The following article is an article written by the knowledgeable Dutch numismatist Bert van BeekEnjoy, Pieter...
BERT VAN BEEK
(c) copyright 1986 by Chicago Coin Club
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INTRODUCTION
Jetons or counters were used as calculation instruments in Europe in the middle ages. According to medieval taste, they were always decorated. These decorations always had a purpose, sometimes religious, but usually related to the user or the principal. In the 16th century, jetons were mostly used to propagate political messages and to glorify the deeds of the ruler. There was such a great need to make propaganda through jetons that they continued to be struck long after jetons ceased to be used as counters. In France and in the Netherlands this new image of the jeton began about the end of the 16th century. The jeton became a small commemorative medal only suitable as a collectors item. The development in Germany was slightly different. In the course of the 17th century the counters became smaller and smaller, for little by little they were only used as chips for card-playing. Real jetons are metallic thin flat discs and are struck like coins. The differences from coins are: the metal is generally copper or brass and seldom silver. Gold jetons are very rare. The measure is always between ca. 20 mm and ca. 28 mm. Smaller or larger pieces cannot be used as reckoning counters. The relief is always low for easy pushing and making piles. (In France the jetons were mostly laid down overlapping, as shown in the figure). Jetons are not coins, so they never have an indication of value.
The copper jeton shown in Figure 1 is a good example of a reckoning counter of the Low Countries of the 16th century. The type on the obverse is heraldic. The legend gives the name and the title of the principal of this jeton, Maximilian of Bergen op Zoom, bishop of Cambray (now in France). The legend of the reverse is the motto of the bishop: "neither quick nor rash," which is symbolized by a beautiful clock. The jeton is dated as usual in this period.
COUNTERS AS A CALCULATING INSTRUMENT
In ancient times the Greeks and Romans mostly used pebbles or bone disks for their calculations. This was cheaper than a beadframe, although we know that the Romans also used abaci. Usually the pebbles were half bulb-shaped pieces of limestone. The Romans called them "calculi" (singular: calculus = limestone, pebble), the origin of our word "calculation." In counting the pebbles were pushed over a counter-board with lines. The counter-board was used in the same way as the counter-frame.
EXAMPLES OF CALCULATION WITH JETONS
Calculating with jetons was always accompanied by registering the numbers in Roman figures.
I = 1
II = 2
V = 5
VI = 6
X = 10
XVII = 17
L = 50
LX = 60
C = 100
CLV = 155
D = 500
DXIII = 513
M = 1000
MDCCCCLXXXV = 1985
There were no strict rules for higher numbers. XXVIII.CCCCXXXII and XXVIIImIIIIcXXXII were both possible for 28,432. Abbreviations as MCM for 1900 were not usual in the middle-ages.
After the fall of the Roman Empire, international trade was reduced, therefore the need of calculating became less. However, thanks to churches and convents which had to figure out the dates of the changing church festivals, calculating with jetons had not been forgotten and the revival of trade in Northern Italy and France in the 12th and 13th centuries made it necessary again. In the meantime in Western Europe the beadframe abacus had definitely made room for the jetons which were exclusively made of metal and usually, just like coins, struck in copper and brass.
The calculating took place on a board with lines. Counter-boards with inlaid lines have been kept through the ages in private collections or museums. A cloth with embroidered lines was used very incidentally (for example at the yearly verification of the city-accounts) because of the quick wear and tear.
Figure 2 is a woodcut from Gregor Reisch's Margarita Philosophica, Freiburg, 1503, an early German book about arithmetic. Here "Arithmetica" is symbolized by a woman holding two books with the two different ways of calculation. The mathematician Pythagoras is shown calculating with jetons on a counter-table, while the philosopher Boethius is ciphering with Arabic figures. Figure a shows a counter-board with the figure 123. The cross at the fourth line, or thousand-line, was intended to help the eye like the comma that marks off the thousands in Arabic figures.
Figure 3 shows the same figure 123 on a reckoning-cloth, made by the wife of the author.
Figure 4 shows the author putting down the figure 194.
In the course of the 13th century scientists of Western Europe gradually learned how to make use of Arabic figures and discovered the meaning of the figure zero (= an empty space on the counter-board). Now also the Christian world knew how to make calculations by pen-reckoning and the abacus and Roman figures were no longer needed. It still took a few centuries before everyone at school learned how to pen-reckon. Invention of the printing-press quickened this process. Printed arithmetic books reached many more people than had ever been possible through oral instructions. Below are some examples of calculating with jetons or counters. Here is dealt with only the most simple form of plain calculation. Other systems were used for money-counting.
ADDITION
Adding on the counterboard is quite simple.
