T R I

760 T R I

styles two, bifid; capsule bristly, four-valved, many-seeded.There is only one species, viz. T. Laurifolia, a native of the woodsof Guiana .

TRICtlOCEPIIALUS, in natural history, a genus of thevermes intestina class and order. Body round, elastic, and vari-ously twisted ; head or foie-part much thicker, and furnished witha slender exsertile proboscis; tail or lower part long, capillary,and tapering to a point. There are six species enumerated, andnamed from the animals in which they are found : T. Hominis in-habits the intestines of sickly children, generally the ccecum, andin considerable numbers; it is usually about two inches long, andin colour it resembles the ascarides. The head is obtuse and fur-nished with a very slender proboscis, which it can eject or retractat pleasure.

TR1CHODA, in natural history, a genus of the'.vermes infu-soria. Worm invisible, pellucid, hairy, or horned. There areseventy or eighty species in sections. A. hairy. B. furnished withcirri. C. horned.

TR1CHOMANES, in botany, a genus of the cryptogamiafilices class and order. Natural order, Fdices or ferns. Fructifi-cations inserted into the margin of the frond, separate ; invo-lucres urn-shap«d, undivided, opening outwards; columns ex-tending beyond the involucres, like styles. There are twenty-seven species, chiefly natives of the West-Indies .

TRICHOSANTHES, in botany, a genus of the monoeciasyngenesiaclass and order. Natural order, Cucurbitacex. Calyxfive-toothed; corolla five-parted, ciliate: male, filaments three;female, style trifid; pome oblong. There are seven species.

TRICOCCiE, [Tfiif three, and xsxxo; a grain,] the name ofthe 38th order in Linnaeus ’s Fragments of a natural method, con-sisting of plants with a single three-corned capsule, having threecells,or internal divisions,each containing a single seed.SeeBoTAN y.

TRICOSTEMA, in botany, a genus of the didynamia gym-nospermia class and order. Natural order, Verticillatae or Labiat*Corolla, upper lip sickle-shaped ; stamina very long. There arethree species.

TRIDAX, in botany, a genus of the syngenesia polygamiasuperflua class and order. Natural order, Compositae Oppositi-foliae. Calyx imbricate, cylindrical; corollets of the ray three-parted ; down many-rayed, simple ; receptacle chaffy. Thereis only one species, viz. T. procumbens.

TRIENS, in antiquity, a copper-money of the value of one-third of an as, which on one side bote a Janus’s head, and on theother a water-rat. '

TRIENTALIS, in botany, a genus of the heptandria mono-gynia class and order. Natural order, Rotaceae. Calyx seven-leaved ; corolla seven-parted, equal, fiat; berry juiceless. Thereis but one species, viz. T. Europaia, chick-weed-winter-green.

TRIESTE, a sea-port in lslria, on the gulf of Venire, 8miles N. of Capo d’Istria, and 80 N. E. of Venice. Lon. 14. 4.E. Lat. 45. 56. N.

TR1FOL1UM, Trefoil, or Clover; in botany, a genus ofplants of the class diadelphia, and order decandria, natural order,Papilionacex. Flowers in a head ; legume scarcely longer thanthe calyx; nectary opening, deciduous. There are fifty-onespecies. T. officinale or melilot, has naked racemous pods, dis-permous, wrinkly, and acute, with an erect stalk. It grows incorn-fields, and by the way-sides, but is not common. Thestalk is erect, firm, striated, branched, and two or three feet high ;the leaves ternate, smooth, obtusely oval, and serrated; theflowers are small, yellow, pendulous, and grow in long closespikes at the tops of the branches; the pod is very short, turgid,transversely wrinkled, pendulous, and contains either one or twoseeds. The plant has a very peculiar strong scent, and disagreea-ble bitter acrid taste, but such, however, as is not disagreeableto cattle. The flowers are sweet-scented. It communicates aloathsome flavour to wheat and other grain, so as to render itunfit for making bread. See Husbandry.

