quadratic 
mensions. 2. In crystal., tetragonal or di- 
metric : applied to the system that includes the 
square prism and related forms. See crystal- 
lography Quadratic equation, group, logarithm, 
mean, modulus, etc. See the nouns. Quadratic fig- 
ure, a figure of two dimensions ; a superficial figure. See 
cubical. Quadratic reciprocity, the relation between 
any two prime numbers expressed by the law of reciprocity 
(which see, under law^). Quadratic residue, a number 
left as remainder after dividing some square number by a 
given modulus to which the quadratic residue is said to 
belong. Thus, 1, 3, 4, 5, and 9 are quadratic residues of 11, 
for 1 = 12 0.11, 3 = 52 2.11, 4 = 92 7.11, etc. ; but 2, 
6, 7, 8, and 10 are quadratic non-residues of 11. 
II. . 1. In <ilg., an equation in which the 
highest power of the unknown quantity is the 
second, the general form being 
, aa + 2 he r c = 0. 
Such an equation has two solutions, real, equal, or imagi- 
nary, expressed by the formula 
2. pi. That branch of algebra which treats of 
quadratic equations Adfected quadratic, a quad- 
ratic equation having a term containing the unknown to 
the first degree, and another not containing the unknown. 
Simple quadratic. See simple. 
quadratically (kwod-rat'i-kal-i), adv. To the 
second degree To multiply quadratically, to 
raise to the second power. 
Quadratifera (kwod-ra-tif'e-ra), n. pi. [NX.., 
ueut. pi. of quadratifer: see quadratiferous.} 
Those vertebrates which have a distinct quad- 
rate bone, as birds and reptiles; a series of 
Vertebrata intermediate between the higher 
Mallei/era (mammals) and the lower Lyrifera 
(fishes proper and selachians). 
quadratiferous (kwod-ra-tif'e-rns), o. [< NL. 
quadratifer, < L. quadratus, tide quadrate mus- 
cle, + L. ferre = E. bear*.} Having a distinct 
quadrate bone, as an animal or its skull ; of or 
pertaining to the Quadratifera. 
quadratiformis (kwod-ra-ti-for'mis), n. ; pi. 
quadratiformes (-mez). [NL., < L. quadratus, 
the quadrate muscle, + forma, form.] The 
square muscle of the coxal group; the quad- 
ratus femoris. Coues. 
quadratipronator (kwod-ra/ti-pro-na'tor), . 
[< L. quadratus, square, + NL. prbnatof, <. v.] 
A square pronator of the forearm : same as pro- 
nator quadratus. See pronator. Coues. 
quadratocubic (kwod-ra-to-ku'bik), a. Of the 
fifth degree Quadratocubic root, the fifth root 
quadratojugal (kwod-ra-to-jo'gal), a. and n. 
I. a. Connected with or representing elements 
of the quadrate and of the jugal or malar bone ; 
common to these two bones: as, the quadrato- 
jugal arch; the quadratojugal articulation. 
II. . A bone of the zygomatic arch of birds, 
etc., interposed between the quadrate bone be- 
hind and the jugal or malar bone before: gen- 
erally a slender rod forming the hinder piece of 
the zygoma. By some it is identified with the squa- 
mosal of mammals a determination to which few now 
assent See cuts under Qallinte, girdle-bone, temporo- 
maitoid, and Trematosaurus. 
quadratomandibular (kwod-ra"to-man-dib'u- 
lar), a. Of or pertaining to the quadrate bone 
and the lower jaw: as, the quadratomandibular 
articulation. See cut under Lepidosiren. 
quadratopterygoid (kwod-ra"to-ter'i-goid), a. 
