672 



TllEVISO TRIBONIAN. 



gate, from its colour, is the most important Roman 

 monument it: licnn:ni\ . 



TKKV1SO, DrKE OF. See Mortier. 



TREWES. See Highlands. 



TRIAD (three in one). The number three was 

 thought holy in the earliest antiquity. (See, for 

 in-taiici-, NumbiTS xix, 12.) This must have its 

 reason in the nature of the number. The number 

 three represents to us unity and opposition, the 

 principle and the moments of developement, or op- 

 position, and the connecting unity (synthesis). It 

 is the first uneven number in which the first even 

 one is contained ; herein lie its peculiar significa- 

 tion and perfection. Even in antiquity, it could 

 not escape attention, that this number is to be 

 found wherever variety is developed. Hence we 

 have beginning, middle, end, represented in the 

 heavens by rise, point of culmination, and setting ; 

 morning, noon, evening, and evening, midnight, 

 morning; and in general, in the great divisions of 

 time, the past, the present, and the future. In 

 space, also, this number three occurs, as in above, 

 midst, and below; right, midst, and left; and in 

 general, in the dimensions of space, as length, 

 breadth, and thickness or depth. To the eye, the 

 number three is presented in the regular figure of 

 the triangle, which has been applied to numberless 

 symbolical representations ; the ear perceives it 

 most perfectly in the harmonic triad. (See the 

 next paragraph.) As the triple is also the basis of 

 symmetry, the three-figured form is found in archi- 

 tecture and in simple utensils, without any parti- 

 cular reference to symbolical or other significations. 

 Of this kind are the triglyphs in architecture, the 

 tripod, the trident, the three thunder-bolts of Ju- 

 piter, the ancient three-stringed lyre ; though the 

 number three has in these objects, as well as in the 

 three-headed Cerberus, other more symbolical rela- 

 tions. Even in our thoughts, we meet the triad in 

 position (thesis), opposition (antithesis), and union 

 (synthesis). 



Triad, Harmonic; a compound of three radical 

 sounds, consisting of a fundamental note, its third, 

 and its fifth. Of these three sounds, the gravest is 

 called the fundamental, the fifth the excluded sound, 

 and the third the harmonical mean. This division of 

 the fifth into two thirds is performed in two ways ; 

 first, harmonically ; as when the greater third is 

 lowest, in which case, the triad is said to be per 

 feet and natural ; secondly, arithmetically ; when 

 the lesser third is lovest ; and then the triad is 

 called flat or imperfect. 



TRIAL. See Jury, and Process. 



TRIANGLE, in geometry ; a figure of three 

 sides and three angles. Triangles are either plane 

 or spherical. A plane triangle is one contained by 

 three right lines; and a spherical triangle is one 

 contained by three arcs of great circles of the sphere. 

 Triangles are denominated, from their angles, right, 

 obtuse, and acute. A right-angled triangle is that 

 which has one right angle ; an obtuse-angled tri- 

 angle is such as has one obtuse angle ; and an 

 acute-angled triangle is that which has all its angles 

 acute. The triangle is the most important figure 

 in geometry ; and its various lines bear the most 

 interesting relations to each other. See Trigono- 

 metry. 



TRIANGULAR COMPASSES are such as 

 have three legs, or feet, whereby to take off any 

 triangle- at once ; much used in the construction of 

 maps, globes, &c. 



TRIANGULAR NUMBERS are a kind of 



polygonal numbers, being the sums of arithmetical 

 progressions, the difference of whose terms is 1. 

 Thus, from the arithmetical numbers 1, 2, 3, 4, 5, 

 6, are formed the triangular numbers 1, 3, 6, 10, 

 15, 21. 



TRIANGULATING. In surveying, the larger 

 the space the more complicated is the labour. A 

 number of points are taken as the apexes of the 

 angles of triangles, into which the space is suppo-i-d 

 to be divided. This process is called trinn<ii<l<itin<j. 

 Triangles are chosen on account of the ease, with 

 which, if some parts of these figures are given, 

 the others can be calculated. In those surveys in 

 which the spheroidal form of the earth must be 

 taken into consideration, astronomical operations 

 are necessary ; accurate instruments are to be pre- 

 pared for measuring angles, such as theodolites, re- 

 flecting sextants, &c. The longitude and latitude 

 of places, at least 140 miles distant from each 

 other, must be accurately determined, and their 

 meridians must be marked on the ground. These 

 points then form a network, to be afterwards filled 

 up, and are supported by a great basis, obtained as 

 well from accurate measurement as from trigono- 

 metrical calculations or careful triangulating. This 

 basis is situated, if possible, in a meridian, and is 

 astronomically determined. In each of the chief 

 triangles, a system of smaller triangles is calcu- 

 lated ; the whole is then divided into square sec- 

 tions, each of which contains some of the points 

 trigonometrically ascertained in what we have called 

 the network. These furnish the means of survey- 

 ing in detail, and of examination. 



TRIANON ; the name of two palaces near Ver- 

 sailles. Great Trianon (le Grand Trianon) has a 

 front of 384 feet, and is remarkable for the beauty 

 and luxuriance of its gardens, laid out by Lenotre. 

 The palace, built by Mansard in the Oriental style, is 

 hut one story high. At the end of the park of Great 

 Trianon is le Petit Trianon (Little Trianon), 

 which consists merely of a pavilion in the Roman 

 style, with English gardens. This little palace 

 was the favourite resort of Marie Antoinette, and 

 was therefore exposed to the violence of the popu- 

 lace during the revolution. Great Trianon was 

 much visited by Napoleon, and the decree of 

 August 3, 1810, was dated here. See Continental 

 System. 



TRIBE (tribus). Romulus divided the inhabi- 

 tants of Rome into three bodies, thence called 

 tribes, each of which had a presiding officer (tribu- 

 MS), and was divided into ten curies. Servius Tul- 

 lius divided the inhabitants into four parts, which 

 still retained the name of tribes. To these four 

 city tribes (tribus urbanai) were added the rural 

 tribes (tribus rustics), the number of which was 

 gradually increased to thirty-one. In the comitia 

 tributa, in which the people voted by tribes, the 

 lower magistrates, the ordinary magistrates, and 

 the provincial magistrates, were chosen, laws were 

 made, and criminal trials, not capital, conducted, &c. 



TRIBONIAN, a celebrated statesman under 

 Justinian, a native of Side, in Pamphylia, was dis- 

 tinguished for his great learning, particularly in 

 jurisprudence, which gained him the favour of the 

 emperor, and raised him to the highest offices of 

 state. He became questor of the palace and con- 

 sul ; but his vices made him obnoxious, and he was 

 removed (532), in consequence of a sedition, but 

 again restored to his former dignities. He was no- 

 torious for avarice and taking bribes; but his learn- 

 ing and ability preserved him the confidence of 



