He employs not on us the hammer and the chizzel, with an intent to wound or mangle us, but only to square and fashion our hard and stubborn hearts. Boyle's Seraphick Love. We live not on the square with such as these, Such are our betters who can better please. Dryden. His preaching much, but more his practice wrought; A living sermon of the truths he taught: Men should sort themselves with their equals; for a rich man that converses upon the square with a poor man, shall certainly undo him. L'Estrange. SQUARE, among mechanics, an instrument consisting of two rules or branches, fastened perpendicularly at one end of their extremities, so as to form a right angle. It is of great use in the laying down perpendiculars. description and mensuration of right angles, and SQUARE, HOLLOW, in the military art, body of foot drawn up with an empty space in the middle, for the colors, drums, and baggage, faced and covered by the pikes every way, to keep off the horse. SQUARE NUMBER is the product arising from a number multiplied by itself. Thus 4 is the square of 2, and 16 the square of 4. The series of square in 1 16 tegers is 1, 4, 9, 16, 25, 36, &c. which are the squares of 1, 2, 3, 4, 5, 6, &c. Or the square fractions 4, 3, fo, 13, 38, 1, &c. which are the squares of,,, 1, 1, 4, &c Square numbers have remarkable properties, of which the following are some of the most interesting, viz.-1. Every square number is of one of the forms 4 n or 4 n + 1; that is, every square, when divided by 4, will leave either 0 or 1 for a remainder; and, understanding this expression still in the same sense, the following table will express the forms of square numbers to the moduli or divisors, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12. Id. 3 3n Id. I shall break no squares whether it be so or not. This instrument is for striking lines square to other lines or straight sides, and try the squareness of their work. Moxon. Some professions can equally square themselves to, and thrive under, all revolutions of government. South. 6n+3 6n+ 4 7n+2 7n + 4 8 8n 8n+1 8n +4 9n 9n+1 9n+4 9n+7 1010n 10n+1 10n+ 4 10n+5 1111n 11n+1 11n +3 11n+5 11n +9 12 12 n 12n+1 12n + 4 12n +9 These formulæ, as they involve no higher power of the indeterminate n than the first, are called linear forms; but, by means of them, we easily arrive at a variety of quadratic formulæ, which it is extremely useful to be acquainted with, in practising the diophantine or indeterminate analysis. A person unacquainted with these exclusions, required to find two such numbers, that double the square of one, added to triple the square of the other, should be a square, would see nothing impossible in the proposition, and might therefore lose many useless hours in the research; whereas, by a little attention to the impossible and possible forms, he would find the problem absolutely impossible, and hence spare himself much useless labor. 3. The method of deducing impossible quadratic forms from the linear ones above given will be seen immediately from a single example. Let it be required to ascertain whether the equation 2 + 3y2w be possible or impossible. First, we may assume r, y, and w, prime to each other; for, if x and y have a common divisor, w must have the same, and the whole equation may be divided by it; whereby it will be reduced to another equation 2 x2 + 3 yw', in which these quantities have no longer a common divisor, or in other words they are prime to each other. Since, then, and y are prime to each other, they cannot be both of the form 3 n; for, in this case, they would have a common divisor 3. Let then, first, be of the form 3n, and y2 of the form 3n+1; then 2 r2 is of the form 3 n', and 3 y2 of the form 3n+ 3, and consequently their sum will have the form 3n, which is impossible, because, in this case, w and r would have a common divisor 3; and, if we suppose 2 of the form 3 n + 1, and y2 of the form 3 n, then 2x+3y is of the form 3n+2, which is an impossible form: and, lastly, if we assume both of the form 3n+1, then 2 2 + 3y2 would have again the same impossible form 3n+2; therefore, in no case can 22+ 3y w be possible in integral numbers. In the same manner a variety of other impossible forms may be deduced, of which the following are those which most commonly occur. 8 t2 + 3 u2 = w2 (3 p + 2) t2 + 3 u2 = w2 6. Modulus 5. 2 p2± 5 u2 = w2 7 ± 5 u2 = w2 (5 p± 2) t2 ± 5 u2 = w2 Or the two latter general forms may be rendered more comprehensive, by the introduction of another indeterminate q; observing only that, in this case, the quantity must always be prime to the modulus. With this condition the two latter may be written thus: (3 p + 2) t + 3 g u2 = w2, and · (5 p± 2) t° ± 5 qu2 = w2. (7 p + 3) t2 ± 7 q u2 = w2 These might also be carried to a much greater extent and many collateral properties drawn from them relative to the impossibility of some higher powers; we must not, however, carry the subject farther in this place. The reader who is desirous of more detailed information may consult Barlow's Elementary Investigation of the Theory of Numbers, where this part of the doctrine of Numbers is carried to a considerable extent. We shall merely select a few other distinct properties of squares, as they are given by the same author in his Mathematical Dictionary. 