Salamis Tablet

The salami niche board is considered the oldest surviving abacus on the principle of the abacus and was ( in the Saronic Gulf, two kilometers from the coast of Piraeus, the port of Athens) discovered in 1846 during excavations on the island of Salamis. The panel is made of white marble and is about 1.49 m long, 0.75 m wide and 4.5 cm high. It is dated approximately to the period 300 BC and is in the National Museum in Athens ( Epigraphical Museum, Lobby room 2 ) was preserved.

Engraved on the panel are calculating headings, Attic numerals for job title and Münzsymbole. In one part there are five parallel lines, in the other part eleven parallel lines, which are bisected by lines perpendicular thereto. The points of intersection of the 3rd, 6th, 9th line are indicated by a cross. On this Rechentafel you could loose counting stones back and forth move. Moritz Cantor explained the position of the panel in the history of mathematics.

Description

Kubitschek published the following description of the board of Adolf Wilhelm ( spelling citation adjusted):

" The Abacus of Salamis, a 0.754 [m ] wide, 1.49 [m ] high, 0.045 [m ] to 0.075 [m ] thick slab of white marble, now broken into two pieces, pointing to the top of a smooth, but not completely flat, but towards the middle to a little sunken area that runs up against the outer edge to a little and does not go into sharp edges, but in a light round the smooth side face similar overlaps in part, the lower surface. On the back of the dilution of the plate is so strong that the thickness at the thinnest point only 4.5 cm ... The underside is smooth, but not flat, and is damaged by holes that have set in the aftermath of a bad vein marble. This also occurs on the top in stripes, cracks and holes to light and has inflicted by the necessity of processing the wave nature of the surfaces. It is still not noticed that, calculated on the last of the eleven horizontal lines from the edge, is seated in the middle of a curve ( ... ), and also (only, probably due to damage of the stone, unbalanced) a second curve on the innermost of five lines the opposite side ( ...); because I believe that to recognize their only five: the line below them, which could be considered as a sixth ( from the inside ), goes wrong and is probably equal to a few other random lines random ingredient and not registered in advance. It is my further noticed that 4.8 cm away from the innermost of the five lines of the marble is lighter and the lighter field against the darker as by a line appears limited, however the rest of line system does not run completely parallel; just as clearly can be seen on the opposite side of the field up to a distance of ... cm, also bounded by the innermost line dark and brighter then by a not fully parallel line; perhaps as a result of the original painting. The five lines are shorter (0.22 ) as the other side of the eleven (0.38 ); also they are entered in lower spaces and not equal to the latter terminate in sharp points. "

Operation

Shown on the panel are Greek numbers. Even in the ionic period number systems have emerged for the written use that were necessary because of the expanding commercial activity. Two different number of quotations have been developed, the older Attic or Herodian number system and the younger, Milesian system, which was later replaced by the Indo- Arabic system.

The two number systems differ in their use: the Attic served mainly the commercial life for the fixation of money and commodities information, and the designation of the column on the abacus. For written calculations the Attic numeral system was not suitable. The Milesian number system, in which you also then assigned letters of the alphabet numbers was suitable for scientific mathematics. For example, Archimedes calculated and Diophantus of Alexandria milesisch.

The salami niche panel has horizontal lines on which the counting stones were pushed back and forth. The job titles were printed on one side with Greek numerals from 1 to 1000, on the other hand were Münzsymbole ( 1/8 Obol to 6000 drachmas ) recorded. In Greece, the counting stones ( pebbles ) were pushed from left to right. The Greek writer Herodotus ( 485-425 BC ) in his travelogues about Egypt, that the Egyptians, in contrast to the Greek custom of moving their pebbles on the computer boards from right to left. This was the basis for all other variants of the abacus.

Steve Stephenson believes that the salami niche board is a monument, which documents the great progress in terms of the arithmetic operations, which this tool allows people. These calculations included the mathematics, astronomy, science, engineering, architecture, the Heads of State and tax accounting and bookkeeping African kaufman. He justifies this claim with the fact that the marble tablet is too big as a tool, and you would have no other boards found. Stephenson classifies the Abacus as ancient, scientific calculator ( "Ancient Scientific Calculator " ) and has created a modern abacus, which is constructed on the system of salami niche panel.

Quote

Athenaeus are in III. Book of his Deipnosophistai ( altgr. Δειπνοσοφισταί; German Banquet of scholars) in the following example for the use of an abacus:

The chef settles

In the play The eyes Ill be fee is required to be a communal meal from a guest: