Triangle

Collier's New Encyclopedia (1921)

in building, a gin formed by three spars; a staging of three spars. In draughting, a three-cornered straightedge, used in conjunction with the Tsquare for drawing parallel, perpendicular, or diagonal lines. It has one right angle, the two others being each of 45°, or one of 30° and the other of 60°. In ecclesiology, a symbol of the Holy Trinity represented by an equilateral triangle. In geometry, a portion of a surface bounded by three lines, and consequently cor having three angles . Triangles are either plane, spherical, or curvilinear. A plane tria riangle is a portion of a plane bounded by three straight lines called sides, and their points of intersection are the vertices of the triangle. Plane triangles may be classified either with reference to their sides or their angles. When classified with reference to their sides, there are two classes: (1) Scalene triangles, which have no two sides equal. (2) Isosceles triangles, which have two sides equal. The isosceles triangle has a particular case, called the equilateral triangle, all of whose sides are equal. When classified with reference to their angles, there are two classes: (1) Right-angled triangles, which have one right angle. (2) Oblique-angled triangles, all of whose angles are oblique; subdivided into (a ) acute-angled triangles, which have all their angles acute; and (b) obtuseangled triangles, which have one obtuse angle. The sides and angles of a triangle are called its elements; the side on which it is supposed to stand is called the base, and the vertex of the opposite angle is called the vertex of the triangle; the distance from the vertex to the base is the altitude. Any side of a triangle may be regarded as a base in the right-angled triangle one of the sides , though about the right angle is usually taken. The three angles of a plane triangle are together equal to two right angles, or 180°; its area is equal to half that of a rectangle or parallelogram having the same base and altitude; in a right-angled plane triangle the square of the side opposite the right angle is equal to the sum of the squares the other two sides. In music, a bar of steel bent into the form of a triangle. It is suspended by one angle and struck with a small rod. In pottery, a small piece of pottery placed between pieces of biscuit ware in the seggar to prevent the adherence of the pieces when fired. In surveying, since every plane figure may be regarded as composed of a certain number of triangles, and as the area of a triangle is easily computed, the whole practice of land surveying is nothing more than the measurement of a series of plane triangles. Arithmetical triangle, a name given to a table of numbers arranged in a triangular manner, and formerly employed in arithmetical computation. It is equivalent to a multiplication table. 1 11 121 133 1 1 4 6 4 1 1 5 10 10 5 1 1 6 15 20 15 6 1 Curvilinear triangle, a triangle whose sides are curved lines of any kind whatever; as, a spheroidal triangle, lying on the surface of an ellipsoid, etc. Mixtilinear triangle, a triangle in which some of the lines are straight and others curved. Spherical triangles take the names, right-angled, obtuseed, obtuseangled, acuteangled, scalene, isosceles, and equilateral, in the same cases as plane triangles. Two spherical triangles are polar, when the angles of the one are supplements of the sides of the other, taken in the same order. A spherical triangle is quadrantal, when one of its sides is equal to 90°. 1878, he moved the resolution on the extension of the County Franchise, which was lost by 52 votes. Trevelyan's literary works comprise : "Letters from a Competition Wallah" (1864); "Cawnpore" (1865); "Ladies in Parliament and other Poems" (1869); "Life and Letters of Lord Macaulay " (2 vols. 1876; 2d ed. 1877); "The Early History of Charles James Fox" ( 1880); "American Revolution" (1909); "George III. and Charles Fox" (1914). TREVENA, JOHN, pseudonym of an English novelist, Ernest George Henham, born in 1873. Delicate in health he sought health in wandering and finally settled at Dartmoor, the scene of several of his novels. The works under his own name include: "Menotah: A Tale of the Canadian North West"; "God, Man and the Devil"; "Trenbrae"; " Bonanza: A Story of the Outside"; "Scud: The Story of a Feud"; "The Plowshare and the Sword"; "Krum: A Study of Consciousness." Works under his pseudonym include: "A Pixy in Petticoats"; "Furze the Cruel"; "Arminel of the West"; "Heather "; "The Dartmoor House that Jack Built"; "Matrimony "; "Moyle Church Town." TREVES, a city of Rhenish Prussia; on the Moselle; in a valley between low vine-covered hills of ruddy sandstone; 69 miles S. W. of Coblenz and 111 S. S. W. of Cologne. The river is crossed here by an eight-arch bridge, 623 feet long , whose Roman piers date from 25 B. c. "A quiet, old-fashioned town, Treves," Freeman says, "has a body of Roman remains far more numerous and varied, if not individually more striking, than any other place north of the Alps can show." These include the "Porta Nigra," 118 feet long, and 95 high, one probably of the five gates by which Trèves was entered in Constantine's time; the so-called Roman baths (more probably part of an imperial palace ); and a