Near the centre of the inner city, most of the streets in which are narrow and irregular, is the cathedral of St Stephen, the most important mediaeval building in Vienna, dating in its present form mainly from the 14th and 15th centuries, but incorporating a few fragments oi the original 12th-century edifice. Among its most striking features are the fine and lofty tower (450 feet), rebuilt in 1860-64; the extensive catacombs, in which the emperors were formerly interred; the sarcophagus (1513) of Frederick III.; the tomb of Prince Eugene of Savoy; thirty-eight marble altars; and the fine groined ceiling. A little to the south-west of the cathedral is the Hofburg, or imperial palace, a huge complex of buildings of various epochs and in various styles, enclosing several courtyards. The oldest part of the present edifice dates from the 13th century, and extensive additions are now being made according to the plans of the architect Fischer von Erlach (1656-1723). In addition to private rooms and state apartments, the Hofburg contains a library of 400,000 volumes and 20,000 MSS.; the imperial treasury, a storehouse of objects of the greatest historical interest and intrinsic value; a cabinet of coins and antiquities; and other important collections. In the old town are the two largest of the Höfe, extensive blocks of buildings belonging to the great abbeys of Austria, which are common throughout Vienna. These are the Schottenhof (once belonging to the “Scoti,” or Irish Benedictines) and the Mölkerhof, adjoining the open space called the Freiung, each forming a little town of itself. As in most Continental towns, the custom of living in flats is prevalent in Vienna, where few except the richer nobles occupy an entire house. Of late the so-called “Zinspaläste” (“tenement palaces ”) have been built on a large and magnificent scale, often profusely adorned without and within with painting and sculpture. Some of the finest of these, a characteristic feature of Vienna architecture, are also to be seen in the old town. Other notable buildings within the line of the old fortifications are the Gothic Augustine church, containing a fine monument by Canova; the Capuchin church, with the burial vault of the Hapsburgs; the church of Maria-Stiegen, an interesting Gothic building of the 14th century; the handsome Greek church, by Hansen; and the old rathhaus. At the corner of the Graben is the “Stock im Eisen,” the stump of a tree, said to be the last survivor of a holy grove round which the original settlement of Vindomina sprang up (see p. 222 below). It is full of nails driven into it by travelling journeymen.

In the number of its large and handsome modern buildings Vienna can hold its own with any European capital. Most of these are found in or adjoining the Ring-Strasse, which certainly ranks as one of the most imposing achievements of recent street architecture. Opposite the Hofburg, the main body of which is separated from the Ring-Strasse by the Hofgarten and Volksgarten, rise the handsome monument of the empress Maria Theresa and the imperial museums of art and natural history, two extensive Renaissance edifices with domes, matching each other in every particular and grouping finely with the new part of the palace. Hans Makart’s painted dome in the natural history museum is the largest pictorial canvas in the world. Adjoining the museums to the west is the palace of justice (1881), and this is closely followed by the houses of parliament (1883), in which the Grecian style has been successfully adapted to modern requirements. Beyond the houses of parliament stands the new rathhaus, an immense and lavishly-decorated Gothic building, erected in 1873-83. It was designed by Friedrich Schmidt, who may be described as the chief exponent of the modern Gothic tendency, as Hansen and Semper, the creators respectively of the parliament house and the museums, are the leaders of the Classical and Renaissance styles which are so strongly represented in Viennese architecture. The central tower and the tapering steeple of the rathhaus are surmounted by a colossal bronze figure of a knight. Opposite the rathhaus, on the inner side of the Ring, is the new court theatre, another specimen of Semper’s Renaissance work. To the north stands the new building of the university, a Renaissance structure by Ferstel, rivalling the rathhaus in extent. Near the university, and separated from the Ring by a garden, stands the votive church in Alsergrund, erected to commemorate the emperor’s escape from assassination in 1853, one of the most elaborate and successful of modern Gothic churches, in which the efforts of the architect (Ferstel) are supported by a profusion of sculpture and stained glass windows. The other important buildings of the Ring-Strasse include the magnificent opera house, the sumptuous interior of which vies with that of Paris, the Academy of Art, the industrial museum, and the exchange. On the north side the Ring-Strasse gives place to the spacious Franz Joseph’s quay, flanking the Danube Canal. The municipal districts outside the Ring also contain numerous handsome modern buildings. Among the churches may be instanced those of Wieden (St Carlo Borromeo) and Lerchenfeld, the former an 18th-century imitation of St Peter’s at Rome, the latter a plain but graceful building in an early mediaeval Italian style. The secular buildings include several large barracks and hospitals, various institutions connected with the university, the arsenal (with a collection of weapons), the Belvedere (see below), and the polytechnic institute, markethalls, &c. In the outlying districts are numerous villas of great taste and elegance.