Example: CCXIII + LXXXVIII (213 + 88 = )
Put the figures down, separated by the vertical line. (figure b)
Actually we already have the answer, but after simplification the result is shown much clearer: Remove 5 counters from the bottom line and put instead a counter in the V-space between the I-line and the X-line. This one together with the counter already being in the V-space are replaced by one counter on the X-line. Now we have five counters on the X-line which we replace by one in the L-space. (If you cannot see through anymore there is only one solution: Draw a few lines on a piece of paper and do the addition yourself with a few dimes or something like it.) Finally we replace the two L-counters by one on the C-line and we see the number CCCI or 301. (figure c)
Subtraction is done in the same way.
MULTIPLICATION
It is more difficult to multiply and divide. Yet the operations on the counter-board are easier to understand than pen-reckoning. Example: CCLXXXV x XXIII (285 x 23 = ) Put down both figures (Figure 5).
First we multiply 285 by 10. In Arabic figures a zero is added to 285: 285 x 10 = 2850. On the counter-board it is as easy. Push all the counters one line up (Figure 6, right). Double this result, which makes the multiplication 20 times (Figure 7). First simplify. To indicate that we have multiplied by 20, we remove the 2 X-counters from 23. (Figure
.
Multiplying by 3 is done the easiest on the left side of the board. 3 x 285 is carried out as 3 x 200 + 3 x 80 + 3 x 5 (Figure 9).
Finally the two figures are joined, see Figure 10, and simplified (Figure 11).
You may verify the result with pen-reckoning or calculator (Figure 12).
DIVISION
The arithmetic book of Robert Recorde, The Grounds of Artes Teaching the Worke and Practice of Arithmetik, first published in 1542 in London, provides us with the last example. This book contains not only the teaching of pen-reckoning but also how the old method with counters could be used together with the new Arabic figures. "If 225 sheepe cost 45 ?, what did each sheep cost? To know this, I should divide the whole somme, that is 45 ? by 225, but that cannot be: Therefore must I first reduce that 45 ? into a lesser denomination, as into shillings, then I multiplie 45 by 20, and it is 900: these two numbers therefore I set thus. (figure d)
Then I begin at the highest line of the dividend, and seeke how often I may have the divisor therein, and that I may doe foure times..." The explanation that follows is not very clear. Probably Recorde hasn't calculated with counters very often himself. Division is explained only in a few of the arithmetic books from the 16th century that I consulted.
According to those books the pupil had to do by heart all the multiplications that were necessary for dividing; only subtraction was done on the counter-board. We may say that dividing was one of the least practised operations.
To understand by experience, I divided XXVIII.CCCCXXXII by CCCVII (28,432 divided by 357). Including laying out the necessary multiplications it took about 10 minutes before I found out that the answer was LXXVIIII with a remainder of CCXXVIIII. I needed 43 counters for this calculation. It seemed sensible to do the verification by a calculator.
A trained reckoner could probably do it much faster, although a counter-board was always slower than a bead-frame abacus, for pushing is done more quickly than putting down and taking away.
In his The Japanese Abacus (1954), Takashi Kojima describes a contest between the Japanese abacus or soroban and the electric calculating machine (not a modern electronic one!) which was held in Tokyo on November 12, 1946 under the sponsorship of the U.S. Army newspaper, the Stars and Stripes. In reporting the contest, the Stars and Stripes remarked: "The machine age took a step backward yesterday at the Ernie Pyle Theater as the abacus, centuries old, dealt defeat to the most up-to-date electric machine now being used by the United States government ... The abacus victory was decisive."
Figure 13 is a small modern Japanese soroban with bamboo rods and with four beads on the lower section and one on the upper. Each of the four beads on the lower section of a rod has the value of 1, while the bead on the upper section of the rod has the value of 5. Each of the 1-unit beads below the beam obtains its value when it is moved up toward the beam, and loses its value when it is moved back down. The 5-unit bead obtains its value when it is moved down to the beam, etc. The soroban in the illustration shows the figure 123.
One of the different systems of counting with jetons is shown in Figure 14. This is the title page of Robrecht van Heusden's Reken-boechsken, Antwerp, 16th century. At the far left is laid down a column (vertical) of jetons, generally called the "tree." The lowest marks the row of unit jetons, the next above the ten jetons, and so on. The five jeton has to be placed in the space between the lowest and the second jeton of the tree.
THE FIRST JETONS
The word jeton for counter comes from the French verb "jeter," used in the sense of "to push," because the counters were pushed over the abacus during the calculation.
The first counters were flat or bun-shaped discs, usually about 2 cm in diameter and made of stone, glass, bone or brass. These "calculi" are often found at Roman sites. They were also used as "gaming counters" on board games. The first numismatic counters or jetons have to be dated a little before 1200. From that time on, the brass discs were struck like coins in Italy and France by the same men who struck the coins.
It is nearly impossible to say where the first jetons were struck because the oldest Italian and French jetons were mute (they bear no inscriptions), so dating is very difficult. Commonly they have an heraldic sign or a coat of arms in the field and sometimes some isolated characters (Figure 15).