,Of or pertaining to the quadrate and pterygoid 
bones : as, the quadratopterygoid articulation. 
quadratoquadratic (kwod-ra'to-kwod-rat'ik), 
a. Of the fourth degree Quadratoquadratic 
root, the fourth root 
quadrator(kwod-ra'tor), . [< LL. quadrator, 
a squarer (used only in sense of ' stone-cutter, 
quarrier' : see quarrierl), < L. quad-rare, square : 
see quadrate.'} A circle-squarer. 
quadratosquamosal (kwod - ra" to - skwa -mo'- 
sal), a. In anat., of or pertaining to the quad- 
rate and the squamosal: as, the quadratosqua- 
mosal articulation. 
quadratrix (kwod-ra'triks), n. [NL. (tr. Or. 
TeTpaywvl&vaa), fern, of LL. qnadrator, squarer: 
see quadrator.} In geom., 
a curve by means of which 
can be found straight lines 
equal to the circumference 
of circles or other curves 
and their several parts ; a 
curve employed for find- 
ing the quadrature of 
Other Curves. Quadratrix of Uinostratiis. 
Deinostratus, to whom ia ascribed the invention of the 
quadratrix for solving the two famous problems the tri- 
section of the angle and the quadrature of the circle. 
The Academy, June 1, 1889, p. 381, 
4884 
Quadratrix Of Dinostratus, a curve probably invented 
by Hippias of Elis about 480 IS. <'., and named by Dinos- 
tratus a century later. Its equation is r sin 6 = ad. 
Quadratrix of Tschirnhausen (named from its inven- 
tor, Count E. W. von Tschirnhausen, 1661-1708], a curve 
of sines, bavins the distance between two successive in- 
tersections with the line of abscissas equal to the greatest 
difference of the ordinatcs. 
quadratum (kwod -ra' turn), .; pi. gttadrcita 
(-tji). [L., neut. of quadratus, square : see 
//ii'ddrate, a.} 1. In soo'l., the quadrate bone: 
more fully called os quadratum. 2. In medii'i-ul 
music, a breve. 
quadrature (kwod'ra-tur), n. [= F. quadra- 
ture = Sp. cuadraturu = Pg. It. quadraliira, < 
LL. quadratum, a making square, a squaring, 
< L. quadrare, pp. quadratus, square: see quad- 
rate.] 1. In geom., the act of squaring an area ; 
the finding of a square or several squares equal 
in area to a given surface. 2. A quadrate; a 
square space. [Rare.] 
There let him [God] still victor sway, . . . 
And henceforth monarchy with thee divide 
Of all things, parted by the empyreal bounds, 
His quadrature, from thy orbicular world. 
Milton, P. L., x. 881. 
3. The relative position of two planets, or of a 
planet and the sun, when the difference of their 
longitudes is 90. 
But when armtllffi were employed to observe the moon 
in other situations ... a second inequality was discov- 
ered, which was connected, not with the anomalistical, 
but with the synodical revolution of the moon, disap- 
pearing in conjunctions and oppositions, and coming to 
its greatest amount in quadratures. What was most per- 
plexing 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 disap- 
peared. Small, Account of the Astronomical Discoveries 
[of Kepler (London, 1804), 5 11. 
Neptune . . . is in quadrature with the sun on the 23d. 
Sci. Amor., N. 8., LVIL 64. 
4. A side of a square. [Rare.] 
This citie [Cambaln] is foil re square, so that enery quad- 
rature or syde of the wall hath In it thre principal portes 
or gates. R. Eden, tr. of Sebastian Minister (First Books 
(on America, ed. Arber, p. 26). 
Indefinite quadrature, a rule for the quadrature of the 
circle, applicable to any sector of It Mechanical quad- 
rature, an approximate quadrature of a plane surface, 
effected by the division of it by parallel lines into parts 
so small that they may be regarded as rectilinear or other 
quadrable figures ; also, the integration of any expression by 
an analogous method. Method of quadratures, the ap- 
proximate integration of an expression between given nu* 
merical limits by the summation of parts in each of which 
the difference between the limits is so small that the inte- 
gral is practically equal to that of some integrable expres- 
sion. The problem of the quadrature, or the quad- 
rature Of the Circle, the problem of squaring the circle, 
of which there are two varieties: first, the arithmftical 
quadrature, exactly to express in square measure the area 
of a circle whose radius is some exact number in long 
measure ; second, the geometrical quadrature, to describe 
or draw with the rule and compasses alone a square equal 
in area to a given circle. Both problems have been proved 
to be insoluble. 
quadratus (kwod-ra'tus), .; pi. quadrati (-ti). 
