SCHLÖMILCH’S THEOREM
SCHLÖMILCH’S THEOREM In Section 4.3, we provide a modern English-language translation of Schlomilch paper [22]. Since the basis of his argument comes from the Mean Value Theorem for Integrals, which he refers to as the “well-known” theorem, we will provide a few preliminaries in Section 4.2 by introducing and arguing the following three results: (1) Rolle’s Theorem, which will be used to prove (2) the Mean Value Theorem, then extend that to (3) the Mean Value Theorem for Integrals. 4.1 Oscar Schlomilch ¨ Oscar Xavier Schlomilch (13 April 1823 - 7 February 1901) was a German mathematician. ¨ He studied mathematics and physics primarily in Jena, Berlin and Vienna. Most of his work was strongly influenced by Johann Peter Gustav Lejeune Dirichlet (1805-1859). In 1844, Schlomilch received his doctorate from Friedrich-Schiller-Universität. From 1851 to 1874, he was a professor at Dresden teaching Higher Mathematics and Analytic ...