Vienna is the intellectual as well as the material capital of Austria,—emphatically so in regard to the German part of the empire. Its university, established in 1365, is now attended by nearly 6000 students, and the medical faculty enjoys a world-wide reputation. Besides an adequate supply of elementary and secondary schools, the other educational institutions include a large polytechnic, an agricultural academy, a military school, Roman Catholic and Protestant theological seminaries, a conservatorium of music, a training school for aspirants to a diplomatic career, a commercial college, and numerous technical and special schools. Its scientific institutions are headed by the Academy of Science. The Academy of Art was founded in 1707. Few European capitals possess more valuable art collections than Vienna. The picture gallery in the Belvedere Palace, formerly the residence of Prince Eugene, is unsurpassed for its specimens of Rubens, Dürer, and the Venetian masters. The Lower Belvedere, at the other end of the garden, contains the famous Ambras collection of armour, curiosities, and antiquities. The private picture galleries of Prince Liechtenstein, Count Harrach, and Count Czernin are of great extent and importance; and the collection of drawings and engravings known as the “Albertina,” in the palace of the archduke Albert, is familiar to all connoisseurs. The collections of the various museums, &c., which are not unworthy of the handsome buildings in which they are exhibited, and the extensive military collections of the arsenal must also be mentioned.

In 1880 the population of Vienna proper, i.e., the ten municipal districts, amounted to 705,402, a number which gave it the fourth place among the cities of Europe. . Including the suburbs, the total population rose to 1,082,812. The above figures are exclusive of the garrison of 20,700 men. The overwhelming majority of the inhabitants are Roman Catholics; the Jews number about 75,000, and the Protestants 26,500.

Owing to the peculiarities of its situation, the population of Vienna is of a very cosmopolitan and heterogeneous character. The German element is, of course, largely in the ascendant; but there are also large numbers of Czechs, Hungarians, and Slavs. As a general rule the Viennese are gay, pleasure-loving, and genial, and they possess a bonhomie which differentiates them markedly from the inhabitants of the other great German capital. The Viennese women are often distinguished by beauty and elegance; and dressing as a fine art is cultivated here with almost as great success as in Paris. As a rule the Viennese are passionately fond of dancing; and the city of Strauss, Lanner, and Gungl provides the civilized terpsichorean world with waltzes and polkas. Opera, especially in its lighter form, flourishes, and the actors of Vienna maintain with success a traditional reputation of no mean order. The above description must not be understood to convey a negation of more solid qualities, especially industry, frugality, and sobriety. Its chief place in the history of art Vienna owes to its musicians, among whom are counted Haydn, Mozart, Beethoven, and Schubert. The Viennese school of painting is of modern origin; but some of its members, for instance, Hans Makart, have acquired a European reputation.

The Prater, a vast expanse (2000 acres) of wood and park on the east side of the city, between the Danube and the Danube Canal, is greatly frequented by all classes; and here all phases of Viennese life may be studied, from the fashionable corso in the Haupt-Allee in May down to the boisterous and Derby-day-like jollity of a Sunday in the Wurstel Prater or people’s Prater. The great exhibition of 1873 was held in this park, and several of its buildings, including the large rotunda, have been left standing. Smaller parks are the Hofgarten, the Volks-garten, and the Town Park, all adjoining the Ring-Strasse. The environs of the city of Vienna contain many points of beauty and interest. Among the most popular resorts are the parks and gardens belonging to the imperial châteaux of Schönbrunn and Laxenburg.