Written sources give us no idea either because jetons were first mentioned in manuscripts at the end of the 13th century. Probably there is connection between the introduction of jetons and the crusades. The crusades had stimulated the rising money-trade in Italy immensely. In addition, the West became acquainted with the copper coins of the Byzantine Empire and the Islamic countries. In order to finance the crusades, the European rulers had to borrow enormous amounts of money from the Italian bankers. If the jetons were first used in Italy, it is imaginable that, through these contacts, they also became known in France, the Low Countries and England.
In 1920 the well-known English numismatist and specialist in jetons F.P. Barnard tried to date the earliest Italian jetons. With considerable doubts, the oldest one has been dated to about 1190. This specimen was attributed to the Genoese Andrea de Rivegno or to the Bolognese banker Guiliano Arardi. Both of them belonged to the financers of the English king Richard Lionheart who borrowed money from them for the Third Crusade. The first jeton that can be dated exactly was struck for the court of the French queen Blanche of Castile. In 1218 she married the later king Louis VIII (1223-1226). After his death, she was regent for the minor Louis IX (St. Louis). She also became regent for her son during his crusade to Egypt (1248-1252) (Figure 16).
Her jeton has on the obverse a single lys (France) and on the reverse the castle of Castile between two lys.
The oldest jetons of the queen's court are easier to date than those of the royal court because the older jetons of the king are only decorated by the lys.
The earliest English jetons belong to the year 1280. They bear on the obverse a king's head crowned, surrounded by a border of alternate strokes and rosettes. On the reverse is a pattern composed of a cross with stars and crescents with a similar border. The star and crescent was a royal badge last used by king Edward (1272-1307). The English numismatist L.A. Lawrence discovered, in 1938, that the portraits of these jetons are identical with those on various issues of the coins of 1280. "This identity," he wrote, "leaves no room for doubt that the jetons were made from the same irons and punches as the coins and are the work of the London Mint" (Figure 17).
After the series struck since the reign of Edward 1, the production of English jetons diminished in the 14th century and French jetons were imported in large quantities.
Jetons were not used over a long period in Italy. In 1202 a revolutionary new book on mathematics appeared, the Liber Abaci, by Leonardo Fibonacci, better known as Leonardo of Pisa. The word "Abaci" in the title refers only to calculation in general and not to the use of the abacus. On the contrary, in this book he introduced the modern algebra with the new Arabic numerals. The use of the abacus disappeared very quickly in Italy. In 1299, the merchants of Florence were forbidden to keep their books "in abaco" and were ordered to use figures. The last Italian jetons were struck in the 14th century.
In the 15th century the manufacturing of jetons was concentrated in France and the Low Countries (now Belgium and Holland). There were two types: official jetons ordered by a special administration of a prince or a town, and common cheap ones for general use. The first type bears the names, arms and badges of their users; the common type is often an imitation of an official one.
In the 16th century a very large proportion of the counters for common use in Europe were manufactured at Nuremberg, Germany.
LOW COUNTRY JETONS
Within the limited space of this chapter it is impossible to deal extensively with all the European jetons. Therefore this chapter has been restricted to a more detailed description only of the jetons of the Low Countries and some general information on the jetons or "Rechenpfennige" of Nuremberg, Germany.
Shortly after the introduction of jetons at the Royal Court, the French high nobility adopted the use of counters for calculating; a bit later the cities and public institutions did so too. At the end of the 13th century their use even occurred in the Southern Netherlands; accordingly, early French jetons are quite important because they have been the example for all the Dutch counters (Figure 18a + b) (Figure 19a + b).
The most important ruler in the Netherlands at that time was the Flemish count. It is obvious to expect that he would be the first one in the Netherlands to have jetons struck. However, the oldest known jetons are of count John II of Hainault and Holland (1280-1304). As with the jetons of the English king, they were imitations of his coins (Figure 20a + b).
Also in the important trading-town Bruges (Flanders) jetons were used as early as 1284. Since 1303, the Dutch name "worpghelt" (cast-money) had been applied to jetons.
What we do know about the Flemish count is that as early as 1337 he gave his receiver silver jetons. Sometimes these silver jetons were used as counters, but mostly they were meant as a valuable gift in an attractive shape. Most of the silver (and gold) jetons were sold quickly and melted down (Figure 21).
The great development of the Dutch jetons took place during the reign of the Burgundian dukes. In 1433 duke Philip the Good of Burgundy established his power over the most important territories in the Low Countries - Brabant, Flanders, Hainault, Holland and Zeeland. He introduced the jeton as an instrument of propaganda. A number of important events of his government were commemorated on counters and the jeton became a small history medal. His successors, the archdukes of Austria and the kings of Spain, continued and enlarged this custom. When the new Chamber of Accounts was opened in Gelderland in 1559 during the reign of Philip II, the officials received several tens of silver jetons each and the rest of the personnel shared 2500 copper jetons, although counters were hardly used for calculating anymore. Tradition was stronger than practice and, besides, everybody was eager to get those beautiful medals with the portraits of the king and queen in his possession. This attitude changed considerably during the Dutch Revolt (1568-1648).
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to be continued on the next posting
