trial 
Kule of trial and error, tin- rule of false. See petition, 7. 
Stat6 trials, tile mime Kiven to *evend collection* of re- 
port * ul ] MI I til. ptii-eciitions, especially for ottense* 
government III til pnlilie peace .-mil order. TO PUt to trial 
"r OH trial. () T" lu'ln^ fpei'oi e ;i n t ;i ml jury fin- ex- 
amination nnil de, i .lirlngtoatcst; try. Trial 
at bar. trial at nisi prlus, trial by battle, an- imr > , 
''in/, 'i. --Trial balance, in ./<"<, ,,r/-v /,-. 
keejnii'f. a mi Iho.l M| tr-lin;; the correctness of tin- posting 
of tin- luilmT (1) as' regards till- Minis posted, anil I 
gards the side to which they an' posted. This is effected 
y NiiniminK the tlrliil and credit balances respectively 
(if tllr p. tson-ll ;,. eoilnt.s, anil linn adding I" till' ile.lll 
side of this Humiliation the difference in iui > n the two 
sides of a nlmilar summation of I In- mi rclmnilise aeei.nni - 
should Hie two sides o( this linal summation exactly I. il 
ance cadi other, thr pnsiimpt ii'ii is Ui;it the ledger has 
lirt-n coneclly posted as regards the particulars ahcailv 
mentioned, hut not HS regards Hie individual items lieiiiu' 
posted to the riulit account. Trial by certificate, an 
oid mode of determining :i e.iuse aecojdinL' In the written 
di duration of some person, usually a liuhllc officer, who 
was deemed liest infi Mined on ill {mint, anil whose certifi- 
cate "as accordingly Ireateil as llnal. Trial by Ordeal. 
See unii'iii. I. Trial by proviso, by record, by tan- 
ghln, etu. see yirwixe,, etc. Trial Judge, jury, Justice. 
See jiitl<n\ etc. Trial Of the pyx. See 1'i/z. (See also 
arurgiii'i-tri'il, li: lil-trial). =&yn.l. Trial, Trit, proof. Trial 
is the more general ; tr*t is the stronger. Test more often 
than irinf represents that which is final ami decisive: as, 
the guns, aftera severe public text, were accepted. 2. At- 
tempt, endeavor, effort, essay, exertion. 5. Trouble, af- 
fliction, distress, tribulation. 7. Touchstone, ordeal. 
trialate (tri-a'lat), a. [< L. ires (tri-), three, 
+ alatuf, winged: see atote 2 .] In bot., three 
winged; having three wings. 
trial-case (tri'al-kas), it. Same as triiil-nii/lit. 
trial-day (tri'al-da), n. The day of trial. 
Brought against me at my trial-day, 
Shak., 2 Hen. VI., UL 1. 114. 
trial-fire (tri'al-fir), . A fire for trying or 
proving; an ordeal-fire. 
With trial-tire touch me his finger-end. 
Shak., M. W. of W., T. 5. 88. 
trial-glasses (tri'al-glas'e/,), n. )>1. A gradu- 
ated set of concave and convex lenses and 
prisms used for testiug the vision. 
trial-ground (tri'al-ground), . A locality for 
the trying or testing of anything. 
The Mont Cenis tunnel formed the greatest trial-ground 
ever brought to the attention of inventors and makers of 
either rock-drills or air-compressors. Ure, Diet., IV. 823. 
trial-heat (tri'al-het), . In mciiuj, a prelim- 
inary trial of speed between competitors. 
trialism (tri'a-lizm), H. [< " trial 1 * (see Maliti/i 
+ -i'/.] Tie doctrine that man consists of 
body, soul, and spirit, or other three essentially 
different modes of substance. 
triality (tri-al'i-ti), . [< *triaP (< L. tri-, three, 
+ -al) T -ity.] A union or junction of three: 
threeness : a word invented after the model of 
duality. [Rare.] 
There may be found very many dispensations of triality 
of beneHces. H. Whartan. 
trial-jar (tri'al-jBr), n. A tall glass vessel for 
holding liquids to be tested by a hydrometer, 
or a jar in which mixed liquids are allowed to 
stand that they may separate by gravity. 
trialogue (tri'a-log), . [< ML. trialogus, a 
colloquy of three persons: a blundering forma- 
tion, based on the erroneous notion that dia- 
logue (L. dialogits) means ' a discourse between 
two' (as if < Gr. ifa>, two, + Wjof, discourse), 
and intended to represent a compound of Gr. 
rpeZf (rpi-), three, + ?ojof, discourse (cf. trilo- 
gy).] Discourse by three speakers ; a colloquy 
of three persons. H'ood, Athente Oxon., I. 24. 
