Arithmetic master
Arithmetic master describes an initially medieval profession that gained particular importance in the early modern period . The arithmetic masters taught arithmetic and elementary mathematics in German or the respective vernacular . In doing so, they met the growing demand created by the rapidly increasing trade. Mathematics played no essential role in the Latin church school system.
At the beginning of the 16th century, arithmetic masters created so-called arithmetic books , which were mostly used for teaching at their private arithmetic schools . In addition, mathematical writers and town clerks mainly wrote works suitable for self-study . Arithmetic books were among the first instructive and vernacular writings to be printed.
Neglected basic education
Elementary arithmetic was practically non- existent in public schools in the 15th century. In the 16th century only about half of the school regulations included parts of mathematics in the classroom, but rarely as a subject with equal status. One learned in German schools of the late Middle Ages to read and later to write the German language; There was no room for mathematical education beyond reading and writing numbers and the multiplication tables . Mathematics was mostly dealt with - if at all - as part of the one-hour weekly music lesson. Those who wanted to know more had to take care of it privately.
In the Latin schools of teaching Latin stressed most of the time. Practical parts of math were not taught. There was no commercial arithmetic. Mathematics first came to fruition at universities in the form of arithmetic and geometry in the quadrivium of the study of the seven liberal arts of the artist faculty .
Trade required arithmetic
The need for knowledge of arithmetic increased dramatically with the development of commerce around 1500. The money economy had replaced barter. The merchants and others now had to keep books, write numbers and do arithmetic. Since they could not learn this in their home office, the rich merchants sent their sons to the large, highly developed trading centers in Italy. The call for general mathematical education grew within the cities north of the Alps.
Private teacher and writer as trainer
Teachers at lower urban schools or private schools, most of whom were still active in public administration, gradually closed the gap. They called themselves arithmetic masters and opened their own arithmetic schools . With their lessons, they took on an educational task that the existing schools did not or only insufficiently. In larger cities they united to form guilds with similar statutes and customs as the craft guilds and also trained the next generation. Even without a patent from a state education authority, a quality guarantee for education and personal integrity was given. The math schools in Nuremberg, Augsburg and Ulm had a special reputation.
Different number systems
The Greeks and the Romans had a number that was almost unsuitable for arithmetic. However, the abacus compensated for this disadvantage for simple calculations. It was later replaced in the Middle Ages by the abacus and calculating on lines, which was characteristic of the 16th century .
The Indian numerals we are familiar with today came to the West via Arabized Spain. The mediators between India and Europe were the Arabs. They already knew about the Indian numerals in the 8th century. The nature and value of the Indian numerals were not yet recognized in Central Europe. The information withered in the learned monastery rooms. The Indian numerals came to Germany a second time from Italy around 1200 thanks to Leonardo of Pisa.
However, the population north of the Alps showed great mistrust of the new "Welschen" system. In particular, the previously unneeded number 0 was very unsettling, because standing on its own it meant “nothing” , but together with other numbers it multiplied the number on the left by 10. In addition, it seemed too easy to forge into a 6 or 9 by hand. And besides, you got along with the German (= Roman) notation when writing and reading and calculating on lines without any problems . Even when calculating on lines, multiples of 10 were used as base values (the "ones") with five-fold auxiliary base values (the "fives") in a place value system characterized by lines and spaces, but one did not work with numerals, but with arithmetic units that include Arithmetic pennies were shown.
As long as it was not necessary to calculate but only to represent, the numerical representation adopted by the Romans was simple, safe and practical. One had become so used to them that one spoke of the “German” numbers.
Three methods were available for arithmetic
- The finger-reckoning : The long common conventional method, even if it is rarely mentioned in the literature.
- The abacus or calculating on lines : a process that is similar to the impressively fast abacus that is still used in Asia today.
- The numeric calculations : The granddaddy of Rechenmeister from the High Middle Ages, the brilliant patrician son of Leonardo di Pisa (Fibonacci) had previously met 300 years the Arabs the Indian 10-place value system with nine digits characters including the number zero and the mathematical approach in his masterpiece liber abaci described. Coming from a respected family of merchants, he laid the foundations for the highly developed commercial arithmetic and bookkeeping skills in the northern Italian trading cities.
Well-known arithmetic masters and their works
(Abstract)
- Fibonacci , Leonardo da Pisa (* perhaps around 1180, † perhaps after 1241), is considered the most important mathematician of the Middle Ages
- Liber abbaci (1202), first work written by a practitioner maestro d'abaco in vernacular instead of Latin on arithmetic operations that are important for commercial practice.
- Ulrich Wagner († around 1490), worked as arithmetic master in Nuremberg
- Bamberg calculation book 1482 and 1483
- Johannes Widmann (* around 1460, † after 1498), master's degree in liberal arts and teacher of mathematics at the University of Leipzig; introduced the symbols + and - for the arithmetic operations plus and minus in the literature
- Mercantile Arithmetic or Behêde and pretty calculation auff allen kauffmanschetzt (1489) with borrowings from the Bamberg calculation book
- Balthasar Licht , worked as arithmetic master around 1500
- Algorithm linealis cum pulchris conditionibus Regule detri: septem fractionum…
- Johann Huswirth (Sanensis), worked as a German mathematician around 1500, because of his Latinized name, Sayn in the Westerwald is believed to be the place of birth
- Enchiridion novus Algorismi… (arithmetic on lines)
- Gregor Reisch (* around 1470 in Balingen (Württemberg), † 1525 in Freiburg im Breisgau) studied around 1487 in Freiburg, joined the Carthusian Order and became prior in Freiburg and confessor of Emperor Maximilian I.
- Margarita philosophica (1503) for calculating on lines.
- Unknown author:
- Algorithm… Several writings from the turn of the 15th and 16th centuries. Century
Up until the time before Köbel, all arithmetic books written in German dealt exclusively with numerical arithmetic , while arithmetic on lines with the title Algorithmus linealis ... was taught in Latin.
- Jakob Köbel (* 1462 in Heidelberg; † 1533 in Oppenheim), town clerk of Oppenheim, printer, publisher, mathematical writer
- Eynn Newe ordered rake booklet vf the lines with rake (1514)
- Eynn Newe classified Vysir Book (1515)
- With the Kryde od 'nibs - Rechepüchlein (1520)
- From the origin of the division / measure of measurement of the Ertrich der Ecker (1522)
- Arithmetic and sights (1532)
- Geometric / Refrain from artificial measurement (1575)
- Adam Ries (* 1492 in Staffelstein, Upper Franconia; † 1559 probably in Annaberg, Erzgebirge), the most famous arithmetic master of the time, opened an arithmetic school in Annaberg (Saxony) in autumn 1525
- Invoice on the line (1518)
- Calculation on the lines and feathers ... (1522)
- Coß (manuscript 1524, printed 1992)
- Ein Gerechent booklet / auff den Schöffel / bucket / and pound weight ... (Manuscript 1533, printed 1536, also known as "Annaberger Brotordnung")
- Calculation according to the length / on the lines and pen. (1550)
- Petrus Apianus (Bienewitz) (* 1495 in Leisnig, † 1552 in Ingolstadt), professor of astronomy in Ingolstadt
- Eyn newe vnd well-founded vnderweysung of all merchant accounts (1527)
- Andreas Reinhard (* 1571 in Schneeberg, Erzgebirge; † 1613 there)
- Three arithmetic registers for Practic . (around 1598/99)