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• W4236036853 abstract "I. G. Spasskii, observing that the counting board appeared in Rus' at the end of the 16th century, called attention to reports dated from the end of the 16th and first half of the 17th century of the practice in Rus' of calculating with two types of fruit pits carried in a bag [1, pp. 300, 301]. It was then hypothesized that the precursor of the counting board in Rus' was calculations using these fruit pits placed according to rules analogous to the rules of the counting board, but on any suitable, relatively even surface [1, pp. 283, 301, 302, 372; 2, pp. 47, 48]. The ancient abacus, i.e., an abacus without a frame (table) and rods (notches) has existed since ancient times in different countries of the world. Common to most of these types of abacus is the use of two types of counting elements (stones, buttons, etc.), one type to designate units and another to designate fives, for all the digits in the decimal system of calculation. The ancient Greek abacus was a board separated into sections by parallel vertical lines between which the counting elements (pebbles) were arranged. On the abacus there were three groups of lines corresponding to the three types of ancient Greek monetary units, halkas, drachmas, and talents, and the value of the standard counting element was determined in accord with the lines between which it was situated. If we look at that section of the abacus on which the drachmas were placed, we find that the parallel vertical lines separated successively the digits (units, tens, hundreds, etc.) as well as semi-digits (units and fives) from one another in each row. The abacus was placed in front of the person doing the calculating, and calculation was done from right to left (Figure 1, 1***). In the medieval Western European calculating on lines, the unit buttons were placed on horizontal lines and the five buttons were placed between the lines. The abacus was placed perpendicularly and calculations done from bottom to top (Figure 1, 2). In both the ancient Greek abacus and in counting on lines, the number of unit elements did not exceed four, while the number of five elements did not exceed one. These two types of abacus were akin, since counting on lines is essentially the ancient Greek abacus turned 90 degrees, where the feature that obstructed the transformation of the ancient abacus into a counting board remained unchanged; this feature was the identical spatial alignment of neighboring rows (units and tens, tens and hundreds), and of neighboring semi-digits (units and fives) in each row. For this reason, the counting board did not emerge in ancient Greece and medieval Western Europe. Although it is possible to imagine counting boards with wires on which four and one stone are arranged in turn, there was evidently a psychological obstacle to the transformation of such an abacus into a counting board, whereas a similar obstacle did not exist in the case of an abacus in which the unit elements and the five elements were located on the same line. I. G. Spasskii demonstrates that, despite the description of counting on lines in Russian medieval textbooks, counting on lines was never used in Rus': counting buttons, discovered by archaeologists in stores of valuables, were used as money or as decoration; the descriptive term counting on lines is a translation from a foreign textbook and could be used for calculating on an abacus of any structure [1, pp. 298-300, 302, 372; 3, pp. 12-15]." @default.
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• W4236036853 date "1986-07-01" @default.
• W4236036853 modified "2023-09-30" @default.
• W4236036853 title "New Evidence of the Existence of an Ancient Russian Abacus" @default.
• W4236036853 doi "https://doi.org/10.2753/rss1061-1428270214" @default.
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