Add

Books containing precalculated results, known as “ready reckoners”, appeared after the invention of the printing press and were widely used from the sixteenth until well into the twentieth century. They included all kinds of precalculated values: sums, subtractions, multiplications and divisions – all organised in double-entry tables – as well as tables of percentages, interest figures, and special calculations for particular guilds or tasks.

During this period, some of the first devices invented with the aim of mechanising the most basic arithmetic operations (at least partially) were also popularised. Addition, the most basic operation and the basis of all the others, was the first challenge to which the early inventors and builders of devices, machines or engines – the first engineers – applied their learning and ingenuity.

Among these early devices was the Addiator, also called the Troncet Type after its inventor. This popular portable device came in both pocket and desktop models for all kinds of business uses (II-2), and calculators of this kind were even given out as promotional gifts (II-1). When the sum of two digits was greater than ten, users had to perform the “carry one” operation themselves with a simple stylus movement. Other adding machines were operating using sliders or keys (II-3). But it was the mathematician and philosopher Blaise Pascal who in 1642 came up with a mechanical solution to the problem of carrying one, creating a device that became known as the Pascaline. The design of this calculator was the basis of most mechanical adding machines until well into the twentieth century. All devices of this kind were operated using a stylus inserted at points where digits were marked on their wheels (II-4).

Years earlier, another great mathematician, John Napier – best known as the developer of logarithms (a discovery he published in 1614), one of the conceptual tools that most dramatically revolutionised scientific calculation – also invented a small instrument for performing basic calculations, known as “Napier’s bones” (II-5).