92 T R I 
stem diffused, leaflets roundish. Root biennial.—Native of 
Siberia. 
3. Trigonella striata.—Legumes peduncled, nearly up¬ 
right, distant; peduncles larger than the leaf.—Native of 
Abyssinia. 
4. Trigonella polycerata, broad-leaved, or Spanish fenu¬ 
greek.— Legumes subsessile, heaped, erect, nearly straight, 
long, linear; peduncles awnless. 
5. Trigonella hamosa, or Egyptian fenugreek.—Legumes 
peduncled, racemed, declined, hooked round; peduncles 
spiny, longer than the leaf. Annual.—Native of Egypt. 
6. Trigonella spinosa, or thorny fenugreek.—Legumes 
subpeduncled, heaped, declined, sickle-shaped, compressed; 
peduncles thorny, very short.—Native of the island of Candia. 
7. Trigonella corniculata, or horse-shoe fenugreek.—Le¬ 
gumes peduncled, heaped, declined, somewhat sickle-shap¬ 
ed; peduncle long, somewhat spiny; stem erect.—Native of 
the South of Europe. 
8. Trigonella monspeliaca, or trailing fenugreek.—Le¬ 
gumes heaped, sessile, bowed, divaricated, inclined, short; 
peduncle mucronate, unarmed.—Native of France, Italy, and 
Algiers. 
9. Trigonella laciniata, or jagged fenugreek.—Legumes 
peduncled, subumbelled, elliptic; leaflets wedge-form, 
toothed ; stipules laciniated.—Native of Egypt. 
10. Trigonella foenum-grsecum, or common fenugreek.— 
Legumes sessile, strict, nearly erect, somewhat sickle-shaped, 
acuminate; stem erect. Leaflets oblong, oval, indented on 
their edges, on broad furrowed foot-stalks. The flowers 
come out singly at each joint from the axils; they are white, 
and sit very close to the stalk.—Native of France, the county 
of Nice, Spain, Germany and Barbary. The wild plant 
differs, in having long runners next the root, all pressed 
close to the ground, the stem only being upright; leaflets 
ohovate, not obtusely lanceolate; with the joints of the leaves 
purple. Legumes more hairy. 
11. Trigonella Indica, or Indian fenugreek.—Legumes 
sessile, subsolitary, subfalcate; leaflets quite entire; stem 
diffused.—Native of the East Indies. 
12. Trigonella pinnatifida.—’Stem prostrate, four-cor¬ 
nered legumes linear, compressed, erect, sessile.—Native of 
Spain, in the neighbourhood of Madrid. 
Propagation and Culture. —Sow the seeds where the 
plants are designed to stand, for they will not bear trans¬ 
planting. If they are sown in autumn, the plants will come 
earlier to flower, and good seeds may be obtained with more 
certainty than from spring plants. All the culture they 
require, is to thin them where they stand too close, and to 
keep them clean from weeds, 
TRIGONIA [so named from the form of the fruit], in 
Botany, a genus of the class diadelphia, order decandria, 
natural order of malpighiae (Juss.)— Generic Character. 
Calyx: perianth one-leated, turbinate: border five-cleft, the 
two upper segments more deeply separated, erect, diverging. 
Corolla papilionaceous; five-petal led : banner erect, flat, 
clawed. Wings reflexed, longer, narrower. Keel two-pe- 
talled, converging. Stamina: filaments ten, connected into 
a sheath, distinct at top, some (3,5,7,) often barren. Anthers 
oblong. Pistil: germ ovate, small. Style short, ascending. 
Stigma headed, flat, girt with a membranaceous margin. Peri- 
ricarp: capsule oblong, three-cornered, three-grooved, acute, 
one-celled, there-valved; valves boat-shaped, doubled; outer 
coriaceous, inner membranaceous, woolly within. Seeds very 
many, roundish, involved in long wool, fastened to three 
threads uniting the valves.— Essential Character. Calyx 
five-parted. Petals five, unequal, uppermost foveolate at the 
base within. Nectary: two scales at the base of the germ. 
