square 
Light diminishes in intensity as we recede from the 
source of light If the luminous source be a point, the in- 
tensity diminishes as the square of the distance increases. 
. . . This is the muaning of the law of inverse squares as 
applied to light. Tyndall, Light and Elect., p. lf>. 
8. Rule; regularity; exact proportion ; hence, 
integrity of conduct; honest dealing. See 
phrases on thr square (c), out of square, etc. 
Read not my blemishes in the world's report : 
I have not kept ray square ; but that to come 
Shall all be done by the rule. 
Shak., A. and C., ii. 3. 6. 
9. A body of troops drawn up in quadrilateral 
form. The formation used in the sixteenth century and 
afterward was a nearly solid body of pikemen, to which 
the harquebusiers, crossbowmen, etc., formed an acces- 
sory, as by being posted on the flanks, etc. In Shakspere's 
time troops drawn up in battle array were primarily in 
squares. At the present time the square is a hollow for- 
mation, composed of four fronts, each from two to five 
ranks deep, having the officers, colors, etc., in the center. 
This formation is used to repel cavalry, or to resist any 
superior force which outflanks or surrounds the body of 
troops. See hollow square, below. 
He alone 
Dealt on lieutenantry, and no practice had 
In the brave squares of war. 
Shot., A. and C., iii. 11. 40. 
Dash'd on every rocky square, 
Their surging charges foam'd themselves away. 
Tennyson, Death of Wellington. 
10. A name given to various squared projec- 
tions or shanks to which other parts of ma- 
chines may be fitted. llf. Level; equality: 
generally with the. See on the square (b), be- 
low. 12. In astral., quartile; the position of 
planets distant 90 degrees from each other. 
See aspect, 1. 
Their planetary motions, and aspects, 
In sextile, miiare, and trine. 
Milton, P. L., x. 669. 
13t. Opposition; enmity; quarrel. Seesquare 1 , 
v. ., 2. 14. Apart of a woman's dress, (a) The 
yoke of a chemise or gown : so called because often cut 
square or angular. [Still in provincial use.] 
The sleeve-hand, and the work about the square on 't 
[a smock). Shak., W. T., iv. 4. 212. 
(6) A square opening in the upper part of the front of a 
bodice, or other garment covering the throat and neck. It 
is usually filled in with another material, except for even- 
ing dress. 
A round Sable Tippet, about 2 yards long, the Sable 
pretty deep and dark, with a piece of black Silk in the 
Square of the neck. 
Advt. quoted in Ashton's Reign of Queen Anne, I. 173. 
15. A puzzle or device consisting of a series 
of words so selected that when 
arranged in a square they may s A T 
be read alike across and down- 
ward. Also called word-square. T 
16. In bookbinding, the parts of v. 
the cover of a bound book that 
project beyond the edge of the 
leaves. 17. The square end of 
the arbor designed to receive the winding-key 
of a watch, or the similar part by which the 
hands of the watch are set. 18. In flooring, 
roofing, and other branches of mechanical art, 
an area 10 feet square; 100 square feet. 19. 
In lier., a bearing representing a carpenters' 
square. (See def. 5.) It is represented with or 
without the scale. 20. In organ-building, a 
thin piece of wood, in or nearly in the shape 
of a right-angled triangle, pivoted at the right 
or largest angle and connected with trackers 
at the other angles. It serves to change the 
direction of the tracker-action from vertical to 
horizontal, or vice versa.- A deep square, a long 
projection. A small square, a narrow projection. At 
squaret, in opposition ; at enmity. 
Marry, she knew you and I were at square 
At least we fell to blowes. 
Promos and Cassandra, ii. 4. (Nares.) 
She falling at square with hir husband. 
Bolinshed, Hist. Eng., iv. 8. 
By the square, exactly ; accurately. 
Not the worst of the three but jumps twelve foot and a 
half by the squier. Shak., W. T., iv. 4. 348. 
