Reckoning tables

Many of the surviving reckoning tables and cloths designate the gaps with symbols of monetary units. On the reckoning table of Dinkelsbühl the Gulden symbol and the older pound symbol are juxtaposed. Both currencies were used in West Franconia during the 15th century. The adjacent gaps are so-called coin-strips: the gaps are for counting coins of unit value while the lines are for counting 5-bundles.

This so-called “counting on lines” worked as follows. A counter placed on one of the lines represents the corresponding value. On a simple reckoning table with no other currency symbols, a counter on the lowest line represents a 1, two counters represent a 2, etc. One line up, one counter represents 10, two represent 20, etc. Thus, the third line records 100 per counter, the fourth 1000 per counter, etc. On the other hand, a counter placed in the gap between two lines represents five times the value of the lower line.

The “counting on lines” method was superseded during the 15th century by the so-called “counting with the pen” method. This is recorded in the early German arithmetic books – the first printed documents apart from religious texts. They usually explain the use of reckoning tables in detail. The more advanced and up-to-date texts also describe the new “counting with the pen” method using Indo-Arabic numbers and compare it with the older method. This evidence indicates that the “counting on lines” method prevailed for at least 1800 years in Europe.

Despite its widespread and successful use, the “counting on lines” method was not really a fast method of calculating. Even so, it had great advantages over calculating with Roman numerals and the result was easily transformed back into Roman numerals.