SCHWEIKART, FERDINAND KARL

(b. Erbach, Germany, 28 February 1780; d. Königsberg, Germany [now Kaliningrad, R.S.F.S.R.], 17 August 1859)

mathematics.

Schweikart studied law at the University of Marburg from 1796 to 1798 and received his doctorate in law from Jena in the latter year. After practicing at Erbach from 1800 to 1803, he worked as a private tutor until 1809; his pupils included the prince of Hohenlohe-Ingelfingen. In 1809 Schweikart became extraordinary professor of law at Königsberg, where he also earned a doctorate in philosophy.

Schweikart published extensively in his principl field of endeavor, including a work on the relationship of natural and positive law (1801). Early in his life he also became interested in mathematics, and he holds an important place in the prehistory of non-Euclidean geometry. While a student at Marburg, the lectures of J,K.F. Hauff had stimulated him to consider the problem of parallel lines, which provided the subject of his only publication in mathematics (1807). His approach was still completely Euclidean; but later he arrived at the beginnings of a hyperbolic geometry, which he called astral geometry. He made this advance independently of Guass, Bolyai, Labachevsky, as is proved by the correspondence cited by Engel and Stäckel in Die Theorie der Parallellinien von Euklid bis Guass The astronomer Christian Gerling, a student of Gauss, wrote in a letter to Wolfgang Bolyai, the father of János Bolyai, that in 1819 Schweikart had reported on the basis elements his “astral geometry” to colleagues at Marburg. Schweikart also wrote on this topic to his nephew Taurinus in Cologne. Stimulated by his uncle’s work, Taurinus had virtually discovered hyperbolic trigonometry; but unlike his uncle, he still believed in the sole validity of Euclidean geometry.

The three chief founders of hyperbolic geometry surpassed Schweikart only because of the thoroughness with which they examined specific topics of this subject. The demands of his legal career undoubtedly prevented him from finding sufficient time to undertake similarly extensive research.

BIBLIOGRAPHY

Schweikart’s only mathematical work is Die Theorie der Parallellinien, nebst einem Vorschlag ihrer Verbannung aus der Geometrie (Jena-Leipzig, 1807).

A secondary source is Friedrich Engel and Paul Stäckel. Die Theorie der Parallellinien von Euklid bis Gauss (Leipzig, 1895), 243–252.

Werner Burau