# Calculate

Counting and adding are the simplest operations, but they are the basis of all the other arithmetic operations. You can subtract by adding the additive inverse to a number, multiply using repeated addition, and divide using repeated subtraction. In school, we learn the multiplication table, procedures (or “algorithms”) for adding and subtracting (if you know how to carry), and methods for multiplying and dividing. Sometimes children have even been able to practise using toys designed to make learning fun (III-1).

Historically, what was not so easy was designing and building mechanical instruments that could automate all these arithmetic operations (partially or completely). The earliest such device, which disappeared for centuries, was a calculator constructed at the end of the seventeenth century by the mathematical genius Gottfried Leibniz, who also laid the foundations of modern calculus, or mathematical analysis. Somewhat earlier, in 1673, he had invented the basic mechanism of his calculator, the Leibniz stepped drum, which served as a model for later calculators, including the handcrafted devices of the eighteenth century and the industrially produced calculators of the nineteenth and the first half of the twentieth century.

Following the commercial success of the Arithmometer (invented by the Frenchman Charles X. Thomas de Colmar) and its many successors, in the mid-twentieth century, the limits of mechanical calculation were reached with the astonishing Curta (III-2). The device, which marks the apogee of miniaturisation in pre-electronic calculators, was popularly known as the pepper grinder due to its appearance. After addition had been automated, the names of devices began to call to mind other arithmetic operations (III-3), and their physical forms became more varied (III-4). Eventually, devices that could be used to print operands and results appeared (III-4-3). For individual uses of a more demanding and professional character, some manufacturers developed more robust portable calculators (III-5).