fr. quadragesi mal; Lat. quadragesima. Lenten; belonging to or used in Lent.

I have composed prayers out of the church collects, adventual, quadragesimal, paschal, or pentecostal. Sanderson.

QUAD'RANGLE, n. s. Lat. quadratus and angulus. A square; a surface with four right angles.

My choler being overblown
With walking once about the quadrangle,
I come to talk.
Shakspeare. Henry VI.
The escurial hath a quadrangle for every month in
the year.
Howel.

I was placed at a quadrangular table, opposite to Spectator. the mace-bearer. Common salt, shooteth into little crystals, coming near to a cube, sometimes into square plates, someGrew. times into short quadrangular prisms.

Each environed with a crust, conforming itself to the planes, is of a figure quadrangular. Woodward. QUADRANS, a farthing, the fourth part of a Before the reign of Edward I. the penny. smallest coin was a sterling, or penny, marked with a cross; by the guidance of which a penny might be cut into halves for a halfpenny, or into quarters or four parts for farthings; till, to avoid the fraud of unequal cuttings, that king coined halfpence and farthings in distinct round pieces. QUAD'RANT, n. s. Lat. quadrans. QUADRAN'TAL, adj. The fourth part; QUAD'RATE, adj., n. s., & the quarter; the QUADRATIC, adj. [v. n. quarter of a circle; QUADRATURE, n. s. an instrument for measuring altitudes: quadrate is square; fourfold; divisible into four parts; suited; fitted: a square; in astrology, an aspect of the heavenly bodies, wherein they are distant from each other ninety degrees, and the same with quartile: as a verb neuter, to suit; fit; be accommodated: quadratic, an algebraic term applied to such equations as retain, on the unknown side, the square of the root or the number sought: quadrature is the act of squaring; state of being square; a quadration square; the first and last quarter of the moon.

And 'twixt them both a quadrate was the base,
Proportioned equally by seven and nine;
Nine was the circle set in heaven's place,
All which compacted, made a goodly diapase.

Spenser. Whether the exact quadrate or the long square be the better is not well determined; I prefer the latter, provided the length do not exceed the latitude above one-third part.

Wotton.

Some tell us that the years Moses speaks of were somewhat above the monthly year, containing in them thirty-six days, which is a number quadrate.

Hakewill on Providence.

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To our understanding a quadrate, whose diagonal is commensurate to one of the sides, is a plain contradiction. More.

The obliquity of the ecliptick to the equator, and from thence the diurnal differences of the sun's right ascensions, which finish their variations in each quadrant of the circle of the ecliptick, being joined to the former inequality, arising from the excentricity, makes these quarterly and seeming irregular inequalities of natural days.

Holder on Time.

It is full moon when, the earth being between the sun and moon, we see all the enlightened part of the moon; new moon when, the moon being between us and the sun, its enlightened part is turned from us and half moon, when the moon being in the quadratures, we see but half the enlightened part.

Locke.

Tatler.

Some had compasses, others quadrants. Aristotle's rules for epick poetry, which he had drawn from his reflections upon Homer, cannot be supposed to quadrate exactly with the heroick poems which have been made since his time; as it is plain his rules would have been still more perfect, could Addison. he have perused the Æneid.

Thin taper sticks must from one centre part; Let these into the quadrant's form divide. Gay. Sir Isaac Newton discovered a way of attaining the quantity of all quadrible curves analytically, by his method of fluxions, some time before the year Derham. 1688.

To fill that space of dilating, proceed in straight lines, and dispose of those lines in a variety of paralels: and, to do that in a quadrantal space, there appears but one way possible; to form all the intersections, which the branches make, with angles of forty-five degrees only.

Id.

The speculations of algebra, the doctrine of infinites, and the quadrature of curves, should not intrench upon our studies of morality.

Watts.

QUADRANT, in geometry, is the arch of a circle, containing 90°, or the fourth part of the entire periphery. Sometimes also the space or area included between this arch and two radii drawn from the centre to each extremity thereof, is called a quadrant, or more properly a quadrantal space, as being a quarter of an entire circle.

