TRI 



TRI 



Triangle spherical. A figure dra^n 

 upon the superficies of a sphere, com- 

 prehended by three arcs of three great 

 circles, each of which is less than a 

 semicircle. In any right-angled spherical 

 triangle, the complement of the hypo- 

 tenuse, the complements of the angles, 

 and the two sides, are called the circular 

 parts of the triangle, as if they were fol- 

 lowing each other in a circular order, 

 from whatever part we begin. Thus, if 

 any three of these five be taken, they 

 either will be all contiguous or adjacent, 

 or one of them will not be contiguous to 

 either of the other two : in the first case, 

 the part which is between the other two 

 is called the middle part, and the other 

 two are called adjacent extremes ; in the 

 second case, the part which is not con- 

 tiguous to either of the other two is 

 called the middle part, and the other two 

 opposite extremes. 



TRIANGLE, ARITHMETICAL. A 

 table of certain numbers disposed in the 

 form of a triangle. The first column 

 contains units only; the second, the 

 series of consecutive numbers ; the third, 

 the series of triangular numbers; the 

 fourth, the series of pyramidal numbers ; 

 and so on (See Number). The columns 

 maybe continued vertically to any ex- 

 tent — 



Any number in the table is obtained by 

 adding the number immediately above it 

 in the same column, to the number in 

 same horizontal line in the next preced- 

 ing column ; further, it will be found 

 that the oblique diagonal rows, beginning 

 from the left side, are the same as the 

 vertical columns. One of the properties 

 of the table is, that numbers taken on 

 the horizontal lines, are the co-efficients 

 of the different powers of a binomial. 



TRIANGLE OF FORCES. The 

 "Parallelogram of Forces" (See Force) 

 may be stated under another form, 

 termed the triangle of forces ; for it is 

 the same thing whether we say of three 

 straight lines that they are the sides and 

 diagonal of a parallelogram, or that they 

 will form a triangle ; hence we may 

 assert, that forces will be in equilibrium 

 ■when they are proportional to the sides 

 344 



of a triangle formed by drawing lines 

 parallel to their directions. 



TRIANGULAR COMPASSES. Com- 

 passes having three legs, capable of 

 taking oflf three points at once, and used 

 in the construction of maps and charts. 

 Two of the legs open as in the common 

 compasses, while the third turns round 

 an extension of the central pin of the 

 other two, besides having a motion on its 

 own central joint. 



TRIANGULAR NUMBERS. A series 

 of numbers formed by the successive 

 sums of the terms of an arithmetical pro- 

 gression, of which the common difference 

 is 1. Thus— 



Arith. Progression 1, 2, 3, 4, 5, 6, &c. 

 Triangular Numbers 1, 3, 6, 10, 15, 21, &c. 



The general formula for the series 

 is ^ » (n + 1 ). See Number. 



TRI ANGULATION. A name given 

 to the net-work of triangles with which 

 the face of a country is covered in a 

 trigonometrical survey. 



TRIA'NGULUM. The triangle; a 

 northern constellation, consisting of six- 

 teen stars, surrounded by Perseus, An- 

 dromeda, Aries, and Musca. The tri- 

 angulum australe is a modern southern 

 constellation, consisting of five stars, 

 lying between Ara, Centaurus, and the 

 South Pole. 



TRIA'SSIC SYSTEM. New red sand- 

 stone and saliferous marls. A geological 

 system, forming the base of the great 

 central plains of England, and sur- 

 mounted by the saliferous marls and red 

 arenaceous beds which pass under the 

 great oolitic terrace, or rather the succes- 

 sion of terraces which stretch across 

 England from the coast of Devonshire to 

 the north-eastern coast of Yorkshire. 



TRIE A'SIC SALTS. The name given 

 to a class of oxygen-acid salts, which, in 

 the language of the old theory, contain 

 three atoms of base to one of acid, and 

 of which the tribasic phosphates are the 

 type. 



TRICA. Gyroma. In the botanical 

 nomenclature of lichens, this term de- 

 notes a shield, the surface of which is 

 covered with sinuous concentric furrows. 



TRICHI'DIUM (Tp£x«5toi/, from epi^, 

 a hair). Pecten. A botanical term for 

 a tender, simple, or sometimes branched 

 hair, which supports the sporules of some 

 fungaceous plants, as geastrum. 



TRICHO'PTERA (Opi^, rpixos, hair, 

 nrepov, a wing). An order of insects, 

 distinguished by the hairy covering of 

 their wings and bodies. Their larvae are 