basilica built of Roman brick by Constantine for a court of justice, but demolished in great measure to make room for an electoral palace in 1614. This , however, was removed, and the basilica fitted up for a Protestant church in 1856 . Beyond the walls are the ruins of an amphitheater that could seat 30,000 spectators; and 6 miles off is the "Igelsäule" or "Heidenthurm," a monumental column , 71 feet high, sculptured with bas-reliefs of the 2d century. The cathedral of SS. Peter and Helena is an interesting structure of various antiquity, but chiefly in the early German Romanesque style of the 11th century. The most famous of its relics is the seamless or "Holy Coat," which consists of "connected fragmentary particles of material ." Said to have been brought to Treves by the Empress Helena, it is first referred to in 1106 by an anonymous monk, and was not a source of revenue till 1512. It was visited by nearly 2,000,000 pilgrims in 1891, the first time of exhibition since 1844. A "Holy Coat" is also shown at Argenteuil and in 19 other places. Connected with the cathedral by a cloister is the beautiful Liebfrauenkirche (1243); and there is a library of over 100,000 volumes and many MSS., among them the "Codex Aureus" of the Gospels, presented to the abbey of St. Maximin by Charle- A university, magne's sister, Ada . founded in 1472, was suppressed in 1798. The industries comprise manufactures of woolens, cottons, and linens, besides a wo brisk trade in corn, timber, and Moselle wine. Pop. about 47,000. Trèves, which claims to be 1,300 years older than Rome, derives its name from the Treviri, a Gallic or, more probably, a Belgic people, who in Cæsar's time inhabited a large district between the Meuse and the Rhine . Their capital, Augusta Trevirorum, seems to have become a Roman colony in the reign of Augustus, and ultimately was the headquarters of the Roman commanders on the Rhine, and a frequent residence of the emperors, especially Constantine. Sacked by Attila in 451, it passed to the Franks in 463, to Lorraine in 843, to Germany in 870, and back to Lorraine in 895, and was finally united to Germany by the Emperor Henry I. The Archbishop of Treves was, as chancellor of Burgundy, one of the electors of the empire, a right which originated in the 12th or 13th cen , tury, and which continued till the French Revolution. The last elector removed to Coblenz in 1786; and Trèves was the capital of the French department of Sarre from 1794 till 1814, since which time it has belonged to Prussia . TREVES, SIR FREDERICK, a British surgeon, born in Dorchester, in 1853 . He was educated at the Merchant Taylors' School and became Hunterian professor of anatomy and Wilson professor of pathology at the Royal College of Surgeons in 1881-1886 and examiner in surgery at Cambridge in 1891-1896 . He was lord rector of Aberdeen University from 1905 to 1908. He acted as consulting surgeon in the South African War, was surgeon-extraordinary to Queen Victoria, and in 1902 operated on Edward VII. for perilyphilitis. He wrote "System of Surgery," and has published other works on medicine, war experience , and travel. Strait of Juan de Fuca C. Flattery PA ruden ICTORIA racortes Paro Woolley Bellingham bakc Kootenai S Port Angeles Se ہے Olymp Townsend M Olympus E Marysville Republic Snohomish Colville bonders Breme Plon Edmonds Columbia Shelton Pu Aberdeen Cheha Centa Chelan Montesano El thead Prus Prlust yeha C cattle Leavenworth Lake AC Hoquia Sanu Pom Kent Wenatchee Weet MS Frenchmane? tehsh HIN Cosm ild Libly Sage South Beau Chehalis Olympia Columbia R. M mibia Fall Valter •Tenino Shelby Galata Spirit Loke C. Dissappointment GREAT PLAIN 6 Elum aftspell G dru Conind Cheste TON uscor Chinos dinsdale PrAdame Winlock nsburg OF THE Harrisoner Astoria Ramier Ft Assueborn Box Elder Bear Paw North Yakima Thompson Mt. 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Bre Cooba Kissimmee A Dade City Plant City Lakeland Tarpon Sp Tampa Bartow Kunm Indian River Inlet West LITTLE ABACO 1. tung EuMeade Wauchula St. Peter Ft.l 26 Tamp F Brak GREAT 0 Arcadia Lake upiter ABACO I GREAT BAHAMA I. Okechoble Palm Beach MA Punta Gorda West Beach aloosadate H Charlotte Hor A Meyers B PINE t.Lauderdale ELEUTHERA BERRY 18 Swanmp Bemon Marco Plorida Miami NEW C. Romano no Bay PROVIDENCE 1. TEN THOUBAND D ISLANDS AN 24 amos de Leon Bay 0 S Sable C ANDROS Bay EXUMA REY LONG KET BIG PINE KE VACCAG RID BUGARLOAF KEY BOCA CHICK Key We ORT GAB TORTUGA FLO MARQUESAS SAND KEY REYS 88 86 84 82 80 78 76 74 TOKIO A SELF-REVISING REFERENCE WORK WITH LOOSE-LEAF FEATURES IN TEN BOUND VOLUMES WITH 515 ILLUSTRATIONS AND NINETY-SIX MAPS, SUPPLEMENTED BY A LOOSE-LEAF VOLUME VOLUME TEN P. F. COLLIER & SON COMPANY NEW YORK Copyright, 1921 By P. F. COLLIER & SON COMPANY DR. WILLIAM A. NEILSON, CHAIRMAN PRESIDENT SMITH COLLEGE, NORTHAMPTON, MASS. FORMER PRESIDENT OF NAVAL WAR COLLEGE, NEWPORT, R. I. DR. JOSEPH H. ODELL DIRECTOR, SERVICE CITIZENS OF DELAWARE, WILMINGTON, DEL. DR. KENNETH C. M. SILLS PRESIDENT BOWDOIN COLLEGE, BRUNSWICK, ME. DR. HENRY S. CANBY EDITOR LITERARY REVIEW, NEW YORK, N. Y. DR. W. T. COUNCILMAN DEPARTMENT OF PATHOLOGY, HARVARD MEDICAL SCHOOL, BOSTON, MASS. DR. CHARLES F. THWING PRESIDENT WESTERN RESERVE UNIVERSITY, CLEVELAND, OHIO DR. EDWIN GREENLAW