Filaments: some barren. Capsules leguminose, three-cor¬ 
nered, three-celled, three-valved. 
1. Trigonia villosa.—Leaves obovate beneath, tomentose, 
hoary. Branches round, smooth below, villose above; 
branchlets hoary-tomentose. Leaves on the younger branch- 
lets petioled, opposite, two or three inches long, ovate. 
Racemes from the last axils quite simple, terminating, com- 
T R I 
pound ; branches opposite, spreading very much, decreasing 
upwards. Pedicels opposite or alternate, spreading very 
much, with a yellowish down on them like the peduncles.— 
Native of Cayenne. 
2. Trigonia laevis.—Leaves oblong on both sides, smooth 
shining.—Native of Guiana. 
TRIGONOMETRICAL, adj. Pertaining to trigono¬ 
metry. 
TRIGONOMETRICALLY, adv. According to the rules 
of trigonometry.—In the years 1741 and 1742, Mr. J. Ren- 
shaw, my agent, went round the coast of England, and sur¬ 
veyed it trigonometrically. Whiston. 
TRIGONOMETRY, s. [from the Gr. ryyovot;, a triangle, 
and juerpoy, a measure .] The science of determining the 
sizes and proportions of the parts of triangles. This branch 
of geometry being available to measure many inaccessible 
dimensions from some known parts, is the foundation 
of many of the important conclusions in the sciences of 
astronomy, navigation, &c. Strictly speaking, however, 
trigonometry has a still more extensive signification ; for 
the laws deducible from measuring the angles of three-sided 
figures are applicable to the analysis of angles in general, 
and this again to the determination of the sizes and proportion 
of other figures. Trigonometry is of two kinds, plane and 
spherical. We shall commence with a brief account of the 
former, referring those who are desirous of going deeper 
to the numerous and well-known elaborate treatises on the 
subject. 
Def. I. The tangent of an arch, or angle, is that por¬ 
tion of the geometrical tangent at one extremity of the arch, 
which is intercepted between the sides of the corresponding 
angle. Thus in plate 1. fig. ]., ah is the tangent to the 
arch ad, or to the angle acd. 
II. The secant of an arch, or angle, is that portion of a 
geometrical secant through one extremity of the arch, which 
is intercepted between a tangent at the other and the centre 
Thus in fig. 1., ch is a secant of the arch ad or of the an¬ 
gle ACD. 
III. The complement of an arch, or angle, is the differ¬ 
ence between it and a quadrant, or right angle. Thus db 
is the complement of the arch ab, and the angle dcb the 
co. of the angle dca. 
IV. The sine of an arch, or angle, is the perpendicular 
drawn from one extremity of the arch to the opposite side of 
the angle. Thus (fig. 1.) dg is the sine of the arch ad, or 
the angle acd. 
V. The versed sine of an arch, or angle, is the intercept 
of the diameter between the sine and tangent. Thus ga is 
the versed sine of the arch ad or angle acd. 
VI. The supplement of an arch, or angle, is the differ¬ 
ence between it and a semicircumference, or two right 
angles. Thus the arch da is the supplement of the arch 
de, and the angle dca the supplement to the angle dce. 
These definitions being understood, we proceed to make 
the following assertions. 
1. The square of the secant of an angle is equal to the sum 
of the squares of the tangent and of the radius. 
2. The rectangle under the tangent and cotangent of an 
arch, or angle, is equal to the square of the radius. 
3. The square of the radius is equal to the sum of the 
squares of the sine and cosine of an arch or angle. 
4. The ratio of the sine to the cosine of an angle is the 
same as that of the tangent to the radius. 
5. The rectangle under the secant and cosine of an angle 
is equal to the square of the radius. 
6. The sine of an angle is equal to the sine of its supple¬ 
ment. 
7. The sine of an angle is equal to half the chord of twice 
the corresponding arch. 
8. The rectangle under the radius and the sine of twice an 
angle is equal to twice the rectangle under its sine and cosine. 
9. The rectangle under the radius and the cosine of twice 
an angle is equal to the difference between the square of the 
radius and twice the square of the sine of the angle. 
10. Let 
