Kastner, Abraham Gothelf

, an eminent mathematician, and professor of mathematics at Gottingen, was born at Leipsic, Sept. 27, 1719. He had part of his | education at home, under his father and uncle, both of whom were lecturers on jurisprudence, and men of general literature. In 1731 he attended the philosophical lectures of the celebrated Winkler, and next year studied mathematics under G. F. Richter, and afterwards under Hausen; but practical astronomy being at that period very little encouraged at Leipsic, he laboured for some years under great difficulties for want of instruments, and does not appear to have made any great progress until, in 1742, he formed an acquaintance with J. C. Baumann, and by degrees acquired such helps as enabled him to make several observations. Heinsius was his first preceptor in algebra; and, in 1756, he was invited to Gottingen, to be professor of mathematics and moral philosophy, and afterwards became secretary of the royal society, and had the care of the observatory on the resignation of Lowitz in 1763; but, notwithstanding his talents in astronomy and geography, the services he rendered to the mathematical sciences in general are more likely to convey his name to posterity. He exerted himself with the most celebrated geometers of Germany, Segner, and Karsten, to restore to geometry its ancient rights, and to introduce more precision and accuracy of demonstration into the whole of mathematical analysis. The doctrine of binomials that of the higher equations the laws of the equilibrium of two forces on the lever, and their composition are some of the most important points in the doctrine of mathematical analysis and mathematics, which Kastner illustrated and explained in such a manner as to excel all his predecessors. Germany is in particular indebted to him for his classical works on every part of the pure and practical mathematics. They unite that solidity peculiar to the old Grecian geometry with great brevity and clearness, and a fund of erudition, by which Kastner has greatly contributed to promote the study and knowledge of the mathematics. Kiistner’s talents, however, were not confined to mathematics: his poetical and humorous works, as well as his epigrams, are a proof of the extent of his genius; especially as these talents seldom fall to the lot of a mathematician. How Kastner acquired a taste for these pursuits, we are told by himself in one of his letters. In the early part of his life he resided at Leipsic, among friends who were neither mathematicians nor acquainted with the sciences; he then, as he tells us, contracted “the bad habit of laughing at others;”' | but he used always to say, Hanc veniam damns petimusque vicissim.

Kastner died at Gottingen, June 20, 1800. Besides works on the pure and practical mathematics, we are indebted to Kastner for a history of the mathematics, from the revival of literature to the end of the eighteenth century. Vol. I. contains arithmetic, algebra, the elements of geometry, trigonometry, and practical geometry, and was published at Gottingen, 1796, and an appendix in 1797. Vol. II. which appeared at the same time, embraces perspective geometrical analysis, and the higher geometry, mechanics, optics, and astronomy. ¹