![]() ![]() It consisted of a rectangular wooden frame with a bar running down its length dividing the abacus into two parts. As the abacus was used in more societies, its form changed, but the principles of computation remained the same.īy 1300 a device resembling the modern abacus was in common use in China. The abacus was called a choreb by the Turks and a stchoty by the Russians. This term spread to Rome where counting boards were called abaci. This may have come from the Semitic word abaq, meaning dust. The Greeks used the word "abax" to denote the surface on which they placed their counting lines. It was first adopted by the merchants in each society because they had to perform many calculations in their daily business activities. The abacus is believed to have spread from Europe along trade routes to the east. The more modern wire and bead abacus began in the Middle East during the early Middle Ages, c. These later counters came to be called jetons from the French verb jeter, meaning "to throw." They were quite common and at one time manufacturing jetons was a major industry in Europe. As soon as five counters appeared on a line or space, they were removed and replaced by one counter on the next higher space or line.Įarly counters were usually pebbles, but by the thirteenth century in Europe, counters resembled coins. Each space between two lines represented numbers having five times the value of the line below the space. ![]() The bottom line was the units place and each subsequent line represented ten times the value of the line below it. It was a table upon which lines were drawn to represent the place value of the counters to be put on the lines. Since negative numbers were not used at the time, smaller numbers would be subtracted from larger ones.īy the thirteenth century a standard form of the counting table was prevalent in Europe. For subtraction, counters would be taken away, with any borrowing done manually. At the end of the operations, the total value of the counters on the table indicated the sum. If there were numbers to be carried, counters were removed from one line and an additional counter was placed on the line to represent the next higher number. Additional counters were placed on appropriate lines to make up subsequent numbers to be added. To add numbers using a counting board or table, counters would be placed on the appropriate lines to denote the first number to be added. No one is certain what it was used for, but it could have been used for addition, subtraction, multiplication, and division. Greek symbols appear along the top and bottom of the tablet. The table is marked with 11 vertical lines, a blank space between them, and horizontal lines crossing the vertical ones. It is now in two pieces, but it was once a very large marble slab, approximately 5 feet by 2 1/2 feet. One of the few counting tables still in existence was found on the Greek island of Salamis. One such calculation was computing the interest due on a loan. –425 b.c.e.) described counting tables that used pebbles and wrote examples of the calculations for which they could be used. In the fifth century b.c.e., the Greek historian Herodotus (c. However, they must have been common because they are often mentioned in wills and inventories. Our modern words "calculate" and "calculus" come from this root word. The pebbles the ancient Romans used for their counting boards were called calculii. Some of the cultures that used these place value devices for computations then recorded the results of these calculations using a number system that did not use place value, such as Roman numerals. Since the value assigned to a counter depended on the line on which it was placed, these early counting devices used a place value system. The parallel lines represented numbers, and pebbles or other counters placed on the lines denoted multiples of that number. In the Western hemisphere, the Mayans, Aztecs, and Incas used kernels of grain as counters. Counting BoardsĪncient cultures such as the Greeks, Babylonians, and Romans marked parallel lines on a table and placed pebbles on the lines for counting. Pencil and paper eventually replaced these early counting boards, but a modern form of the abacus may still be seen in use in parts of Russia and Asia in the twenty-first century. Most early cultures evolved some form of a counting board or abacus to perform calculations. ![]() Early humans counted and performed simple calculations using tools such as their fingers, notches in sticks, knotted strings, and pebbles. ![]()
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