Raffaello Bombelli

Raffaello Bombelli, a Bolognese mathematician of the 16th century. He published in 1572 a treatise on algebra, in which he first attempted the solution of the "irreducible case " in cubic equations. He gave the geometrical solution depending upon the trisection of an angle, which latter problem, he observed, could be reduced to a cubic equation. He was also the first to attempt the extraction of the cube root in the result of Cardan's formula.

Ragatz

Ragatz, a watering place of Switzerland, in the canton of St. Gall, adjoining Pfäfers, and situated at the junction of several railways and at the mouth of the gorge through which the Tamina flows into the Rhine. It is one of the so-called indifferent thermal springs used for rheumatism and nervous diseases,'and the place is generally overcrowded in summer. It has a fine bathing establishment, with terrace gardens to which water is conveyed from Pfäfers in wooden pipes. It contains an English chapel and a monument of Schelling, who is buried in the Catholic cemetery.

Ragotzky

See RÁkÓczy.

Rains

Rains, a N. E. county of Texas, watered by Lake fork and other tributaries of the Sabine river; area, about 220 sq. m. It has been formed since the census of 1870. The surface is undulating and the soil fertile. There is considerable timber. Indian corn, wheat, cotton, tobacco, sweet potatoes, cattle, etc, are raised. Capital, Emory.

Rain Crow

See Cuckoo.

Rainy Lake

Rainy Lake, a body of water, 50 m. long and of irregular width, on the border of Minnesota and British America, discharging through Rainy or Rainy Lake river (100 m. long) into the lake of the Woods. It receives the river La Seine, the outlet of Lac des Mille Lacs, from the northeast, and from the east the waters of a chain of lakes lying along the international frontier, and having their source in the height of land dividing the streams that flow into Lake Superior from those that flow into Lake Winnipeg. It contains numerous islands. Near its outlet are the falls of Fort Francis, 20 ft. high. The lake and Rainy river below the falls are navigable by steamers.

Rajahmundry, Or Rajamahendri

Rajahmundry, Or Rajamahendri, a town of British India, in the province and 280 m. N. N. E. of the city of Madras, capital of a district formerly of the same name, but now known as the district of Godavery; pop. between 15,000 and 20,000. It is on the N. bank of the Godavery river, here nearly two miles wide. The houses are mainly of mud, but one story high, and roofed with tiles. - The district (pop. in 1872, 1,584,179) includes the rich alluvial delta region of the Godavery, which has been made very prosperous by the existing system of irrigation. The chief products are rice, millet, maize, cotton, indigo, tobacco, and sugar cane. Coringa, at the mouth of the Godavery, is the principal port.

Rakos

See Pesth.

Ralls

Ralls, a N. E. county of Missouri, separated from Illinois by the Mississippi river, and intersected by Salt river; area, about 525 sq. m.; pop. in 1870, 10,510, of whom 1,255 were colored. The surface is broken or undulating, comprising prairie and timber land in nearly equal proportion. The soil is very fertile. The chief productions in 1870 were 158,728 bushels of wheat, 292,534 of Indian corn, 125,677 of oats, 15,740 of potatoes, 32,533 lbs. of wool, 127,793 of butter, and 8,962 tons of hay. There were 4,715 horses, 1,150 mules and asses, 3,668 milch cows, 11,470 sheep, and 16,660 swine. Capital, New London.