Why, you can tell us by the squire, neighbour, 
Whence he is call'd a constable. 
B. Jomon, Tale of a Tub, iv. 2. 
Cyclical square. See cyclical. Face of a square. See 
/ocei. Geometrical square. Same n&quadrat, 2. Gun- 
ners square. Same as quadrant, 6. Hollow square 
a body of infantry drawn up in square with a space in the 
middle to receive baggage, colors, drums, etc. When or- 
ders or proclamations are to be read to troops, it is usual 
to form a hollow square, with the files facing inward. See 
def. 9. Incuse square. See incuse. In squaret, 
Then did a sharped spyre of Diamond bright 
Ten feete each way in square, appeare to mee. 
Spenser, Visions of Bellay, 1. 30. 
Magic square. See mayic. Method of least squares, 
the method used by astronomers, geodesists, and others 
of deducing the most probable or best result of their 
A T 
O A 
ENS 
D E T 
N E 
S T 
V E 
E R 
Square. 
a 
5876 
observations, in cases in which the arithmetical mean of 
a number of observations of the same quantity is the 
most probable or best value of that quantity. The 
adoption of the mean value of a number of observations 
may be considered as the simplest application of the 
method of least squares. When the observed values de- 
pend upon several unknown quantities, the rule which re- 
sults from the principle of the arithmetical mean is to 
adopt such values for the unknown quantities as to make 
the sum of the squares of the residual errors of the ob- 
servations the least possible. When there are certain con- 
ditions that must be fulfilled, as for example, in geodesy, 
that the sum of the angles of each triangle must equal 
two right angles plus the spherical excess, the rules be- 
come still more complicated. There are also rules for 
calculating probable errors, etc. Naslk squares. See 
the quotation. 
Squares that have many more summations than in rows, 
columns, and diagonals have been investigated by the Rev. 
A. H. Frost(Cambridge Math. Jour., 1857), and called KaiOc 
squares from the town in India where he resided ; and he 
has extended the method to cubes (called Nasik cubes), 
various sections of which have the same singular proper- 
ties. Kneyc. Brit., XV. 216. 
Naval square, a rectilinear figure painted on a ship's 
deck in some convenient place, for the purpose of aiding 
in taking the bearings of other ships of a squadron or of 
objects on shore. Normal square, the mathematical 
instrument called a square, for determining right angles. 
On or upon the square, (a) At right angles ; straight : 
as, to cut cloth on the square, as opposed to bias. Hence, 
figuratively (i>) On an equality ; on equal terms. 
They [the Presbyterians] chose rather to be lorded over 
once more by a tyrant . . . than endure their brethren 
and friends to be upon the square with them. 
Milton, Ans. to Salmasius, x. 
We live not on the square with such as these ; 
Such are our betters who can better please. 
Dryden, tr. of Juvenal's Satires, iii. 179. 
(c) Honest ; Just ; fairly ; honestly. 
Keep upon the square, for God sees you ; therefore do 
your duty. Penn, To his Wife and Children. 
"Was the marriage all right, then?" "Oh, all on the 
square civil marriage, church everything." 
George Eliot, Felix Holt, xxi. 
Optical square, an instrument used in surveying for 
laying out lines at right angles to each other. It consists 
of a circular brass box containing two 
Srincipal glasses of the sextant, viz. 
le index- and horizon-glasses, fixed 
at an angle of 45*. The method of 
using this instrument is obvious. If 
the observer moves forward or back- 
ward in the straight line AB, until 
the object B seen by direct vision 
coincides with another object C, seen 
by reflection, then a straight line 
drawn to C from the point at which r 
he stands, as D, when the coinci- 
dence takes place will be perpendicular to AB. Out Of 
square, (a) Not drawn or cut to right angles. (6) Out 
of order ; out of the way ; irregular ; incorrect or incor- 
rectly. 