[Rare.] 
trial-piece (tri'al-pes), . 1. A specimen of 
any aggregate ; a sample taken from a mass, or 
one of the first productions of some process, 
by which to determine the quality or character 
of the rest. 
Thomas Simon most humbly prays your Majesty to com- 
pare this his tryall-piece with the Dutch. 
Inscription on Simon's Petition Crmrn, 1663. 
2. A production from which to determine the 
capacity or ability of the producer, 
trial-plate (tri'al-plat), . In coinage, a plate 
of gold or silver of the fineness to which all 
coins are to be conformed. 
The coins selected for trial are compared with pieces 
cut from trial plates of standard fineness. 
Encyc. Brit., XVI. 484. 
trial-proof (tri'al-prof), H. In eiigrariiig, an im- 
pression taken while an engraved or etched 
plate is in progress of making, to test the con- 
dition of the work. 
trial-sight (tri'al-sit). . A case of lenses used 
by an oculist to test the sight of his patients. 
/':. n. Kiiifiif. 
trial-square (tri'al-skwar), n. A carpenters' 
square. 
f. 163 
trial-trip itn';il-trip), . An experimental trip: 
especially, u trip made by a new vessel (.. i< >1 
her sailing qualities, rate of i-peeil, the work- 
ing of her machinery, etc. 
triant (tri'ani, it. Same as trim. 3 . In Ulan as- 
pect. See atcjM-ct and three^uartered. 
triander (tn-an'dert, n. [<(ir.r//i, (r^-),tlnv<-, 
+ 8W^>(ov(i/<-), a male (in mod. but. ;i slam 
A monoclinous or hermaphrodite plant having 
three distinct and equal stamens. 
Triandria ftn-anMri-ii )..//.. |NI-.: see triii ii- 
ik'i:] The third class of plants in the sexual 
system of Linna-us. It comprises those plants which 
have hennaphrodlte flowers with three distinct and equal 
stamens, as the crocus, the valerian, and almost all the 
grasses. H comprehends three orders, Monagynia. IH 
;t!'ni'i, and Triyjfnift, Triandria Is also the name of sev- 
eral orders In other classes of the Llnnean system, the 
plants of which orders have three stamens. 
triandrian (tri-an'dri-an), a. [< Triandria + 
-.] Belonging to the Liuueau class Triiuidriu. 
triandrous (tri-an'drus), a. [< Triandria + 
Ollf.] 1. Having three stamens: as, a triim- 
i/i-iiii.i flower. 2. Same as triamlrinii. 
triangle (tri'ang-gl), a. and n. [Early mod. K. 
also tri/ini<ili'; < OF. (and F.)trittngli; = I'r. Iri- 
iiinjle = Sp. Iriiiin/nlii = I'g. triiim/tilo = It. tri- 
iiiii/i>li>, three-cornered, as a noun a triangle, < 
L. triniKjulus, three-comered, having three an- 
gles, neut. triiiiii/iiliini, a triangle, < tri's (tri-), 
three, + anyulus, angle: see anglt^.] I. a. 
Three-cornered ; three-angled; triangular. 
No Artificer but can tell which things are triangle, which 
round, which square. Z/cyurod, Hierarchy of Angels, p. 158. 
I sent to my house, by my Lord's order, his shlpp and 
trianyle virginall. Ptpyt, Diary, I. 195. 
Triangle-counter-trlangle, in her., divided into trlan- 
gles which correspond to one another, base to base, and 
are two alternating tinctures ; the same as oarry bendy 
lotenay cmtnterchamjed, or harry bendy dexter and linitter 
eounterchanged, the two tinctures being always mentioned. 
II. n. 1. In geniit., a figure composed of three 
lines which meet two by two in three points, 
called the vertices of the triangle; especially, a 
rectilinear figure of this description. The lines 
measured in the shortest way from vertex to vertex are 
called the tide* of the triangle. The angles between the 
sides at the vertices measured so that each subtends a 
side are called the anylei of the triangle. 
2. Any three-cornered or three-sided figure, 
body, or arrangement; anything having a tri- 
angular form or bounding a three-sided space. 
Trianyle space between the Lines of Head, Life, and 
Kate, or Health. A'. >v. Hill, Grammar of Palmistry, vu. 
The older " vowel triangles" from which the trigram is 
adopted. Kitfiie. Brit., XXII. 385. 
3. A musical instrument of percussion, made 
of a rod of polished steel bent into the form 
of a triangle, and open at one of its angles. It 
is sounded by being struck with a small steel rod. It Is 
frequently used In modem orchestral music for brilliant 
and sparkling effects. 
4. [cp.] In astroti, same as Triamjnluni. 5. 
Eccles., a symbol of the Trinity. The equilateral 
triangle, as symbolizing the Trinity, is of frequent occur- 
rence, in various combinations, in Christian ornament. 
