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The beginning of the calculus

The first calculations were carried out with the fingers, in Latin "digitus" from which comes the word "digital".

Were later used stones, marking the results on pieces of bone or wood. At this moment the history of calculation begins.

The oldest know calculation tool is the Ishango's bone, found in Africa and dated to 20,000 BC. There are marked groups of numbers that make up a sum, as they do even today the shepherds, and this way of representing the figures remained until recent times. The official use was abolished in England only in 1826!

The Ishango's bone

The marks on the Ishango's bone

The Ishango's bone

The next step was the abacus, a simple tool to organize piles of stones (in Latin "calculi" and hence the term "calculate"), while the numbers were now represented by symbols and recorded on clay tablets. This is a digital calculator. Below you can see the attempt to solve the Pythagorean Theorem on a Babylonian tablet and in Excel, really very similar. The systems created by the use of the fingers are often in base 12 (10 fingers + 2 hands) or its multiples. The Babylonians counted in sexagesimal and trace remains in the division of time and angles.

Plimpton 322   Babylonian tablet in Excel

Babylonian tablet (1800 BC) and the same calculation made in Excel

The abacus, invented around 2500 BC in Mesopotamia, spread everywhere in various forms. The older models had the bottom filled with sand ('Abaq in Sumerian) to keep track of the operations: it was the first silicon memory!

Roman abacus    Modern abacus

Roman abacus and its modern equivalent

Suanpan cinese

Chinese's Suanpan

The abacus is not a real calculator because it merely assist the operator in performing the operations, but allows to add and subtract very quickly. It was abandoned by Europeans in the Middle Ages and only in Russia continued to be used in stores until the collapse of the Soviet Union.

Abacus     Schoty

European abacus and Russian Schoty

There was also the abacus “exchequer” consisting of a board divided into squares on which were moved some small stones, called "jetons". Hence the term "Chancellor of the Exchequer" which designates the English Minister of Finance. His predecessors kept the accounts of the crown thanks to an abacus of this type located in the London's tower.

Exchequer abacus

Exchequer abacus

In the sixteenth century for the development of science was necessary to calculate with big numbers and the old systems were no longer sufficients. Many searched for a solution.
At the end of '500 Galileo was perhaps the first to develop a tool that help to solve mathematical operations. Multiplication, division, roots, calculation of areas and volumes, measuring gauges of guns.
His "Compasso geometrico et militare", based on the proportionality of corresponding sides of two triangles, was very practical for aiming artillery pieces.
Galileo advertised it with modern methods, selling it throughout all Europe, accompanied by a booklet entitled "Le operazioni del Compasso".

Riproduction of the del Galileo's Compass

Reproduction of the Galileo's Compass (@ Museo Galileo - Firenze)

The Galileo's Compass did not carry out complex calculations, only in 1614 with the discovery of logarithms it was possible to print very precise calculation tables. However, logarithms are difficult to use and for all engineering calculations, which require less precision than astronomical ones, they were printed on the analog slide rule.
This instrument does not add and subtract: for accounting calculations were used the first digital mechanical calculators, invented in the second half of the 1600s by Blaise Pascal and Gottfried Leibniz.
The history of the different calculators is told in the specific sections, before continuing let's see the difference between Analog and digital.

Links: Beginning of calculus on Wikipedia
The abacus on Wikipedia
Napier's bones on Wikipedia

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