QUADRANT is also a mathematical instrument of great use in astronomy and navigation, for taking the altitudes of the sun and stars, and for taking angles in surveying, &c. It is variously contrived, and furnished with different apparatus, according to the various uses it is intended for. See ASTRONOMY and NAVIGATION. The common surveying quadrant is made of brass, wood, or any other solid substance; the limb of which is divided into 90°, and each of these farther divided into as many equal parts as the space will allow, either diagonally or otherwise. On one of these semidiameters are fitted two moveable sights; and to the centre is sometimes fixed a label, or moveable index, bearing two other sights; but in lieu of these last sights there is sometimes fitted a telescope; also from the centre there is hung a thread with a plummet; and on the under side or face of the instrument is fitted a ball and a socket, by which it may be put into any position. The general use of it is for taking angles in a vertical plane, comprehended under right lines going from the centre of the instrument, one of which is horizontal, and the other is directed to some visible point. But, besides the parts already described, there is frequently added on the face, near the centre, a kind of compartment, called the quadrat, or geometrical square. This quadrant may be used in different situations; for observing heights or depths, its plane must be disposed perpendicularly to the horizon; but, to take horizontal distances, its plane is disposed parallel thereto. Again, heights and distances

may be taken two ways, viz. by means of the fixed sights and plummet, or by the label. QUADRANT, GUNNER'S, called also gunners' square, is that used for elevating and pointing cannon, mortars, &c., and consists of two branches, either of brass or wood, between which is a quadrantal arch divided into 90°, beginning from the shorter branch, and furnished with a thread and plummet. The use of the gunners' quadrant is extremely easy; for if the longest branch be placed in the mouth of the piece, and it be elevated till the plummet cut the degree necessary to hit a proposed object, the thing is done. Sometimes on one of the surfaces of the long branch are noted the divisions of diameters and weights of iron bullets, as also the bores of pieces.

QUADRANT, GUNTER'S, so called from its inventor Edmund Gunter, besides the usual apparatus of other quadrants, has a stereographical projection of the sphere on the plane of the equinoctial. It has also a kalendar of the months, next to the divisions of the limb.

QUADRANT, HADLEY'S, is an instrument of great utility both in navigation and practical astronomy. It is named from Mr. Hadley, who first published an account of it, though the invention originated with the celebrated Dr. Hooke, and was completed by Sir Isaac Newton. Its utility arises from the accuracy and precision with which it enables us to determine the latitude and longitude, and to it navigation is much indebted for the very great and rapid advances it has made of late years. It is easy to manage, and of extensive use, requiring no peculiar steadiness of hand, nor any such fixed basis as is necessary to other astronomical instruments. It is used for taking angles in maritime surveying, and with equal facility at the mast head as upon the deck, by which its sphere of observation is much extended; for supposing many islands to be visible from the mast head, and only one from deck, no useful observation can be made by any other instrument. By this angles may be taken at the mast head from the one visible object with great exactness; and further, taking angles from heights, as hills, or a ship mast's head, is almost the only way of exactly describing the figure and extent of shoals. It has been objected to the use of this instrument for surveying, that it does not measure the horizontal angles, by which alone a plan can be laid down. This objection, though true in theory, may be reduced in practice by a little caution; and Mr. Adams has given very good directions for doing so. No instrument has undergone, since the original invention, more changes than this quadrant. An essential and invaluable property, whereby it is rendered peculiarly advantageous in marine observations, is, that it is not liable to be disturbed by the ship's motion; for, provided the mariner can see distinctly the two objects in the field of his instrument, no motion nor vacillation of the ship will injure his observation.

QUADRANT, MURAL. See ASTRONOMY. QUADRANT OF ALTITUDE is an appendage of the artificial globe, consisting of a lamina, or slip of brass, the length of a quadrant of one of the

great circles of the globe, and graduated. At the end, where the division terminates, is a nut rivetted on, and furnished with a screw, by means whereof the instrument is fitted on the meridian, and moveable round upon the rivet to all points of the horizon. Its use is to serve as a scale in measuring of altitudes, amplitudes, azimuths, &c.