6. A chest made in triangular form to hold a 
priest's cope. [Archaic.] 7. A three-cornered 
straight-cage, with one right angle and the other 
angles more or less acute, used in conjunction 
with the T-square for drawing parallel, perpen- 
dicular, ordiagonal lines. 8. A kind of gin for 
raising heavy weights, formed by three spars 
joined at top. See gin*, 2 (c). 9. Milit., for- 
merly, in the British army, a sort of frame 
formed of three halberds stuck in the ground 
and united at the top, to which soldiers were 
bound to be flogged : generally in the plural. 
10. In ceram., a form of the stilt consisting of 
three metal pins held together in the form of 
a triangle, nee stilt, 5. 11. One of certain 
tortricid moths: an English collectors' name. 
Turtrix rufaiia is the red triangle. Samoutlle. 
12. In eiitom., a large three-sided cell found 
in the wings of many dragon-flies. It lies near 
the middle of the basal half of the wing, and Its form and 
relations to the other cells, both of the anterior and pos- 
terior wings, are of much value in classification. It is of- 
ten called the discoidal triangle, to distinguish it from the 
in', inn! triangle, which adjoins it on the inner side, and 
the anal triangle, which lies close to the anal border of the 
wing. Altitude Of a triangle, the perpendicular dis- 
tance of any vertex to the opposite side considered as the 
base. Annex triangle, one of three triangles deii\><l 
from a primitive triangle All"'. Three points L, M, N are 
so taken that the triangles LBC. AMC, ABS are all per- 
verted equals of ABC : then, taking A at the intersection 
of r.N and Mr, B at the intersection of C'L and N A, and 
l at the Intersection of AM and Lit. the triangles A 1:< , 
ABC. ABC' are annex triangles. Anterior triangle of 
the neck, a triangle on the sutface of the neck bounded 
by the ventral mfdline, the sternoclidomastoid, and the 
lower margin of the mandible. It is divided into the sub. 
maxillary and superior and inferior carotid triangles. See 
cut under mutdei. Arithmetical triangle. See arith- 
omasiom, aim me anterior m-ny 01 me omony 
11 called the triangle uf neeeaitu, as the place for 
i carotid, If It cannot be tied In. the superior 
tangle. See cut under miwfri. Inflexional 
triangle 
metieal, and Jlyurate number (under fcntratf). - Charac- 
teristic triangle, a hpherical triangle tiu\ inn two angles 
t i and the third an aliquot pi >din 
Its n I .iilieiii.il n,t e.idi face of which Is 
I |i<.ed of two r (.Pill Mil II IM:III;-|CS ClTCUlOT tTl- 
angle, a plane figure formed t>> time men <>f circles In- 
terscviinit t M t" in three aniM. t. Conjugate tri- 
angle, (a) A tiianule whose sides are mean proportionals 
between tlie tluee paiM "f nj|Hi-it. e.l-t- of ;i tetrahe- 
dron. (&) Seeeom'u,'/' 'ate. Copo- 
lar triangles, diagonal triangle, see the adjectives. 
Digastric triangle, same a* nbmaxOtary triangle. 
Equiangular triangle. *. triangle all whose angles are 
equal : Itls also equilateral Equilateral triangle, a 
triangle all whose sides are equal : It Is also equiangular. 
Fundamental triangle, the triangle which serves 
t<> define homogeneous coordinates in a plane. - Har- 
monic triangle, a triangular table of the reciprocals of 
successive numbers and their successive differences. 
Hesselbacnlan triangle. See llearlbachian. - Homol- 
ogous triangles, triangles placed projectlvely, so that 
the lines through corresponding angles meet In a point, 
and the Intersections of corresponding sides (produced 
when necessary) lie on a straight Hue. When two trlan 
gles ABC and IYW are homologous when A Is consid- 
ered a* corresponding to I', li to V, and c to W, and also 
when A Is considered as corres|iondiiiK Ui V, B to W, and 
C to U, they are said to be doubly isMttjHsj*; and they 
are then homologous also when A Is considered as corre- 
sponding to W. B to U. and C to N . In-and-clrcum- 
scribed triangle, a triangle whose angles lie on a given 
curve or curves, and whose sides are tangent to a given 
cut ve or curves.- Inferior carotid triangle, a triangle 
on the surface of the neck bounded by the median line, 
the stemomastold, and the anterior belly of the omohy 
old. Alsoc " 
tying the 
carotid triangle. 
triangle, an Imaginary triangle upon whose sides lie. 