The position of the city on the chief European waterway running from west to east early marked out Vienna as one of the great commercial emporia of eastern Europe. The valley of the March, which river here joins the Danube, forms the natural line of communication with the Oder and the Vistula. But the Austrian Government and the corporation of Vienna, by failing to keep the Danube in a proper state for navigation, have let slip the opportunity of making the city the great Danubian metropolis which its geographical position entitles it to be. An extensive trade is nevertheless carried on from Vienna in grain, partly as a direct importation from Hungary and partly in transit between Russia and southern Germany. Other important articles are wine, cattle, colonial wares, and manufactured goods of the most varied description. Though not conspicuous among cities of its own rank as an industrial centre, Vienna nevertheless carries on a considerable number of manufactures; and some of its products, such as its bent-wood furniture and meerschaum pipes, are exported to all parts of Europe. In the number and variety of its leather and other fancy goods it rivals Paris; and among manufactures of a more solid character may be instanced machinery, ironwares, carriages, cotton and silk goods, &c. The beer of Vienna is also famous. The municipal government of Vienna is entrusted to a gemeinderath of 120 elected members, with an executive and police magistracy. The annual income of this body amounts to about one and a half millions sterling. In the national parliament the city is represented by 10 members. The climate of Vienna is changeable, and rapid falls of temperature are not uncommon. The range between January and June is about 40° Fahr. Violent storms often occur in spring and autumn; and the heat of summer is accompanied by a plague of dust. Good water is brought by an aqueduct from the Schneeberg, 50 miles to the south-west. The annual death-rate is about twenty-six per thousand.

History.— For several centuries Vienna filled an important rôle as the most advanced bulwark of Western civilization and Christianity against the Turks, for during the whole of the Middle Ages Hungary practically retained its Asiatic character. The story of Vienna begins in the earliest years of the Christian era, with the seizure of the Celtic settlement of Vindomina by the Romans, who changed its name to Vindobona, and established a fortified camp here to command the Danube and protect the northern frontier of the empire. The fortress grew in importance, and was afterwards made a municipium; and here Marcus Aurelius died in 180. On the decline of the Roman empire Vindobona became the prey of successive barbarian invaders. Attila and his Huns were among the temporary occupants of the place (5th century), and in the following century it came into the possession of the Avars, after which its name disappears from history until towards the close of the 8th century, when Charlemagne expelled the Avars and made the district between the Enns and the Wiener Wald the boundary of his empire. In the time of Otho II. (976) this “East Mark” (Ostmark, Oesterreich, Austria) was granted in fief to the Babenbergers, and in the reign of Frederick Barbarossa (1156) it was advanced to the rank of a duchy. There is no certain record that the site of Vindobona was occupied at the time of the formation of the Ostmark, though many considerations make it probable. It is not likely that the Avars, living in their “ring” encampments, destroyed the Roman municipium; and Becs, the Hungarian name for Vienna to this day, is susceptible of a Slavonic interpretation only, and would seem to indicate that the site had been occupied in Slavonic times. The frequent mention of “Wiene” in the oldest extant version of the Nibelungenlied points in the same direction. Passing over a doubtful mention of “Vwienni” in the annals of 1030, we find the “civitas” of Vienna mentioned in a document of 1130, and in 1156 it became the capital and residence of Duke Heinrich Jasomirgott. In 1237 Vienna received a charter of freedom from Frederick II., confirmed in 1247. In the time of the crusades Vienna increased so rapidly, in consequence of the traffic that flowed through it, that in the days of Ottocar II. of Bohemia (1251-76), the successor of the Babenbergers, it had attained the dimensions of the present inner town. A new era of power and splendour begins in 1276, when it became the capital of the Hapsburg dynasty, after the defeat of Ottocar by Rudolph of Hapsburg. From this time on it has shared the fortunes of the house of Austria. In 1477 Vienna was besieged unsuccessfully by the Hungarians, and in 1485 it was taken by Matthew Corvinus. Of more importance were the two sieges by the Turks (1529 and 1683), when the city was saved on the first occasion by the gallant defence of Nicholas von Salm, and on the second by Rüdiger von Starhem-berg, who held out until the arrival of the Poles and Germans under John Sobieski of Poland. The suburbs, however, were destroyed on both occasions. In 1805, and again in 1809, Vienna was for a short time occupied by the French. In 1814-15 it was the meetingplace of the congress which settled the political affairs of Europe after the overthrow of Napoleon. In 1848 the city was for a time in the hands of the revolutionary party; but it was bombarded by the imperial forces and compelled to surrender on 30th October of the same year. Vienna was not occupied by the Prussians in the war of 1866, but the invaders marched to within sight of its towers. Since then the most important event in its history has been the exhibition of 1873.