QUADRANTAL, in antiquity, the name of a vessel in use among the Romans for the measuring of liquids. It was at first called amphora; and afterwards quadrantal, from its form, which was square every way like a die. Its capacity was eighty libræ, or pounds of water, which made forty-eight sextaries, two urna, or eight congii.

QUADRATE, a mathematical instrument, called also a geometrical square, and line of shadows: it is frequently an additional member on the face of the common quadrant, as also on those of Gunter's and Sutton's quadrants.

QUADRATE, in printing, a piece of metal used to fill up the void spaces between words, &c.

QUADRATURE, in astronomy, that aspect of the moon when she is 90° distant from the sun; or when she is in a middle point of her orbit, between the points of conjunction and opposition, namely, in the first and third quarters. See ASTRONOMY.

QUADRATURE, in geometry, denotes the reducing a figure to a square, or the finding of a square which shall contain just as much surface or area as a circle, an ellipsis, a triangle, &c., is the quadrature of a circle, ellipsis, &c. This question, especially among the ancient mathematicians, was a great postulatum. The quadrature of rectilineal figures is easily found, for it is merely the finding their areas or surfaces, i. e. their squares; for the squares of equal areas are easily found by only extracting the roots of the areas thus found. The quadrature of the curvilinear spaces is of more difficult investigation; and in this respect extremely little was done by the ancients, except the finding the quadrature of the parabola by Archimedes. This he obtained in a very ingenious manner, by inscribing an isosceles triangle in the parabola, then two isosceles triangles on the equal sides of the former, four others on these, and so on, which he found to have a certain relation, decreasing in the proportion 1, t,, &c., the infinite sum of which series would therefore express the area of the parabola, or the area of all the triangles of which he thus conceived it to be composed; and which sum he found to be one and one-third, or two-thirds of the circumscribing rectangle. After this time, a period of near 2000 years elapsed without producing the quadrature of a single curvilinear figure, although the subject seems to have engaged the attention of the most eminent mathematicians during that long interval, particularly the quadrature of the circle. This figure, being the most simple in appearance and construction of any contained under a curve line, was well calculated to excite the curiosity of mathematicians. Archimedes doubtless attempted the solution of this problem; but, failing in producing the exact quadrature, he contented himself with giving an

approximation, showing by the inscription and circumscription of a polygon of ninety-six sides, that the diameter being 1, the circumference was greater than 34, but less than 348.

It would be useless to attempt in this place to enumerate the various absurd quadratures which have been, from time to time, published by minor geometers, with all that conceit and confidence which seldom fail to accompany inferiority. Some attributed their success to divine inspiration; others to their own superior talents some offered large sums of money to those who should discover any error in their investigation, while others expected great rewards from their government as a recompence for their discovery, foolishly attaching great importance to a problem, which, if it could be accurately solved, would serve no other purpose but to gratify the curiosity of mathematicians. Towards the year 1585, Metius, combatting the false quadrature of Simon Duchêne, gave the ratio of 113 to 355, which is very exact. Vieta found a still nearer approximation, carrying it to ten places of decimals, whereas the former is true only to six places.

Adrianus Romanus carried the approximation to seventeen figures, and Ludolph Van Ceulen to thirty-six; which he published in his work, De Circulo et Adscriptis; and of which Snellius published a Latin translation in 1619. He afterwards verified Van Ceulen's approximation by some theorems of his own invention, which greatly facilitated the computation, and which he published in 1621, under the title of Willebrordi Snellii Cyclometricus de Circuli Dimensione, &c.

Descartes gave a geometrical construction from which it was easy to draw an expression in the form of a series; and Huygens afterwards discovered some curious theorems connected with this subject, and formed some useful rules for approximating towards the length of

the circular arc.

A curious discovery connected with this subject was given by Wallis in his Arithmetica Infinitorum, in 1655: where he shows that the ratio of a circle to the square of its diameter is truly expressed by the infinite fraction.

