MÖBIUS, August Ferdinand (1790-1868), astronomer and mathematician, was born at Schulpforta, November 17, 1790. At Leipsic, Göttingen, and Halle he studied for four years, ultimately devoting himself to mathematics and astronomy. In 1815 he settled at Leipsic as privatdocent, and the next year became extraordinary professor of astronomy in connexion with the university. Later he was chosen director of the university observatory, which was erected (1818-21) under his superintendence. In 1844 he was elected ordinary professor of higher mechanics and astronomy, a position which he held till his death, September 26, 1868. His doctor’s dissertation, De computandis occultationibus fixarum per planetas (Leipsic, 1815), established his reputation as a theoretical astronomer. Die Hauptsätze der Astronomie (1836), Die Elemente der Mechanik des Himmels (1843), may be noted amongst his other purely astronomical publications. Of more general interest, however, are his labours in pure mathematics, which appear for the most part in Crelle’s Journal from 1828 to 1858. These papers are chiefly geometrical, many of them being developments and applications of the methods laid down in his great work, Der Bar y centrische Calcul (Leipsic, 1827), which, as the name implies, is based upon the properties of the mean point or centre of mass. Any point in a plane (or in space) can be represented as the mean point of three (or four) fixed points by giving to these proper weights or coefficients,— an obvious principle which leads in the hands of Möbius to what no doubt is the chief novel feature of the work, a system of homogeneous coordinates. Besides this, however, the work abounds in suggestions and foreshadowings of some of the most striking discoveries in more recent times—such, ...