The author and engineer Joh. Eugen Mayer describes in this volume logarithmic slide rules, numerical tables, and calculating machines. The first documented calculating machine was briefly described in a letter by Wilhelm Schickard to Johannes Kepler in 1623. The machine consisted of an addition and subtraction mechanism, as well as a device for multiplication and division similar to Napier's calculating rods. In 1820, the Frenchman Charles Xavier Thomas (1785-1870) received a French patent for his calculating machine design. After further attempts, he began the world's first mass production of calculating machines around 1850. From 1820 to 1878, approximately 1500 devices were produced. The calculating machines were named Arithmomètre and operated based on the principle of stepped rollers with a movable carriage. They functioned reliably.