See Weiss, Gesch. der Stadt Wien (2 vols., 2d ed., 1882-83), containing an ample bibliography; Oesterreich in Wort und Bild, &c., Erste Abth. (1886); Weiss, Topographie der Stadt Wien (1876); victor Tissot, Vienne et la Vie Viennoise (Paris, 1878). (J. F. Μ.)

Of the total area of 1,722,478 acres arable land occupies 1,119,675, grass 76,899, vines 90,750, woods 193,322, and heath, pasture, and uncultivated land 146,971. In 1881 the live stock included 22,637 horses, 7176 mules, 9679 asses, 63,052 cattle, 155,212 sheep of native and 47,970 of improved breed, 66,655 pigs, and 21,744 goats. There were also 11,047 beehives (32½ tons of honey and as much of wax). The crops in 1884 were—wheat 4,557,146 bushels, meslin 245,641, rye 291,673, barley 1,063,647, oats 4,295,742, buckwheat 27,813, maize 51,529, potatoes 3,455,220, beetroot 54,941 tons, colza seed 668 tons, hemp 323 tons, flax 3½ tons, hay 108,955 tons, clover 54,862, lucerne 98,282, sainfoin 53,350, other fodder 10,079 tons, wine 20,288,952 gallons (average for last ten years 21,384,880 gallons). Oak, ash, alder, and birch are the principal forest trees, and among the fruit-trees are the chestnut, walnut, and almond. Iron and manganese occur, and there are numerous quarries of building and lithographic stones, lime, limestone, millstones, marl, and a sort of pebbles which are cut into “Châtellerault diamonds.” There are sulphur and iron mineral springs. The most important industrial establishments are the national arms manufactory and the cutlery works at Châtellerault; in other parts of the department are forges, blast furnaces, wool-spinning mills (580 spindles), hemp-spinning mills (4000 spindles, of which only 1500 are in use, and 28 looms), manufactories of serges and coarse cloth, vinegar, candles, leather, tiles, and pottery, paper-works, breweries, distilleries, rope-yards, lime-kilns, and numerous plaster and flour mills. Corn, wine, brandy, vegetables, fruit, chestnuts, fodder, cattle, cutlery, and dressed hides are exported; butcher’s meat, colonial produce, and coals are imported. The department has 233 miles of railway, 239 of national and 8704 of other roads, and 32 of waterway (the Vienne from Châtellerault, the Dive below Moncontour, and some miles of the Creuse being navigable). The population in 1881 was 340,295 and in 1886 342,785, an increase of 201,795 since 1801. Vienne forms part of the diocese of Poitiers, has its court of appeal and academy at Poitiers, and belongs to the Tours army corps district. The chef-lieu is Poitiers (population 34,628 in 1886), and the department is divided for purposes of administration into 5 arrondissements (Poitiers; Châtellerault, population of town 14,498 in 1886; Civray, 2464; Loudun, 4041; Montmorillon, 4155), 31 cantons, and 300 communes.

