19. Operating Instructions

Chapter “Operating Instructions” gives detailed step-by-step instructions for the most important analog and digital calculating devices and mechanical calculating machines, making it possible to operate historical mathematical aids once again. In many cases, no operating instructions have been preserved. Failure to use such instruments can result in damage. The operating instructions range from heavy stationary desktop machines to lightweight portable pocket calculators, from the abacus (bead frame) through Napier’s bones and slide rules (linear, circular, and cylindrical slide rules), sectors, disc adding machines, and slide bar adders to keyboard adding machines (Schwilgué single-digit adding machine), stepped drum machines (Thomas arithmometer, Madas, Curta), pinwheel machines (Odhner, Brunsviga), and direct multiplying machines (The Millionaire). According to the model, numerical input is by wheels, stylus, setting levers, or keys. The use of the Chinese, Japanese, and Russian bead frames differs only slightly. This is also true for the children’s counting frame. Details for the use of the Roman hand abacus are given in Sect. 3.​3. The numerical notation with the calculating table is described in Sect. 3.​4. Section 4.​6 explains the pantograph. Instructions for the use of proportional compasses are given in Sect. 4.​8. All instructions are derived from trying out. These make very clear how arduous computation was for thousands of years.