Vincenzo Viviam

Vincenzo Viviam, an Italian mathematician, born in Florence, April 5, 1622, died there, Sept. 22, 1703. He was a pupil of Galileo, then old, blind, and under the ban of the inquisition; and for three years he and Torricelli nursed him, until his death (Jan. 8, 1642). Subsequently he continued to study under the latter. He was admitted to the principal Florentine academies. From 1699 he was a member of the French academy and in the enjoyment of a considerable pension from Louis XIV., which he appropriated to a building in commemoration of Galileo; and in all his works he added to his name "pupil of Galileo." He published numerous mathematical works, but is best known by his restoration of the treatise of Aristaeus, De Locis Solidis, and of the fifth book of Apollonius of Perga on the conic sections; the latter was entitled Divinatio in quintum Conicorum Apollonii Pergoei (1659), and the former Divinatio in Aristceum (1701).


Vindelicia, a province of the Roman empire, bounded N. by the Danube, which separated it from Germany; E. by the CEnus (now Inn), which separated it from Noricum; S. by Rhaetia, of which it originally formed a part; and W. by the territory of the Helvetii. It comprised parts of the modern countries of Baden, Würtemberg, Bavaria, Tyrol, and Switzerland. The Vindelici, a Celtic people, formed the principal part of the inhabitants. Vindelicia was conquered by Tiberius in the reign of Augustus.

Vindhya Mountains

Vindhya Mountains, a range extending across the peninsula of India, and connecting through the Satpoora mountains with the N. extremity of the Western Ghauts. They extend from the vicinity of the W. coast, about lat. 22° N., in an E. N. E. direction to the valley of the Ganges in about lat. 25° N., and form the N. boundary of the valley of the Nerbudda, which flows close to their base. The name Vindhya is commonly applied only to the western portion of the chain, its continuations down the Sone valley toward the Ganges being chiefly known as the Kaimur mountains. The maximum altitude is about 2,500 ft. The geological formation is granite and sandstone underlying trap rock.


See Vienna.


See Grape.


See Northmen.


See Violin.

Viola (Ger. Bratsch Alto; Eng. Tenor Viol)

Viola (Ger. Bratsch Alto; Eng. Tenor Viol), an instrument of the violin family, having the appearance of a very large violin. It has four strings, of which two are simple gut and two are wound with wire. These strings, tuned in fifths, are A, D, G, C. It stands an octave above the violoncello, and is chiefly used for the middle part in concerted instrumental music. (See Violin).


Violoncello, an instrument of the violin family, with four strings tuned in fifths, A, D, G, C, the last two of which are wound with wire. It is held between the legs of the performer, and has taken the place of the old viol da gamba. It is a bass instrument, the C string giving that note on the second line below the bass clef; but its tone is the noblest and most touching of all the instruments of the violin family. (See Violin).