| The abacus - the first known calculator, was probably invented by the Babylonians as an aid to simple arithmetic around this time period. This laid the foundations for positional notation and later computing developments.
| Ramon Llull invented the Lullian Circle: a notional machine for calculating answers to philosophical questions (in this case, to do with Christianity) via logical combinatorics. This idea was taken up by Leibniz centuries later, and is thus one of the founding elements in computing and information science
| Kerala school of astronomy and mathematics in South India invented the floating point number system.
| Leonardo da Vinci produced drawings of a device consisting of interlocking cog wheels which can be interpreted as a mechanical calculator capable of addition and subtraction. A working model inspired by this plan was built in 1968 but it remains controversial whether Leonardo really had a calculator in mind. Da Vinci also made plans for a mechanical man: an early design for a robot.
| Scotsman John Napier reinvented a form of logarithms and an ingenious system of movable rods (referred to as Napier's Rods or Napier's bones). These rods were based on the lattice or gelosia multiplication algorithm and allowed the operator to multiply, divide and calculate square and cube roots by moving the rods around and placing them in specially constructed boards.
| French polymath Blaise Pascal invented the mechanical calculator. Called machine arithmétique, Pascal's calculator and eventually Pascaline, its public introduction in 1645 started the development of mechanical calculators first in Europe and then in the rest of the world. It was the first machine to have a controlled carry mechanism. Pascal built 50 prototypes before releasing his first machine (eventually twenty machines were built). The Pascaline inspired the works of Gottfried Leibniz (1671), Thomas de Colmar (1820) and Dorr E. Felt (1887).
| Jonathan Swift described (satirically) a machine ("engine") in his Gulliver's Travels. The "engine" consisted of a wooden frame with wooden blocks containing parts of speech. When the engine's 40 levers are simultaneously turned, the machine displayed grammatical sentence fragments.
| J. H. Müller, an engineer in the Hessian army, first conceived of the idea of a difference engine.
| Joseph-Marie Jacquard developed an automatic loom controlled by punched cards.
| Charles Xavier Thomas de Colmar invented the 'Arithmometer' which after thirty more years of development became, in 1851, the first mass-produced mechanical calculator. An operator could perform long multiplications and divisions quickly and effectively by using a movable accumulator for the result. This machine was based on the earlier works of Pascal and Leibniz.
| Charles Babbage designed his first mechanical computer, the first prototype of the decimal difference engine for tabulating polynomials.
| Babbage and Joseph Clement produced a prototype segment of his difference engine, which operated on 6-digit numbers and second-order differences (i.e., it could tabulate quadratic polynomials). The complete engine, which would have been room-sized, was planned to operate both on sixth-order differences with numbers of about 20 digits, and on third-order differences with numbers of 30 digits. Each addition would have been done in two phases, the second one taking care of any carries generated in the first. The output digits were to be punched into a soft metal plate, from which a printing plate might have been made. But there were various difficulties, and no more than this prototype piece was ever finished.
| Babbage conceived, and began to design, his decimal 'Analytical Engine'. A program for it was to be stored on read-only memory, in the form of punched cards. Babbage continued to work on the design for years,...
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