32. 52. 72. 92. 112. &c. 2. 42. 62. 82. 102. 122. &c.

Such was the progress which mathematicians had made towards the solution of this interesting problem prior to the invention of fluxions, which, by reducing the quadrature of all curves to one general principle, again revived the hopes of success with regard to the circle, notwithstanding some pretended demonstrations of its impossibility; and its quadrature was accordingly again attempted with the greatest eager ness. The quadrature of a space, and the rectification of a curve, were now reduced to that of finding the fluent of a given fluxion but still the problem was found to be incapable of a general solution in infinite terms. The fluxion of a given fluent was found to be always assignable, but the converse proposition, viz. of finding the fluent of a given fluxion, could only be effected in particular cases; and amongst the

exceptions, to the great regret and disappointment of geometricians, was included the case of the circle with regard to every form of fluxion under which it could be obtained. Mr. Glenie in 1812 read a paper before the Royal Society to prove that the true geometrical quadrature of the circle was impossible; which is now indeed generally allowed.

QUADRATUS, a native of Athens, where he was educated, and became a disciple of the apostles. About A. D. 125, when the emperor Adrian visited Athens, and was initiated into the Eleusinian mysteries, a persecution of the Christians arose, wherein Publius bishop of Athens suffered martyrdom. Quadratus succeeded him, and wrote an Apology for the Christians, which he presented to the emperor, who thereupon stopt the prosecution. work is lost, but was extant in the time of Eusebius, who says it showed the genius of the author, and the true doctrine of the apostles. Quadratus was banished from Athens, but nothing certain is recorded of his death.

This

QUADRATUS, a surname of Mercury, because some of his statues were square.

QUADREL, in building, a kind of artificial stone, so called from its being square. The quadrels are made of a chalky earth, &c., and dried in the shade for two years. These were formerly in great request among the Italian architects.

QUADRIFRONS, AND QUADRICEPS, surnames of Janus, because he was represented with four heads and four faces.

QUADRIGA, in antiquity, a car or chariot drawn by four horses. On the reverses of medals, we frequently see the emperor or Victory in a quadriga, holding the reins of the horses; whence these coins are, among the curious, called nummi quadrigati and victoriati.

QUADRILATERAL, adj. Fr. quadrilatere; Lat. quatuor and latus. Having four sides.

Tin, incorporated with crystal, disposes it to shoot into a quadrilateral pyramid, sometimes placed on a quadrilateral base or column. Woodward.

QUADRILLE, a game played by four persons, with forty cards; which are the remains of a pack, after the four tens, nines, and eights are discarded; these are dealt three and three, and one round four, to the right hand player; and the trump is made by him that plays with or without calling, by naming spades, clubs, diamonds, or hearts, and the suit named is

trumps.

QUADRIO (Francis Xavier), a learned JeHe aftersuit, born in the Valteline in 1695. wards became secular priest, and died at Milan in 1756. He published, 1. A Treatise on the in 7 vols. 3. Dissertations upon the Valteline, Italian Poetry. 2. A History of Italian Poetry,

in 3 vols.

QUADRUPED, n. s. Fr. quadrupede; Lat. quadrupes. An animal that goes on four legs.

The different flexure and order of the joints is not disposed in the elephant as in other quadrupeds.

Browne. The fang teeth, eye teeth, or dentes canini of some quadruped. Woodward on Fossils.

Most quadrupedes, that live upon herbs have incisor teeth to pluck and divide them.

The king of brutes,

Arbuthnot.

Swift.

Of quadrupeds I only mean. The cockney, travelling into the country, is surprized at many actions of the quadruped and winged animals. Watts's Logick.

QUADRUPEDS, in zoology, those animals which have four limbs or legs proceeding from the trunk of their body. See ZOOLOGY.

QUADRUPLE, adj. Fr. quadruple; Lat. quadruplus. Fourfold; four times told.

A law, that to bridle theft doth punish thieves with a quadruple restitution, hath an end which will continue as long as the world itself continueth.

Hooker.

