COTES, Roger (1682-1716), an English mathematician and philosopher, born at Burbage, Leicestershire, of which place his father was rector. When only twenty-four years of age he was appointed Plumian professor of astronomy and experimental philosophy in the university of Cambridge. He took orders in 1713; and the same year, at the request of Dr Bentley, he published the second edition of Newton’s Principia with an original preface. He died June 5, 1716, at the age of thirty-three, leaving unfinished a series of elaborate researches on optics, in reference to which Newton observed, “If Mr Cotes had lived, we should have known something.” With regard to pure mathematics, the principal discovery of Cotes consists in a theorem which still bears his name, and which furnishes the means of integrating by logarithms and arcs of the circle the rational fractions whose denominator is a binomial. His papers were collected and published by his successor Dr Robert Smith.

CÔTES-DU-NORD, a maritime department of the north-west of France, formed from the northern part of the province of Brittany, is bounded on the N. by the English Channel, on the E. by the department of Ille-et-Vilaine, on the S. by Morbihan, and on the W. by Finistère, and is situated between 48° 3' and 48° 57' N. lat. To the north the country is flat, but to the south it is rugged and undulating. A chain of granitic hills, the Monts du Menez, runs east to west through the department, dividing it into two unequal parts, of which the southern is the smaller....

CÖTE DOR, a department in the east of France, formed of the northern region of the old province of Burgundy. It is bounded N. by the department of Aube, N.E. by Haute· Marne, E. by Haute-Saône and Jura, S. by Saône-et-Loire, and W. by Nièvre and Yonne, and lies between 46° 55’ and 48’ 2' N. lat. The surface is mostly rugged. A chain of hills runs from north-east to south-west through the centre of the department, separating the basin of the Seine from that of the Saône, and forming the connecting-link between the Cévennes and the Vosges mountains. Extending southwards from Dijon is a portion of this range which, on account of the excellence of its vineyards, bears the name Côte d’Or, whence that of the department. The rivers are numerous but small, the only one navigable being the Saône. The Burgundy Canal, connecting the Rivers Saône and Yonne, traverses the department from south-east to north-west. The soil is generally stony, but rich. Wine in large quantities, cereals, fruit, beetroot, rape-seed, mustard, honey, flax, hemp, and hops are produced; and good horses, sheep, and cattle are reared. The iron mines furnish large quantities of ore; and anthracite, marble, lithographic stone, gypsum, and potter’s clay are worked. The manufactures include iron, steel, nails, tiles, oil, leather, grindstones, paper, cloth, sugar, beer, and spirits. The department is divided into the arrondissements of Dijon, Beaune, Châtillon, and Semur, containing 36 cantons and 717 communes. The chief town is Dijon. The total area is 3382 square miles, and the population in 1872 was 374,510.