TRIG LA, the Gurnard, in ichthyology, a genus of fishesbelonging to the order of thoracici. Head loricated with roughlines ; rays seven ; in the membranes of the gills. There are 14species.

TR1GLOCHIN, in botany, a genus of plants of the class hex-andria, and order trigynia ; natural order, Tripetaloides. Calyxthree-leaved ; petals three ; no style; capsule opens at the base.There are three species.

TR1GLYP11, in architecture, a member of the frize of theDoric order set directly over every pillar, and in certain spacesin the intercolumniatious.

TRIGONELLA, Fenugreek; in botany, a genus of plantsof the class diadelphia, and order decandria; natural order,Papilionacex. Vexillum and ala: nearly equal, patent, resem-bling a tripetalous corolla. There are 12 species.

TRIGONIA, a genus of the diadelphia decandria class andorder of plants. Calyx five-parted ; petals five, unequal ; nectarytwo scales at the base of the germ ; filaments some barren ; cap-sules leguminous, three-cornered, three-celled, three-valved.There are two species, natives of Guiana .

TRIGONOMETRY.

TRIGONOM ETR Y, [Tsiywo; and ^dgov,] the art of measuringthe sides and angles of triangles, either plane or spherical, whenceit is accordingly divided into Plane Trigonometry, and SphericalTrigonometry. By trigonometry we come to know the magni-tude of the eatth, the planets, and stars, their distances, motions,eclipses, and almost all other useful arts and sciences. Accord-ingly we find this art has been cultivated from the earliest ages ofmathematical knowledge. Trigonometry, or the resolution oftriangles, is founded on the mutual proportions which subsist be-tween the sides and angles of triangles; which proportions areknown by finding the relations between the radius of a circleand certain other lines drawn in and about the circle, called chords,sines, tangents, and secants. The ancients, Menelaus, Hipparchus ,Ptolemy , See. performed their trigonometry, by means of thechords. As to the sines, and the common theorems relating tothem, they were introduced into trigonometry by the Moors orArabians, from whom this art passed into Europe , with severalother branches of science. The Europeans have introduced, sincethe 15th century, the tangents and secants, with the theorems re-lating to them. In trigonometry, as angles are measured by arcsof a circle described about the angular points, so the whole cir-cumference of the circle is divided into 360 equal parts, calleddegrees; each degree into 60 equal parts, called minutes; eachminute into 60 equal parts, called seconds. An angle is said to beof as many degrees, minutes, seconds, &c. as are contained in

the arc, or part of the circumference, by which it is measured.Thus, if on the angular point C, a circle be described, the arcDE or AB, (fig. if, Plate CLXXVI.) is the measure of theangle, and the measure is the same whichever arc is used, therebeing the same number of degrees in each. A right angle is mea-sured by the fourth part of the circumference, or 90°; an obtuseangle is greater than 90°, and an acute angle is less than 90°.Degrees, minutes, .Vc. are marked at the top of the figures bywhich the arc is denoted. Thus we say 34° S8' 50", thirty-fourdegrees, twenty-eight minutes, and fifty seconds.

The difference of an arc from 90°, or a quadrant, is called itscomplement; and its difference from 180°, its supplement: thusin Plate CLXXVI. fig. 1, the arc AB is the complement of HB :but AB is the supplement of BD.

A chord, or subtense, is a right line drawn from one extremityof an arc to the other: thus BE is the chord or subtense of the arcBAE, or BDE.

The sine, or, as it is sometimes called, the right sine , of anarc, is a right line drawn from one extremity of the arc, perpen-dicular to the diameter passing through the other extremity : thusBF is the sine of the arc AB, or BD.

The versed sine of an arc is the part of the diameter, inter-cepted between the arc and its sine: thus AF is the versed sine ofAB, and DF of the arc DB.

The cosine of an arc is the part of the diameter intercepted

between