The lives of men on earth might have continued double, treble, or quadruple, to any of the longest times of the first age. Raleigh.

Fat refreshes the blood in the penury of aliment during the winter, and some animals have a quadruple caul. Arbuthnot on Aliments.

If the person accused maketh his innocence appear, the accuser is put to death, and out of his goods the innocent person is quadruply recompensed.

Swift. QUÆRE. Lat. quære. Enquire; seek; a word put when any thing is recommended to enquiry.

Quære, if it is steeped in the same liquor, it may not prevent the fly and grub.

Mortimer's Husbandry.

To QUAFF, v. a. Junius derives this word from the Greek kvapíšɛiv in the Æolic dialect used for kvaličev. Skinner from go off, as go off, guoff, quoff, quaff. It comes from Fr. coeffer, to be drunk, says Johnson: Swed. quæfa, from Goth. kaf, deep. Thomson. To drink; swallow in large draughts.

He calls for wine; a health, quoth he, as if
H'ad been abroad carousing to his mates
After a storm, quafft off the muscadel,
And threw the sops all in the sexton's face.

I found the prince,

Shakspeare.

With such a deep demeanor in great sorrow,
That tyranny, which never quaff's but blood,
Would, by beholding him, have washed his knife
With gentle eye-drops.
Id. Henry IV.

On flowers reposed, and with rich flowerets crowned,

They eat, they drink, and in communion sweet Quaff immortality and joy. Milton's Paradise Lost. Twelve days the gods their solemn revels keep. And quaff with blameless Ethiops in the deep.

Dryden. Belshazzar, quaffing in the sacred vessels of the temple, sees his fatal sentence writ by the fingers of God. South.

Ducks, having larger nerves that come into their bills than geese, quaffer and grope out their meat

the most.

Derham.

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Therewith his sturdy courage soon was quaid, And all his senses were with a sudden dread dismaid. Spenser.

QUAIGH, or QUAFF, a kind of drinking vessel, peculiar to the Highlands, made of different pieces of wood, of various colors joined together by small hoops. They are made of various sizes, to hold from a gill, (or quartern) to a pint or even a quart of Scottish measure. The small ones have two handles (or lugs as they are called) projecting from the brim; the large have four.

QUAIL, v. n. & v. a. Belg. quelen; Teut. qual, is sickness. To languish; lose spirits; sink into dejection; decline: crush; quell.

After Solyman had with all his power in vain besieged Rhodes, his haughty courage began to quail, so that he was upon point to have raised his siege. Knolles.

To drive him to despair, and quite to quail,
He shewed him painted in a table plain
The damned ghosts.

Spenser.

For yet is hope of life and victory.
This may plant courage in their quailing breasts,
Shakspeare.
While rocks stand,
And rivers stir, thou can'st not shrink or quail;
Yea, when both rocks and all things shall disband,
Then shalt thou be my rock and tower.

Herbert.

To pass the quailing and withering of all things by the recess, and their reviving by the reaccess of the sun, the sap in trees precisely follows the motion of the sun. Hakewill.

Three, with fi'ry courage, he assails ; Three, as kings adorned in royal wise; And each successive after other quails, Still wond'ring whence so many kings should rise. Daniel.

QUAIL, N. S. Fr. caille; Ital. quaglia; Belg. quackel; barb. Lat. quaquila. A bird of game and passage.

His quails ever

Beat mine. Shakspeare. Antony and Cleopatra. Hen birds have a peculiar sort of voice, when they would call the male, which is so eminent in quails, that men, by counterfeiting this voice with a quailpipe, easily draw the cocks into their snares. Ray on the Creation. A dish of wild fowl furnished conversation, concluded with a late invention for improving the quailpipe. A fresher gale Sweeping with shadowy gust the field of corn, While the quail clamours for his running mate. Thomson.

Addison.

QUAIL, in ornithology. See PERDIX. QUAIL-PIPES, or quail-calls, are made of a small leather purse, about two fingers wide, and four fingers long, in the shape of a pear; this is stuffed half full of horse-hair, and at the end of

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