TRI 



TRI 



well known under the name of caddice- 

 tvorms. 



TRICHO'TOMOUS {rptxa, in three 

 parts, Tejixvto, to cut). A designation of 

 the mode of branching or of inflores- 

 cence, when the divisions occur in threes, 

 as in the stem of Marvel of Peru. 



TRIDACNI'DiE. The name given by 

 Lamarck to a family belonging to the first 

 section of his monomyarian conchifers, 

 or mollusks furnished with bivalve shells 

 which have a single muscular impres- 

 sion. This family comprises the genera 

 tridacna and hippopus. 



TRIFID, TRISECTED, TRIPART- 

 ED, &c. These and other terms are 

 applied by botanists to the forms of 

 leaves, with especial reference to the 

 number and the depth of their lobes, ac- 

 cording as they have, respectively, fis- 

 sures, segments, or partitions. And, on 

 the other hand, we may, by neglecting the 

 number of the lobes, simply indicate 

 their presence by saying that a leaf is 

 pinnatilobed, palmatilobed, and so on. 

 The lobes themselves are sometimes sub- 

 divided upon the same principle as the 

 leaf itself : thus we say that a leaf is tri- 

 pinnatisected, tripinnatiparted, tripin- 

 natifid, when the subdivisions of the lobes 

 are themselves lobed. 



TRFGLID^. The Gurnard tribe of 

 acanlhopterygious or spiny-finned fishes, 

 generally resembling the Percidae, but 

 having their head armed with spines or 

 hard scaly plates. 



TRIGO'NIDiE (tp/ywvo?, triangular). 

 A family of conchiferous mollusks, named 

 from the genus trigonia, the shell of 

 which is of a subtrigonal form. 



TRIGONO'METRY (tp.'ywi/ov, a tri- 

 angle, juerpeo), to measure). This term 

 originally denoted simply the science by 

 which those relations are determined 

 which the sides and angles of a triangle 

 have to each other, being called p/ane or 

 spherical trigonometry, according as the 

 triangle was described on a plane or a 

 spherical surface. By means of certain 

 proportions always holding good between 

 the three sides and the three angles of a 

 triangle, we are enabled, by the aid of 

 this branch of mathematics, when any 

 three of these six quantities are known 

 (provided that one of these known quan- 

 tities be a side), to find the other three. 

 At present, the term has a much more 

 extensive meaning, as the science now 

 embraces all the theorems expressing the 

 relations between angles and certain 

 functions of them ; it embraces the 

 345 



consideration of alternating and pe- 

 riodic magnitude ; in which quantity 

 is imagined to go through alterations 

 of increase and diminution without 

 end. 



1. Definitions of Trigonometrical Lines. 



1. The complement of an arc is its differ- 

 ence from a quadrant; and that of an 

 angle, its difference from a right angle. 



2. The supplement of an arc is its defect 

 from a semicircle j and that of an angle, 

 its defect from two right angles. 3. The 

 sine of an arc is a line drawn from one of 

 its extremities, perpendicular to the ra- 

 dius passing through its other extre- 

 mity. 4. The tangent of an arc is a line 

 touching it at one extremity, and limited 

 by the radius produced through its other 

 extremity. 5. The secant of an arc is 

 that portion of the radius produced, 

 which is intercepted between the extre- 

 mity of the tangent and the centre. 

 6. The versed sine of an arc is that por- 

 tion of the radius intercepted between 

 the sine and the extremity of the 

 arc. 7. The supplemental versed sine, 

 or suversed sine is the difference be- 

 tween the versed sine and the dia- 

 meter. 8. The sine, tangent, &c. of the 

 complement of an arc, are concisely 

 termed the cosine, cotangent, &c. of that 

 arc. These terms, for conciseness, are 

 usually contracted into sin., tan., sec, 

 vers., suvers, cos., cot., cosec, covers., 

 and cosuvers. 



2. Trigonometrical Functions of an 

 Angle. I. The ratio which the sine ot 

 an angle bears to its cosine is called the 

 tangent of the angle. 2. The inverse of 

 this ratio is called the cotangent. 3. The 

 ratio of unity to the cosine of an angle is 

 denominated the secant ; and that of 

 unity to the sine, the cosecant. 4. The 

 difference between unity and the cosine 

 is called the versed sine. 5. The differ- 

 ence between unity and the sine of an 

 angle is called the coversed sine. These 

 are functions of the angle, and are quite 

 independent of the absolute length of the 

 arc subtending it, or of the radius of that 

 arc. 



3. Signs of the trigonometrical lines. 

 The signs + and — , which in arithmetic 

 indicate addition and subtraction, are 

 used in geometry to point out opposition 

 in direction. Quantities whose signs are 

 + , are called positive, and those whose 

 signs are — , are called negative. If a 

 line be measured from a given point or a 

 given line as its origin, it is reckoned 

 positive when it lies on one side of its 



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