Herodotus, in his Melpomene, scorneth them that make 
Europe and Asia equal], afHrmynge that Europe . . . pass- 
eth them in latitude, wherin he speaketh not greatly out 
ojf square. R. Eden, tr. of Francisco Lopez (First Books 
[on America, ed. Arber, p. 346). 
In St. Paul's time the integrity of Rome was famous ; 
Corinth many ways reproved ; they of Galatia much more 
out of square. Hooker, Eccles. Polity, lit 1. 
Reducing squares, a method of copying designs or 
drawings on a different scale. The original is divided into 
squares by lines drawn at right angles to one another. The 
surface on which the copy is to be made Is divided into the 
same number of squares, smaller or larger, according to 
the scale desired, and the lines of the design are drawn on 
the squares of the copy in the same relative positions that 
they occupy in the original. Instead of marking the 
original design with lines, a frame in which crossed 
threads or wires are set may be laid over it ; or such a 
frame may be used in a similar way in drawing a land- 
scape or any other subject from the original. Rising- 
square, a square having a tongue and two arms at right 
angles to it, used in molding the floor-timbers in wooden 
ships. The tongue is in width equal to the siding size of 
the keel ; and the seat and throat of the floor-timbers are 
squared across it, the risings of the floor at the head being 
squared across the arms. The timber-mold applied to the 
seating on the tongue and rising on the arm gives the 
shape of one side of the floor-timber ; the mold reversed 
gives the other. Solid square (mflit.), a square body of 
troops ; a body in which the ranks and flies are equal. 
Square of an anchor, the upper part of the shank. 
Square of senset. See the quotation. 
I professe 
My selfe an enemy to all other loyes, 
Which the most precious square of seme professes, 
And find I am alone felicitate 
In your deere Highnesse loue. 
Shak., Lear (folio 1673), L 1. 76. 
[This phrase has been variously interpreted by commen- 
tators : Warburton refers it to the four nobler senses 
sight, hearing, taste, and smell ; Johnson makes it mean 
'compass or comprehension of sense'; R. G. White, 'the 
entire domain of sensation'; Schmidt, 'the choicest 
symmetry of reason, the most normal and intelligent 
mode of thinking.'] To break no squarest, to make 
no difference. See the next phrase. To break or breed 
squarest, to break the squaret, to throw things out 
of due or just relation and harmony ; make a difference. 
To reduce the square (milit.). See reduce. To see 
now the squares go, to see how the game proceeds, or 
how matters are going on. 
Atlength they, having an oppertunitie, resolved to send 
M'. Winslow, with what beaver they had ready, into Eng- 
land, to see how y square wente. 
Bradford, Plymouth Plantation, p. 268. 
square 
One frog looked about him to see hnw squares went with 
their new king. >Y, /;. L'Estrange. 
Square 1 (skwar), a. [< ME. m/Hiir<; xi/icare, svsare, 
orig. two syllables, < OF. csquarrc, escarre (equiv. 
to quitrr/'.'i-iirn'; F. carre), < ML. "exqi/adratus 
(equiv. to quadratus), squared, square, pp. of 
"eiquadrare, make square: see square*-, v., and 
cf. square 1 , it., and quadrate, quarry 1 .] 1. 
Having four equal sides and four right angles ; 
quadrate; rectangular and equilateral: as, a 
square room; a square figure. 
Thurgh a wyndow thikke, of many a barre 
Of iren greet, and square as any sparre. 
Chaucer, Knight's Tale, 1. 218. 
A massy slab, in fashion square or round. 
Camper, Task, i. 21. 
2. Forming a right angle; having some part 
rectangular: as, a table with square corners. 
Square tools for turning brass are ground in the same 
manner as triangular tools. 
0. Byrne, Artisan's Handbook, p. 29. 
3. Cut off at right angles, as any body or figure 
with parallel sides: as, a square apse or tran- 
sept; a square (square-headed) window. 
The east ends in this architecture [early Pointed in Eng- 
land] are usually square. 