three by three, the nine points of inflexion of a plane 
cubic curve. -Infraclavlcular, Internal triangle. See 
the adjectives. In triangle, in /"/., arranged^ in the 
form of a triangle : saidof bearings usually more than 
three In number. When three In number, they are gener- 
ally blazoned as two and one; when six In number, they 
are blazoned three, two and one; and the term in triangle 
Is used for a larger or Indefinite number.- Isosceles 
triangle, a triangle two of whose sides are equal ; the 
angles opposite those sides are also equal. Medial line 
Of a triangle, a straight line joining a vertex to the mid- 
point of the opposite side. Null- line of a triangle, a 
straight line the locus of points the sum of whose dis- 
tances from two of the sides of a triangle Is equal to the 
distance from the third side. Every null-line passes 
through three Intersections of sides with bisectors of in- 
ternal or external angles of the triangle. Oblique tri- 
angle, a triangle having no angle equal to Mi'. Occipi- 
tal, ocellar, Pythagorean, quadrantal triangle. See 
the adjectives. Plane triangle, (a) A triangle whose 
sides lie In one plane. ('<) A triangle whose sides are 
rectilinear. Polar triangle, a triangle each vertex of 
which Is In any sense a pole of a side of a primitive tri- 
angle. Posterior triangle of the neck, a triangle on 
the surface of the neck bounded by the anterior border 
of the trapczius, the sternoclidoniastold. and the clavicle. 
It is divided into the suboccfpital and subclavian triangles 
by the omohyold. See cut under tmwck'. Rational 
prime triangle, a triangle whose sides are relatively 
prime multiples of a linear unit, while its area Is com- 
mensurable with the square of that unit : thus, the sides 
may measure lo ( 17, 21, this giving the area 84. Re- 
markable circle of a triangle, a circle having a pecu- 
liar relation to any triangle. Such circles are particularly 
(1) the circvmtenbed circle; (2) the imu-nbed and the three 
escribed circles; (3) the Feuerbach or nine-Vfrint circle; (4) 
the Broeard or seven-point circle; (5) the Tucker or tripti- 
eate-ratio circle ; (6) the sine trijile^tnyle circle (constructed 
as follows : on the sides of the triangle ABC take D and If 
on He, E and I', on AC, K and f on AB such that the an- 
gle AEK = AFE = A, BFD = BD'F'= B. CUE = CETT = C ; 
then the circle In question passes through D, I) , F, E', F, K , 
and DP : EE': Vf= sin 3A : sin 3B : sin :(!'); (T) the Taylor 
or six-point circle, which passes through the six feet of per- 
pendfculars drawn to the sides from feet of perpendlca* 
l.u s on the sides from the vertices of the triangle ; (8) 
the Spieker circle, or circle Inscribed In the triangle whose 
vertices are the mid-points of the sides of the primitive 
triangle. See circle. Remarkable point of a triangle, 
a point having unique metrical relations to the triangle. 
The remarkable points usually considered are (1) the 
centroid, or intersection of median lines; (2) the orthocen- 
ter, or Intersection of perpendiculars from the angles ujxin 
the opposite sides; (8) the circumcenter, or center of the 
circumscribed circle; (i) the center o/ the t'cucrbarh circle; 
(>) the incenter, or center of the Inscribed circle : (6) the 
radical center of the escribed circles; (7) the s]nnmedian. 
Grebe, or Lemoine point, the intersection of the three lines 
each bisecting a side and bisecting a perpendicular from 
an angle upon a side ; (s) the Spielrer point, or mid-point 
between the circumcenter and incenter; (9) the Broeard 
points, two points of the Broeard circle (which see, under 
circle) (through the symmedian point s of any triangle 
All" lines are drawn parallel to the sides of the latter, 
meeting these sides In D and IX on He. E and E' on AC, 
F and F on AB, so that D. S, E' are colllnear. as well as 
E, S, r and F, S, I) ; then the three lines through A paral- 
lel to FD. through B parallel to IT,, and through C parallel 
to EF meet in one Broeard point V, while the lines through 
A parallel to D E', through B parallel to K K 1 . and through 
C parallel to F D' meet In the other Broeard point F) ; 00) 
the center of the triplicate-ratio circle; besides others. 
Respectant In triangle. See rMprefan/.-Bcarpa's 
triangle, a space on the anterior and Inner aspect of the 
Hii.-li just Mow the groin, through which the femoral 
aitety passes. Self-conjugate triangle. See self-con- 
jugate. Slblconjugate triangle. Sec ribiconjugate. 
Spherical triangle, a triangle formed on the surface of a 
sphere by the mutual intersection of three great circles. 
Spherical triangles are divided into HiM^tnyled, obligve- 
angled, emiUateral, isosceles, etc. . as plane triangles are. 
Subclavian triangle, a triangle of the neck bounded by 
the omohyoid, sternoclidomastoid, and clavicle. Sub- 
maxUlary triangle, a triangle on the surface of the neck 