17. The sum of two odd squares cannot be a square. 18. An odd square, taken from an even square, cannot leave a square remainder. 19. If the sum of two squares be itself a square, one of the three squares is divisible by 5. 20. Square numbers must terminate in one of the digits 0, 1, 4, 5, 6, or 9. 21. No number of repetend digits can be a square. 22. The area of a rational right-angled triangle cannot be equal to a square. 23. The two following series are remarkable for being such as, when reduced to improper fractions, the sum of the squares of each numerator and denominator is a complete square; or, which is the same, they are the sides of rational right-angled triangles. These series are as follow, viz. : 1, 2, 3, 4, 5ft, &c. &c. 1, 2, 3, 4, 5, &c. &c. 24. The second differences of consecutive numbers are equal to each other, thus:— square Squares 1, 4, 9, 16, 25, &c. First difference 3, 5, 7, 9, &c. Second difference 2, 2, 2, &c. To these we may also add the following; which are more particularly applicable to the indeterminate and diophantine analysis. 25. If a number be the sum of two squares, its double is also the sum of two squares; for (x2 + y2) x 2 = (x + y)2 + (x − y)2. Square Inches. Square Feet. Sq. Yards. Sq. Poles. S. Chs. Acres. S. Miles SQUARE ROOT. See ALGEBRA. SQUARE-RIGGED, an epithet applied to a ship whose yards are very long. It is also used in contradistinction to all vessels whose sails are extended by stays or lateen-yards, or by booms and gaffs; the usual situation of which is nearly in the plane of the keel; and hence, SQUARE-SAIL, is a sail extended to a yard which hangs parallel to the horizon, as distinguished from the other sails which are extended by booms and stays placed obliquely. This sail is only used in fair winds, or to scud under in a tempest. In the former case, it is furnished with a large additional part called the bonnet, which is then attached to its bottom, and removed when it is necessary to scud. See Scudding. SQUARING THE CIRCLE is the making or finding a square whose area shall be equal to that of any proposed circle. See QUADRATURE. This problem has never yet been solved so as to be precisely exact; but mathematicians, it is said, can come so near it as not to err so much in the area as a grain of sand would cover in a circle, whose diameter is equal to the diameter of Sa SQUASH, n. s. From quash. Any thing soft and easily crushed: hence perhaps the plant of this name: any thing unripe; a sudden fall or shock. Not yet old enough for a man, nor young enough for a boy; as a squash is before it is a peascod, or a codling when it is almost an apple. Shakspeare. Twelfth Night. How like I then was to this kernel, This squash, this gentleman. Id. Winter's Tale. Since they will overload my shoulders, I shall hrow down the burden with a squash among them. Arbuthnot. My fall was stopped by a terrible squash, that sounded louder than the cataract of Niagara. Swift. Squash is an Indian kind of pumpion that grows a pace. Boyle. SQUAT, v. n. & adj. Ital. quattare. To sit cowering; sit close to the ground: cowering; close to the ground. Bruises, squats, and falls, which often kill others, can bring little hurt to those that are temperate. Him there they found, Herbert. Milton. Squat like a toad close at the ear of Eve. How like brutes organs are to ours; They grant, if higher powers think fit, A bear might soon be made a wit; And that, for any thing in nature, Pigs might squeak love-odes, dogs bark satire. In florid impotence he speaks, Prior. And, as the prompter breathes, the puppet squeaks. Pope Zoilus calls the companions of Ulysses the squeaking pigs of Homer. Id. Odyssey. SQUEA'MISH, adj. For quawmish, or SQUEA MISHLY, adv. qualmish, from qualm. SQUEA MISHNESS, n. s.) Nice; fastidious; easily disgusted; apt to take offence. It is used always in dislike either real or ironical: the adverb and noun substantive correspond. Yet, for countenance sake, he seemed very squamish in respect of the charge he had of the princess Pamela. Sidney. Quoth he, that honour's very squeamish, Hudibras. Upon their principles they may revive the worship of the host of heaven; it is but conquering a little Stillingfleet. sqeamishness of stomach. It is rare to see a man at once squeamish and voracious. South. The thorough-paced politician must laugh at the squeamishness of his conscience, and read it another lecture. Id. To administer this dose, fifty thousand operators, considering the squeamishness of some stomachs, and the peevishness of young children, is but reasonable. Swift. His muse is rustick, and perhaps too plain The men of squeamish taste to entertain. Southern. SQUEEZE, v. a., v. n. & n. s. Sax. cpiran; Teut. quetschen; Welsh ysgwasgu. To press,› crush between two bodies: to act in consequence of compression; force a way: compression; pres sure. It is applied to the squeezing or pressing of things downwards, as