VIENNE, a town of France, chef-lieu of an arrondissement in the department of Isère, historically and industrially the first, and by population the second, city of Dauphiné, is situated on the left bank of the Rhone, at the point where it is joined by the Gère, 19 miles S. of Lyons by the railway to Marseilles. On the north, east, and south the town is sheltered by low hills. Its site is an immense mass of ancient débris, which is constantly yielding interesting antiquities. Along the Gère are traces of the ramparts of the old Roman city; on Fort Pipet, to the east of the town, are the remains of a theatre and citadel and some vestiges of a pantheon and an amphitheatre; and in the interior of the town are two arches of a theatre and the balustrade of a magnificent staircase. The ancient aqueducts, restored in 1822, still convey the waters of the Gère from a distance of 4 or 5 miles; and there are several pieces of Roman road to be seen in the neighbourhood. The Plan de 1’Aiguille, a truncated quadrangular pyramid 55 feet high, resting on a portico with four arches, used to be pointed out as the tomb of Pontius Pilate (who, according to tradition, died here), but it is now recognized as having been part of the spina of a large circus, the outlines of which have been traced. The temple of Augustus and Livia, a rectangular building of the Corinthian order, was rebuilt at the end of the 2d century, and in the 5th century was converted into a church. The “festival of reason” was celebrated in it at the Revolution; and it has only lately been restored, and the houses built against it cleared away. The museum in the town-hall is very rich in antiquities. The cathedral of St Maurice, exhibiting the finest Gothic architecture in Dauphiné, was begun at the end of the 12th century in the Transitional Burgundian style, on the ruins of a church which had been finished in 1107, and it was consecrated by Pope Innocent IV. in 1251. There is neither apse nor transept, and the building (315 feet long, 118 wide, and 89 high) is a singular mixture of the Romanesque and Gothic styles. The best part is the façade, finished in 1533, which rises majestically from a terrace overhanging the Rhone. Parts of the church of St André-le-Bas, which was used as a chapel by the dukes of Burgundy, are as old as the 9th century, and most of it was built in 1152. The church of St Peter, at present (1888) undergoing restoration, is one of the oldest in France, dating from the 6th century; the porch is in the most primitive Romanesque style; and the side walls, decorated with two rows of arches resting on marble columns (9th century), are unique in France. The steeple belongs to the 12th century, and the vaults were rebuilt by Soufflot in the 18th century. Among the many tombs is that of St Mamert. In the square fronting the town-hall is a statue of Ponsard the dramatist, who was born at Vienne. The Gère supplies the motive power to numerous factories. About one million yards of cloth are annually produced, and from 8000 to 9000 hides are dressed. The other industrial establishments include a paper-mill, an iron and copper foundry (400 men), iron-works, foundries, lapidaries’ workshops, glass-works, brick-works, and calcining and refining furnaces in connexion with the lead and zinc mines in the neighbourhood. Grain is an important article of commerce. A suspension bridge connects Vienne with the right bank of the Rhone, where the village of St Colombe occupies part of the site of the ancient town. Near St Romain-en-Gal is a tower built by Philip of Valois to defend the right, or French, bank, as distinguished from the left, which belonged to the empire. The population in 1881 was 22,740 (commune 26,060), and in 1886 23,011 (commune 25,480).

Vienne was originally the capital of the Allobroges, and was embellished and fortified by Julius Caesar, who made it a colony. Tiberius granted the citizens the jus Italicum. The ramparts, pierced by five gates, enclosed a lower, middle, and upper town. Vienne was the residence of a praetor, had a senate, consuls, and a garrison of five legions, and was the seat of a celebrated school. A bridge of five arches connected it with the new town on the right bank. Postumus (see vol. xx. p. 776) was proclaimed Caesar here in 259, and Vienne became the capital of a provincial empire, which under himself and his successors, Victorinus and Tetricus, lasted fourteen years. Christianity was introduced by St Crescens in the 2d century, and St Lupicin is named as the first archbishop. The archbishops of Vienne all through the Middle Ages disputed the title of primate of Gaul with those of Lyons. Vienne was conquered by the Burgundians in 438, and sacked by the Lombards in 558 and by the Saracens in 737. It was one of the residences of Boso, king of Burgundy and Provence (879), who died and was buried here. After the fall of the second kingdom of Burgundy, Vienne became the chef-lieu of a county, for which the nobility and clergy disputed, and which was finally seized by the counts of Albon. In 1349 Humbert II. ceded Vienne with all Dauphiné to France. The town was sacked in 1562 by Baron des Adrets, was claimed by both Roman Catholics and Protestants, but declared for the League in 1590, and was compelled to surrender to the duke of Montmorency, who destroyed the citadel and ramparts. The archbishopric was suppressed in 1790. Vienne was the birthplace of St Julian (3d century); and pope Calixtus II. (Guy of Burgundy; ob. 1124) was one of its archbishops.

VIENNE, Haute-, a department of France, formed in 1790 out of Limousin (three-fifths), La Marche (one-fourth), Poitou, and Berry, and formerly known as Haut-Limousin, lies between 45° 26' and 46° 23' N. lat. and 0° 38' and 1° 54' E. long., and is bounded by the Indre on the N., Creuse on the E., Corrèze on the S.E., Dordogne on the S.W., Charente on the W., and Vienne on the N.W. Haute-Vienne belongs to the central plateau of France, and drains partly to the Loire and partly to the Garonne. The highest point (2549 feet) is in the extreme south-east, and belongs to the treeless but well-watered plateau of Millevaches, formed of granite, gneiss, and mica. To the northwest of the Millevaches are the Ambazac (2300 feet) and Blond (1690 feet) Hills, both separating the valley of the Vienne from that of the Gartempe, a tributary of the Creuse. The Vienne traverses the department from east to west, passing Eymoutiers, St Léonard, Limoges, and St Junien, and receiving on the right the Maude and the Taurion. The Isle, which flows into the Dordogne, with its tributaries the Auvézère and the Dronne, and the Tardoire and the Bandiat, tributaries of the Charente, all rise in the south of the department. The altitude and inland position of Haute-Vienne, its geological character, and the northern exposure of its valleys make the winters long and severe; but the climate is milder in the west and north-west. The annual rainfall at Limoges is 36 inches.

