The town is commonly supposed to have given its name to the four-wheeled carriage, with an adjustable divided top for use either open or closed, known as a “landau” (Ger. Landauer). But this derivation is doubtful, the origin of the name being also ascribed to that of an English carriage-builder, Landow, who introduced this form of equipage.
See E. Heuser, Die Belagerungen von Landau in den Jahren 1702 und 1703 (Landau, 1894); Lehmann, Geschichte der ehemaligen freien Reichsstadt Landau (1851); and Jost, Interessante Daten aus der 600 jährigen Geschichte der Stadt Landau (Landau, 1879).
LANDECK, a town and spa in the Prussian province of Silesia, on the Biele, 73 m. by rail S. of Breslau and close to the Austrian frontier. Pop. (1905) 3,481. It is situated at an altitude of 1400 ft. It has manufactures of gloves. Landeck is visited by nearly 10,000 people annually on account of its warm sulphur baths, which have been known since the 13th century. In the neighbourhood are the ruins of the castle of Karpenstein.
See Langner, Bad Landeck (Glatz, 1872); Schütze, Die Thermen von Landeck (Berlin, 1895); Wehse, Bad Landeck (Breslau, 1886); Joseph, Die Thermen von Landeck (Berlin, 1887), and Patschovsky, Führer durch Bad Landeck und Umgebung (Schweidnitz, 1902).
LANDEN, JOHN (1719-1790), English mathematician, was born at Peakirk near Peterborough in Northamptonshire on the 23rd of January 1719, and died on the 15th of January 1790 at Milton in the same county. He lived a very retired life, and saw little or nothing of society; when he did mingle in it, his dogmatism and pugnacity caused him to be generally shunned. In 1762 he was appointed agent to the Earl Fitzwilliam, and held that office to within two years of his death. He was first known as a mathematician by his essays in the Ladies’ Diary for 1744. In 1766 he was elected a fellow of the Royal Society. He was well acquainted with the works of the mathematicians of his own time, and has been called the “English d’Alembert.” In his Discourse on the “Residual Analysis,” he proposes to avoid the metaphysical difficulties of the method of fluxions by a purely algebraical method. The idea may be compared with that of Joseph Louis Lagrange’s Calcul des Fonctions. His memoir (1775) on the rotatory motion of a body contains (as the author was aware) conclusions at variance with those arrived at by Jean le Rond, d’Alembert and Leonhard Euler in their researches on the same subject. He reproduces and further develops and defends his own views in his Mathematical Memoirs, and in his paper in the Philosophical Transactions for 1785. But Landen’s capital discovery is that of the theorem known by his name (obtained in its complete form in the memoir of 1775, and reproduced in the first volume of the Mathematical Memoirs) for the expression of the arc of an hyperbola in terms of two elliptic arcs. His researches on elliptic functions are of considerable elegance, but their great merit lies in the stimulating effect which they had on later mathematicians. He also showed that the roots of a cubic equation can be derived by means of the infinitesimal calculus.
The list of his writings is as follows:—Ladies’ Diary, various communications (1744-1760); papers in the Phil. Trans. (1754, 1760, 1768, 1771, 1775, 1777, 1785); Mathematical Lucubrations (1755); A Discourse concerning the Residual Analysis (1758); The Residual Analysis, book i. (1764); Animadversions on Dr Stewart’s Method of computing the Sun’s Distance from the Earth (1771); Mathematical Memoirs (1780, 1789).