in the presses for printing. Wilkins. He reaped the product of his laboured ground, And squeezed the combs with golden liquor crowned. Dryden. In a civil war people must expect to be crushed and squeezed toward the burden. L'Estrange. Many a public minister comes empty in; but, when he has crammed his guts, he is fain to squeeze hard before he can get off. A subtle artist stands with wonderous bag, That bears imprisoned winds, of gentler sort Than those that erst Laertes' son enclosed: Peaceful they sleep; but let the tuneful squeeze Id. If labouring elbow rouze them, out they dy Melodious, and with spritely accents charm. Philips. The sinking of the earth would make a convulsion of the air, and that crack must so shake or squeeze the atmosphere as to bring down all the remaining vaBurnet. pours. A concave sphere of gold filled with water and soldered up, upon pressing the sphere with great force, let the water squeeze through it, and stand all over its outside in multitudes of small drops, like dew, without bursting or cracking the body of the gold. Newton's Opticks. What crowds of these, impenitently bold, Pope. SQUELCH, n. s. From QUASH. Heavy fall. A low ludicrous word. He tore the earth which he had saved From squelch of knight, and stormed and raved. Hudibras. So soon as the poor devil had recovered the squelch, away he scampers, bawling like mad. L'Estrange. SQUIB, n. s. Ital. schioppo. A small pipe of paper filled with wild fire: any petty fellow. Asked for their pass by every squib, That list at will them to revile or snib. Spenser. The armada at Calais, Sir Walter Raleigh was wont prettily to say, were suddenly driven away with squibs; for it was no more than a stratagem of fireboats manless, and sent upon them. Bacon's War with Spain. The forest of the south compareth the French valour to a squib, or fire of flax, which burns and crackles for a time, but suddenly extinguishes. Howel's Vocal Forest. Lampoons, like squibs, may make a present blaze; But time, and thunder, pay respect to bays. Waller. Seed or kernels of apples and pears, put into a squill, which is like a great onion, will come up earlier than in the earth itself. Bacon's Natural History. 'Twill down like oxymel of squills. Roscommon. The self-same atoms Can, in the truffle, furnish out a feast; nithogalum, or the starry hyacinth: they grow in a long spike, and come out before the leaves. Miller. SQUINT, adj., v. n. & v.a.~ Wiseman. squinte, Belg. oblique, transLooking obliquely; looking verse. not directly; looking suspiciously: to look obliquely; to form or turn the eye obliquely: the two adjectives both mean having the sight oblique to squiny is to look askant or obliquely. He was so squinteyed that he seemed spitefully to look upon them whom he beheld. Knolles's History of the Turks. I remember thine eyes well enough: Dost thou squiny at me? Shakspeare. King Lear. This is the foul Flibertigibbet; he gives the web and the pin, squints the eye, and makes the hairlip. Shakspeare. Some can squint when they will; and children set upon a table, with a candle behind them, both eyes will move outwards, to seek the light, and so induce squinting. Bacon. Perkin began already to squint one eye upon the crown, and another upon the sanctuary, Id. Henry VII. This is such a false and squinteyed praise, Which, seeming to look upwards on his glories, Looks down upon my fears. Where an equal poise of hope and fear Does arbitrate the event, my nature is That I incline to hope rather than fear, And gladly banish squint suspicion. Denham. Milton. The timbrel and the squintifego maid Of Isis awe thee; lest the gods, for sin, Should with a swelling dropsy stuff thy skin. Dryden. Not a period of this epistle but squints towards another over against it. Pope. SQUINTING, or Strabismus, an affection of the eyes, occasioned by the optic axis not converging; in consequence of which the organs of sight appear distorted. Improper habits frequently induce this defect, while the eye and its muscles are perfect; for instance, in children, who accustom themselves to view different things at one time; or who are placed obliquely towards ther cause is malconformation of the retina, or any object that may attract their attention. Anosuch parts as serve to convey impressions to the point of vision; so that persons thus situated are obliged to turn the eye from the object to be investigated, in order that they may be enabled to behold it more distinctly.-Farther, it often proceeds from weakness or defect of either eye, so that both cannot be mutually employed. Besides, it may be consequent on affections of the brain, epilepsy, terror, and defluxions of rheumatic humors. The method of cure to be adopted in this unpleasant distortion varies according to the cause. Thus, in children, and in cases of weakness of the eyes, it may be remedied by mechanical contrivances. Hence, when there is no organic defect in either eye, which is frequently the case with persons who squint from a depraved habit of moving their eyes, the disease may often be cured. Dr. Darwin remarks (Philosophical Transac |