[NL., sc. musculus, the square muscle: see 
quadrate.} In zool. and aitat., the musculus 
quadratus or quadrate muscle of (a) the femur; 
(6) the loins; (c) the chin; (d) the nictitating 
membrane. See quadrate muscle, under quad- 
rate. Quadratus femoris, a muscle situated at the 
back of the hip-joint, arising from the tuberostty of the 
i sell i u in and inserted into a line running from the posterior 
intertrochanteric ridge. Quadratus labii inferioris. 
Same as depressor laMi inferioris (which see, under depret- 
8or). Quadratus labii superioris, the combined leva- 
tor labii superioris aheque nasi, levator labii superioris 
proprius, and zygomaticus minor muscles, the three differ- 
ent parts being called capui anffulare, caput infraorbitale, 
and caput zygomaticum respectively. Quadratus lum- 
borum. See lumbus. Quadratus menti. See mentum. 
quadrauricular (kwod-ra-rik'u-lar), a. [< L. 
quattuor (quadr-), four, + auricula, auricle : see 
auricle.} Having four auricles, as the heart of 
a nautilus. 
quadrel (kwod'rel), . [< ML. quadrellus, dim. 
of L. quadrum, a square: see quarrel^.} 1. In 
arch., a square stone, brick, or tile. The term is 
sometimes restricted in its application to a kind of arti- 
ficial stone formed of a chalky earth molded to a square 
form and slowly and thoroughly dried in the shade. 
2. A piece of turf or peat cut in a square form. 
[Prov. Eng.] 
quadrelle (kwod-rel'), n. [< OF. quadrelle, an 
arrow, shaft, var. of quarele, f., quarel, m., an 
arrow, crossbow-bolt, etc. : see quarrel 2 .} A 
square-headed or four-edged missile. 
quadrennial (kwod-ren'i-al), a. and . [For 
quadriennial, q. v.] I. a. 1. Comprising four 
years: as, a quadrennial period. 2. Occurring 
once in four years: as, quadrennial elections. 
Both States [Montana and Washington] provide for a 
quadrennial election of a governor, lieutenant-governor, 
secretary of state, state treasurer, state auditor, attorney- 
general, and superintendent of public instruction. 
The Century, XXXIX. 506. 
quadriciliate 
II. n. A fourth anniversary, or it* celebra- 
tion. 
quadrennially (kwod-ren'i-al-i), ndv. Once in 
four years. 
quadfenniate (kwod-ren'i-at), n. [< r/f/ir- 
HI'-MHI + -(<#.] A period of four years ; a quad- 
rennium. 
qnadrennium (kwod-ren'i-um), . [For qii/ni- 
ridiiiinm, q. v.] A period of four years. 
Burdening girls, after they leave school, with a quad- 
rennium of masculine college regimen. 
E. H. Clarke, Sex in Education, p. 125. 
quadrequivalent (kwod-re-kwiv'a-lent), a. 
[< L. quattuor (qitadr-), = E\ four, -f E. equiva- 
lent.} Same as quadriralent. 
quadri-. [L., also quadru-, sometimes quatri-, 
combining form of quattuor, = E. four (the 
independent adj. quailrug or quadruus, four- 
cornered, square, fourfold, < quattuor, four, 
being of later use): see four.} An element in 
many compounds of Latin origin or formation, 
meaning 'four.' In qiiinlriiiii/lr, quadrangular 
(as in Latin), and in quadrennial, quadrennium, 
it is reduced to quadr-. 
quadriarticulate (kwod'ri-ar-tik'u-lat), a. [< 
L. quattuor (quadri-), = E. four, -t- articulatua, 
pp. of articulare, divide into single joints: see 
articulate.} Having four articulations or joints. 
quadribasic (kwod-ri-ba'sik), a. [< L. quat- 
tuor (quadri-), = ft. four, + E. basic.} In cheat., 
noting an acid which has four hydrogen atoms 
replaceable by basic atoms or radicals. 
quadriblet (kwod'ri-bl), a. [Irreg. for the later 
(jiiiuirable, q. v.] Capable of being squared. 
