Proof of the theorem that a surface area of a ball is smaller than of any other body of the same volume, by Hermann Schwarz

We present English translation of the classical article of Hermann Amadeus Schwarz (1843–1921) “Proof of the theorem that a surface area of a ball is smaller than of any other body of the same volume” which was published in 1884, in Proceedings of the K"onigliche Gesellschaft der Wissenschaften and the Georg-Augusts-Universit"at, G"ottingen. We preserved the author notations throughout the text and tried to follow his grammar construction of the sentences.