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The Early Modern period in Europe (roughly from the 15th to the 18th centuries) saw the development of many new calculating tools, as well as the revival and adaptation of several from classical and Middle Eastern culture. For instance the astrolabe, invented in antiquity and developed during the Islamic Golden Age (roughly the 7th to the 15th centuries), was a multi-purpose tool used to measure the heights of buildings and record planetary motions.

Most importantly, after 1400 CE new tools and techniques were developed for commerce, exploration, and natural philosophy G , often serving multiple purposes. From the 17th century, the slide rule, for instance, became the most commonly used calculating device for nearly three hundred years. Beginning as a 'line of numbers' arranged on wood, paper, or brass, rulers attached to one another were used to align points along different scales to perform arithmetic and convert units.

» Learn more about slide rules

The Early Modern period was also the dawn of the age of clockwork and automation, which inspired the design of calculating machines. Such devices came together gradually, and were easier to design than to build.

Scottish mathematician John Napier XR , who discovered the method of logarithms, first devised a set of rods for use in multiplication around 1614. A version of the rods in a box **(Image 1)** provided the template for a gear-based 'carry' mechanism to store values, enabling the first mechanical calculating devices. Blaise Pascal XR completed a number of such machines by the mid-17th century, and was followed by Samuel Morland XR and Gottfried Wilhelm von Leibniz XR .

» Learn more about John Napier

The reduction of arithmetic to repeated mechanical manoeuvres influenced Johann Helfrich von Müller to conceive of a 'difference engine' that could handle more complex calculations. Müller's design, published in 1786, was intended to calculate tables of logarithms, replacing human 'computers' (that is, people employed to manually compute such tables) with an error-free machine.

Forty years later, the English polymath Charles Babbage XR designed and attempted to construct a similar machine, capable of not only calculating but also printing tables. Babbage was not able to complete his machine in his lifetime, but a fragment re-constructed by his son Henry XR in the 1870s proved that the concept could work.

» Read more about the fragment of Babbage's difference engine

The designs of Leibniz, Müller, and Babbage, which automated calculation with gears using 'registers' to store information as it was mechanically read, laid the foundation for the digital computers we have today.

Modern computers were first developed to solve mathematical problems. In the 1930s, German engineer Konrad Zuse built his third automatic mechanical calculator, the Z3, which carried out instructions read in by a program.

During World War II in the United States, John Mauchly and J. Presper Eckert built the Electronic Numerical Integrator and Computer (ENIAC), the fastest machine to date, to calculate firing tables for the military. At Bletchley Park G , British codebreakers and engineers produced the world's first programmable electronic digital computer, Colosus, to aid in the cracking of German ciphers.

The first electronic computers with stored programs were also developed in the UK: the 'Baby' computer at Manchester and the Electronic Delay Storage Automatic Calculator (EDSAC) at Cambridge, which was used by many in the scientific community during the 1950s. Early computers were massive and expensive, so their applications had to be well defined and justified, with entire departments within universities and businesses devoted to them.

» Find out more about the EDSAC computer

It may come as a surprise today, but when pocket electronic calculators were first introduced, manufacturers had to justify their expense to individual consumers by convincing him or her that they were in fact faster and more accurate than the ubiquitous slide rule.

Popular devices, such as the Texas Instruments Datamath series **(Image 2)**, cost $150 upon their introduction, which was expensive for a device that only performed simple arithmetic. As they caught on, however, pocket calculators drove advances in microprocessor technology, making computer chips faster and less expensive. Just as importantly, pocket calculators helped show people how computers could fit easily into their daily routines.

Mikey McGovern

Mikey McGovern, 'A brief history of calculating devices continued', *Explore Whipple Collections*, Whipple Museum of the History of Science, University of Cambridge, [http://www.hps.cam.ac.uk/whipple/explore/calculatingdevices/abriefhistory/abriefhistorycontinued/, accessed 19 July 2019]

http://www.hps.cam.ac.uk/whipple/explore/calculatingdevices/abriefhistory/abriefhistorycontinued/