Salamin table
The Salamis Tablet is considered the oldest surviving abacus on the principle of the abacus and was in 1846 during excavations on the island of Salamis (in the Saronic Gulf, two kilometers from the coast of Piraeus , the port of Athens discovered). The table is made of white marble and is around 1.49 m long, 0.75 m wide and 4.5 cm high. It is dated to around 300 BC. And is kept in the National Museum in Athens (Epigraphical Museum, lobby room 2).
Carved on the board are arithmetic rubrics, Attic numerals for job designation and coin symbols. In one part there are five parallel lines, in the other part eleven parallel lines, which are bisected by perpendicular lines. The intersections on the 3rd, 6th, 9th line are marked with a cross. Loose calculation stones could be moved back and forth on this calculation board . Moritz Cantor explained how the blackboard was classified in the history of mathematics .
description
Kubitschek published the following description of the table by Adolf Wilhelm (spelling of the quote adapted):
“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, shows a smooth but not on top Completely flat surface, but rather a little sunk towards the center, which tapers a little towards the outer edge and does not merge into sharp edges, but rather in a slight round to the smooth side surface, which in turn overlaps similarly into the lower surface. On the reverse side, the slab is so thinned that it is only 4.5 cm thick at the weakest point ...
The underside is also smoothed, but not even, and is damaged by holes created by a vein of bad marble to have. This also appears on the upper side in stripes, cracks and holes and is responsible for the wavy nature of the surfaces due to the need for processing.
It has not yet been noticed that on the last of the eleven horizontal lines, calculated from the edge, there is a curve in the middle (...), and also (only, probably because of damage to the stone, asymmetrical) a second curve on the innermost of the five lines the opposite side (...); because I think I can only see five of them: the line underneath, which could be seen as the sixth (from the inside), goes wrong and is probably, like some other random lines, a random ingredient and not entered in advance.
I also noticed that 4.8 cm from the innermost of the five lines, the marble becomes lighter and the lighter field appears to be bounded by a line in relation to the darker one, which, however, does not run completely parallel to the rest of the system of lines; just as clearly one sees the field on the opposite side up to a distance of ... cm from the innermost line dark and only then lighter, also limited by a not completely parallel line; maybe as a result of the original painting. The five lines are shorter (0.22) than the eleven on the opposite side (0.38); they are also entered in smaller spaces and do not end in clear points at the same time. "
functionality
On the board are shown Greek numbers . Number systems for written use emerged as early as the Ionic period, which became necessary because of the expansion of commercial activity. Two different number notations were developed, the older Attic or Herodian number system and the younger Milesian system, which was later superseded by the Indo-Arabic system.
The two number systems differ in their use: the Attic was mainly used in commercial life to fix money and goods information and to designate the columns on the abacus. The Attic number system was extremely unsuitable for written arithmetic. The milesic number system, in which letters of the alphabet were also assigned numbers, was suitable for scientific mathematics. For example, Archimedes and Diophant of Alexandria calculated milesian.
The Salaminische Tafel has horizontal lines on which the counting stones were pushed back and forth. The job titles were given on one side with Greek numerals from 1 to 1000, on the other side there were coin symbols (from 1/8 obol to 6000 drachmas ). In Greece the calculating stones (pebbles) were pushed from left to right. The Greek writer Herodotus (485–425 BC) reports in his travelogues about Egypt that the Egyptians, contrary to Greek custom, moved their pebbles on the abacus from right to left. This was the basis for all other variants of the abacus.
Steve Stephenson is of the opinion that the Salaminische Tafel is a monument that documents the great progress in the arithmetic operations that this tool makes possible for people. These calculations related to mathematics , astronomy , science , engineering , architecture , state and tax accounting, and commercial accounting . He justifies this thesis by stating that the marble tablet is too big as a tool and that no other tablets have been found. Stephenson classifies the calculation table as an ancient scientific calculator ("Ancient Scientific Calculator") and has created a modern abacus based on the system of the Salamin table.
Quote
Athenaios gives in III. Book of his Deipnosophistai (old Gr. Δειπνοσοφισταί; dt. Banquet of the Scholars) the following example for the use of an abacus:
The chef does the accounting
In the play Der Augenkranke , a guest is asked to contribute to a community meal:
- Guest: If you don't give me an account of everything individually, you won't get a red penny from me!
- Koch: That's right! Bring abacus and stones.
- Guest: Come on!
- Koch: It's five groschen for raw salt fish.
- Guest: Next.
- Cook: Seven groschen for mussels.
- Guest: That's good. Further.
- Cook: Sea urchins an obolos.
- Guest: That's right.
- Koch: Then came the radish, which you praised.
- Guest: Yes, it was good too.
- Koch: I paid two obols.
- Guest: What the praise for?
- Koch: Fish cubes: three obols.
- Guest: Free! And the endives cost nothing?
- Koch: You don't know the market, my dear friend. The worms ruined all the greens.
- Guest: And why do you calculate the salt fish twice?
- Koch: It's up to the dealer, go and ask him yourself. The eel makes ten obols.
- Guest: Not too much. And further.
- Cook: I bought the fried fish for a drachma.
- Guest: Like a fever. Once it sinks then it rises again.
- Koch: With the wine. When you were already drunk, I got three jugs, each for ten obols.
Individual evidence
- ↑ Description Epigraphical Museum, 1 Tositsa Str., Τ.Κ. 10682, Athens (Prefecture of Attiki)
- ^ Moritz Cantor: Lectures on the history of mathematics. Volume 1, Leipzig 1907, pp. 133, 134., 319., 440.
- ^ Wilhelm Kubitschek: XII. The Salaminische calculation board. In: Numismatic Journal. Volume 31, Vienna 1899, p. 394 ff.
- ↑ Hans Wussing, HW. Alten, Heiko Wesemüller-Kock: 6000 years of mathematics: a cultural-historical journey through time. 2008, ISBN 978-3-540-77189-0 , p. 150 ff.
- ^ Karl Menninger, Paul Broneer: Number Words and Number Symbols. 1992, ISBN 0-486-27096-3 , p. 300 ff. - Description and calculation examples in English
- ↑ Abaki of the Peoples ( Memento from February 22, 2010 in the Internet Archive )
- ^ A b Stephen K. Stephenson: Ancient Scientific Calculators. - Sample calculations in English (PDF; 126 kB)
- ^ The Stephenson Abacus ™, Site Map
- ↑ Ursula and Kurt Treu (selection and translation): The learned meal. Collection Dieterich, Leipzig 1985, ISBN 3-7350-0064-9 , p. 47f.
Web links
Wikisource: Abǎkus - Article of the 4th edition of Meyers Konversations-Lexikon