Of the total area of 1,360,000 acres 439,215 are cultivated, 4263 are occupied by vineyards, 75,333 by chestnut trees, and 163,135 by dry underwood. The crops in 1884 were—wheat 1,242,271 bushels, meslin 34,298, rye 2,482,557, barley 13,300, oats 318,026, buckwheat 1,529,368, maize 65,579, potatoes 6,710,723, beetroot 189,000 tons, colza seed 1845 tons, hemp seed 1921, hemp 1200, linseed 93, flax 46, hay 387,192, clover 31,527, lucerne 3153, wine 111,430 gallons (average for preceding ten years 141,020 gallons). The live stock included 8371 horses of a shapely and powerful breed, 684 mules, 4975 asses, 146,131 cattle, 507,443 sheep of native and 43,593 of improved breed, 104,263 pigs, and 9642 goats. There were 36,601 beehives (104½ tons of honey and 34½ tons of wax). The department is on the whole unproductive. The chestnut is here characteristic, as the apple in Normandy, and with the potato and turnip it forms the chief food of the people. The brooks are fringed by fine meadows, and the hills are covered with heaths or forests of beech, hornbeam, oak, birch, and chestnut. The mineral wealth consists of iron, copper, tin, wolfram, antimony, serpentine, fine-grained granite, gneiss, garnets, emeralds, and a kind of porphyry, which takes a fine polish. There are inexhaustible supplies of china clay, in which an export trade is carried on with Russia and America. 5800 workmen are employed in porcelain manufactories, 650 in paper and pasteboard mills (annual product, £100,000), 560 in wool and cotton spinning mills and manufactories of flannel, druggets, woollen cloaks, and carpets, 600 in shoe-making (annual product, £100,000), 600 in manufactories of sabots, 340 in glove manufactories, 370 in tan-yards, 325 in leather-dressing works, 130 in coach-building and wheelwrights’ shops, 125 in cabinet workshops, 325 in printing works, and 100 in distilleries (annual product, £480,000). In 1878 1153 tons of iron were produced, and there are forges, foundries, copper-works, and manufactories of agricultural and other implements. Porcelain, china clay, woven goods, boots and shoes, sabots, gloves, leather, cattle, horses, wood, chestnuts, hemp, and paper are exported; corn, wine, coal, raw materials, and various manufactured articles are imported. There are in Haute-Vienne 234 miles of railway, and 234 of national and 3191 of other roads. This department, with that of Corrèze, forms the diocese of Limoges; it belongs to the district of the Limoges court of appeal and army corps, has its academy at Poitiers, and is divided for purposes of administration into 4 arrondissements (Limoges, population of town 63,707 in 1886; Bellac, 4015; Rochechouart, 1829; and St Yrieix, 3556), 27 cantons, and 203 communes. The population in 1881 was 349,332 and in 1886 363,182, an increase of 117,982 since 1801. Limoges is the chef-lieu. St Yrieix has an early Gothic church of the 12th century, kaolin mines, porcelain manufactories, and tan-yards. St Junien (5454) has an interesting bridge and houses of the 13th century, and numerous manufactories of gloves, paper, porcelain, sabots, and woven goods. St Leonard (3427), the birthplace of Gay-Lussac, possesses a remarkable church of the 11th and 12th centuries, tanyards, paper-mills, and copper-works. At Châlus (1675) Richard Coeur de Lion died.

We know of one important service rendered by Vieta as a royal officer. While at Tours he discovered the key to a Spanish cipher, consisting of more than 500 characters, and thenceforward all the dispatches in that language which fell into the hands of the French could be easily read. His fame now rests, however, entirely upon his achievements in mathematics. Being a man of wealth, he printed at his own expense the numerous papers which he wrote on various branches of this science, and communicated them to scholars in almost every country of Europe. An evidence of the good use he made of his means, as well as of the kindliness of his character, is furnished by the fact that he entertained as a guest for a whole month a scientific adversary, Adriaan van Roomen, and then paid the expenses of his journey home. Vieta’s writings thus became very quickly known; but, when Franciscus van Schooten issued a general edition of his works in 1646, he failed to make a complete collection, although probably nothing of very great value has perished.