( '. H. Moore, Gothic Architecture, p. 168. 
4. Having a shape broad as compared with the 
height, with rectilinear and angular rather than 
curved outlines: as, a man of square frame. 
Erode shulders aboue, big of his arrays, 
A harde brest hade the buerne, & his back sware. 
Destruction o/Troi/(E. E. T. S.), 1. 3867. 
My queen's square brows [forehead] ; 
Her stature to an inch. Shak., Pericles, v. 1. 109. 
Sir Bors it was, . . . 
A square-set, man. Tennyson, Holy Grail. 
5. Accurately adjusted as by a square; true; 
just; fitting; proper. 
She 's a most triumphant lady, if report be square to her. 
Shak., A. and C., ii. 2. 190. 
Should he retain a thought not square of her, 
This will correct all. Shirley, Love's Cruelty, ii. 3. 
Hence 6. Equitable; just; fair; unimpeach- 
able. 
All have not offended ; 
For those that were, it is not square to take 
On those that are revenges. 
Shak., T. of A., v. 4. 36. 
Telling truth is a quality as prejudicial to a man that 
would thrive in the world as square play to a cheat 
Wycherley, Plain Dealer, I. 1. 
7. Even ; leaving no balance : as, to make the 
accounts square; to be square with the world. 
There will be enough to pay all our debts and put us 
all square. Disraeli, Sybil, iii. 2. 
If a man 's got a bit of property, a stake in the country, 
he'll want to keep things square. Where Jack isn't safe, 
Tom 's in danger. George Eliot, Felix Holt, xx. 
8. Absolute ; positive ; unequivocal : as, a square 
refusal ; a square contradiction ; a square issue. 
9. Leaving nothing; thorough-going; hearty. 
Vn ferial beuveur. A square drinker, . . . one that will 
take his liquor soundly. Cotgratx (1611). 
By Heaven, square eaters ! 
More meat, I say! Upon my conscience, 
The poor rogues have not eat this month. 
Fletcher, Bonduca, it 3. 
Hence 10. Solid; substantial; satisfying. 
[Colloq.] 
And I've no idea, this minute, 
When next a square meal I can raise. 
New York Clipper, Song of the Tramp. (Bartlett.) 
11. Naut., noting a vessel's yards when they 
are horizontal and athwartships, or at right 
angles to the keel. All square, all arranged; all 
right. Dickens. A square mant. (a) A consistent, 
steadfast man. See bricks, etym. 
The Prince of Philosophers [Aristotle], in his first booke 
of the Ethicks, termeth a constant minded man, euen egal 
and direct on all sides, and not easily ouerthrowne by 
euery HU[e] aduersitie, hominem quadratum, a square 
man. Puttenham, Arteof Eng. Poesie(ed. Arber), p. 113. 
(6) A man who is fair-dealing, straightforward, and trust- 
worthy. 
Then they fill 
Lordships ; steal women's hearts ; with them and theirs 
The world runs round ; yet there are square men still. 
Ford, Lover's Melancholy, iv. 2. 
Fair and square. 8ee/ot>i. Knight of the square 
flag. See bannerets, 1. Square B, in music. See B 
quadratum, under B. Square capitals. See capital!. 
Square coupling. See coupling. Square dance. 
See dance, 1. Square dice, dice honestly made; dice 
that are not loaded. Halliwell. Square fathom, file, 
foot, joint, knot, lobe, measure. See the nouns. 
Square map-projection. See projection. Square 
muscle, a quadrate muscle (which see, under quadrate). 
Square number, a number which is the square of 
some integer number, as 1, 4, 9, 16, 26, etc. Square octa- 
hedron, parsley, rig, roof. See the nouns. Square 
piano. See pianoforte (). Square root, in arith. and 
alg. See roott, 2 (g). Square sail. See taili, 1, and 
squaresail. Square stern. See stern?. Square to, at 
right angles to. 