[Rare.] 
Sir Isaac Newton had discovered a way of attaining the 
quantity of all quadriMe curves analytically, by his method 
of fluxions, some time before the year 1688. 
Derham, Physico-Theol., v. 1, notey. 
quadric (kwod'rik), n. and a. [< LL. quadrus, 
square (< L. quattuor = E. four), + -ic.} I. n. In 
alg., a homogeneous expression of the second 
degree in the variables. Ternary and quaternary 
quadrics, equated to zero, represent respectively curves 
and surfaces which have the property of cutting every 
line in the plane or in space in two points, real or imagi- 
nary, and to such surfaces the name quadric is also ap- 
plied. Modular method of generation of quadrics. 
See modular. 
H. a. In alg. and geom., of the second de- 
gree ; quadratic. Where there is only one variable, 
the word quadratic is usually employed ; in plane geome- 
try, conic; and in solid geometry and where the number 
of non-homogeneous variables exceeds two, quadric. Thus, 
we say quadric cone, not quadratic or conic cone. Quad- 
lie inversion. See inversion. Quadric surface, a sur- 
face of the second order. 
quadricapsular (kwod-ri-kap'su-lar), a. [< L. 
quattuor (quadri-), = E. four, + capsula, cap- 
sule: see capsule, capsniar.} In lot., having 
four capsules. 
quadricarinate (kwod-ri-kar'i-nat), a. [< L. 
quattuor (quadri-), = E. four, + carina, keel: 
see carina, carinate.} In cntom., having four 
carinse, or longitudinal raised lines : specifically 
said of the face of an orthopterous insect when 
the median carina is deeply sulcate, so that it 
forms two parallel raised lines, which, with the 
two lateral carina?, form four raised lines. 
quadricellular (kwod-ri-sel'u-lar), a. [< L. 
quattuor (quadri-), = E. four, '4- NL. cellula, 
cellule: see cellular,] Having or consisting of 
four cells. 
quadricentennial (kwod'ri-sen-ten'i-al), a . and 
n. [< L. quattuor (quadri-), = E. four, + ML. 
centennis, a hundred years old: see centennial.} 
I. a. Pertaining to or consisting of a period of 
four hundred years. 
II. H. The commemoration or celebration of 
an event which occurred four hundred years 
before : as, the Luther quadricentennial. 
quadriceps (kwod'ri-seps), n. [NL., < L. quat- 
tuor (quadri-), = E. four, + caput, head: see 
biceps.} In anat., the quadriceps extensor cru- 
ris of the thigh; the great muscle which ex- 
tends the leg upon the thigh, considered as con- 
sisting of the rectus, cruneus, and vastus in- 
ternus and exteruus. Called triceps extensor cruris 
when the crurseiis is regarded as a part of the vastus in- 
ternus, or when the rectus is separately enumerated. This 
great muscle forms nearly all the flesh upon the front of 
the thigh. See cuts under muscle*. Quadriceps surse, 
the combined gastrocnemius externus and interaus, sole- 
us, and plantaris, forming the bulk of the muscle of the 
quadriciliate (kwod-ri-siri-at), a. [< L. quat- 
tuor (<i/i(iilri-). = E./owr, + NL. ciliiim + -ate^.} 
Having four cilia, or flagelliform appendages. 
M. Thuret informs us that he has seen the biciliate 
spores germinate as well as the quadriciiiate. 
M. J. Berkeley, Introd. to Cryptog. Bot, p. 137. 