The form of Vieta’s writings is what we may call their weak side. He indulged freely in flourishes; and in devising technical terms derived from the Greek he seems to have aimed at making them as unintelligible as possible. None of them, in point of fact, has held its ground, and even his proposal to denote unknown quantities by the vowels A, E, I, O, U, Y,—the consonants b, c, &c., being reserved for general known quantities, has not been taken up. In this denotation he followed, perhaps, some older contemporaries, as Ramus, who designated the points in geometrical figures by vowels, making use of consonants, r, S, t, &c., only when those were exhausted. Vieta is wont to be called the father of modern algebra. This does not mean, what is often alleged, that nobody before him had ever thought of choosing symbols different from numerals, such as the letters of the alphabet, to denote the quantities of arithmetic, but that he made a general custom of what until his time had been only an exceptional attempt. All that is wanting in his writings, especially in his Isagoge in artem analyticam (1591), in order to make them look like a modern school algebra, is merely the sign of equality,—a want which is the more striking because Robert Recorde had made use of our present symbol for this purpose since 1557 and Xylander had employed vertical parallel lines since 1575. On the other hand, Vieta was well skilled in most modern artifices, aiming at a simplification of equations by the substitution of new quantities having a certain connexion with the primitive unknown quantities. Another of his works, Recensio canonica effectionum geometricarum, bears a stamp not less modern, being What we now call an algebraic geometry,—in other words, a collection of precepts how to construct algebraic expressions with the use of rule and compass only. While these writings were generally intelligible, and therefore of the greatest didactic importance, the principle of homogeneity, first enunciated by Vieta, was so far in advance of his times that most readers seem to have passed it over without adverting to its value. That principle had been made use of by the Greek authors of the classic age; but of later mathematicians only Hero, Diophantus, &c., ventured to regard lines and surfaces as mere numbers that could be joined to give a new number, their sum. It may be that the study of such sums, which he found in the works of Diophantus, prompted him to lay it down as a principle that quantities occurring in an equation ought to be homogeneous, all of them lines, or surfaces, or solids, or supersolids,—an equation between mere numbers being inadmissible. During the three centuries that have elapsed between Vieta’s days and our own several changes of opinion have taken place on this subject, till the principle has at last proved so far victorious that modern mathematicians like to make homogeneous such equations as are not so from the beginning, in order to get values of a symmetrical shape. Vieta himself, of course, did not see so far as that; nevertheless the merit cannot be denied him of having indirectly suggested the thought. Nor are his writings lacking in actual inventions. He conceived methods for the general resolution of equations of the second, third, and fourth degrees different from those of Ferro and Ferrari, with which, however, it is difficult to believe him to have been unacquainted. He devised an approximate numerical solution of equations of the second and third degrees, wherein Leonardo of Pisa must have preceded him, but by a method every vestige of which is completely lost. He knew the connexion existing between the positive roots of an equation (which, by the way, were alone thought of as roots) aud the coefficients of the different powers of the unknown quantity. He found out the formula for deriving the sine of a multiple angle, knowing that of the simple angle with due regard to the periodicity of sines. This formula must have been known to Vieta in 1593. . In that year Adriaan van Roomen gave out as a problem to all mathematicians an equation of the 45th degree, which, being recognized by Vieta as depending on the equation between sin φ and sin was 4b resolved by him at once, all the twenty-three positive roots of which the said equation was capable being given at the same time. Such was the first encounter of the two scholars. A second took place when Vieta pointed to Apollonius’s problem of taction as not yet being mastered, and Adriaan van Roomen gave a solution by the hyperbola. Vieta, however, did not accept it, as there existed a solution by means of the rale and the compass only, which he published himself in his Apollonius Gallus (1600). In this paper Vieta made use of the centre of similitude of two circles. Lastly, he gave an infinite product for the number π (see Squaring the Circle, vol. xxii. p. 434).

Vieta’s collected works were issued under the title of opera Mathematica by F. van Schooten at Leyden in 1646. (Μ. CA.)