Arithmetic book

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Title page of the first print of Adam Ries ' third arithmetic book (1550)
Japanese arithmetic book Jinkōki (1641)

The term arithmetic book is used in the context of the history of science as a term for practice-oriented mathematical textbooks from the period between the Middle Ages and the early modern period .

history

The origin of the arithmetic books lies in the collections of mathematical exercises of the early advanced civilizations . While only a few practice-oriented mathematical writings have come down to us from the Greco-Roman antiquity , the oldest surviving arithmetic books from the Indian culture are from the years between 850 and 1150 AD. There are well over a hundred arithmetic books from the Arab region, mostly with a pronounced practical relevance , handed down. The oldest arithmetic book with Indian numerals written in Arabic and known to this day is dated to around 950 AD. The oldest known treatise from the Byzantine Empire was written in 1252, and the arithmetic book of Maximos Planudes was widely used a little later .

In Europe, in connection with the economic upswing in the High Middle Ages and inspired by Fibonacci's Liber abbaci , published in 1202, the first in Italy was created by practitioners (so-called arithmetic masters , Italian maestri d'abbaco ) in the vernacular instead of Latin, the arithmetic operations important for commercial practice . Inspired by these Italian treatises originated in Germany for the first time in the late 15th century, then expanded in the 16th and 17th centuries a number of vernacular computing books dealing primarily with responsibilities of applied arithmetic , more rarely with the German speaking under the contemporary term Coss known Algebra . The first printed arithmetic books included Treviso Arithmetic in Italy (1478), arithmetic books by Francesc Santcliment in Spain and the Bamberg arithmetic book. The latter is considered the oldest fully preserved printed arithmetic book in German and was published by Ulrich Wagner in 1483. The printer Heinrich Petzensteiner is named as the author in the colophon . The Bamberg arithmetic book is possibly based on an older German treatise written before 1450. The best-known early modern arithmetic book is the second arithmetic book Rechenung auff der Linihen und federn in zal / measure and weight of the Erzgebirge arithmetic master Adam Ries, first printed in 1522 and published in numerous new editions . By Michael Stifel 1546 appears arithmetic book from the French-speaking and German Practick .

The Sumario Compendioso was published in Mexico in 1556 as the first mathematical textbook outside of Europe .

The occidental arithmetic books usually begin with a short presentation of the Indian numerals - which were still uncommon in late medieval Europe in many places - and the basic arithmetic operations with them, and then teach their application using sample tasks from commercial practice. Due to their distribution, the printed arithmetic books contributed significantly to the implementation of this new script-based method of Indo-Arabic numerical calculation and thus to the replacement of the previously common calculation on lines using abacus boards.

In Japan during the Edo period (1603–1868), numerous practice-oriented arithmetic books were also published - independent of the European works and intended for arithmetic with the Japanese abacus ( Soroban ). The Jinkōki of Yoshida Mitsuyoshi , which appeared in several editions between 1627 and 1641, was particularly influential .

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Modern print editions

Reprints of well-known arithmetic books (selection)

  • The Bamberg arithmetic book from 1483 by Ulrich Wagner . Reprint of the Bamberg 1483 edition with an afterword by Eberhard Schröder, Weinheim 1988, ISBN 3-527-26725-5 .
  • The 1st arithmetic book by Adam Ries . Reprint of the 2nd edition Erfurt 1525 with a short biography, a content analysis, bibliographical information, an overview of the technical language and a metrological appendix by Stefan Deschauer, Munich 1992, ISBN 3-89241-005-4 .
  • Jinkōki . Wasan Institute, Tokyo 2000 (contains the June 1641 edition and parts of the November 1641 edition as facsimile and in English translation, extensive notes and explanations).
  • Calculation on the lines and feathers in number, measure and weight on all kinds of handling made and read together by Adam Riesen von Staffelstein Rechenmeyster zu Erffurdt in 1522 Jar . Reprint of the first edition Erfurt 1522 with a short biography, bibliographical information and an overview of the technical language by Stefan Deschauer, Munich 1991, ISBN 3-89241-004-6 .
  • Adam Ries: Arithmetic book on lines and zip lines in all kinds of trades, trades and sales [...]. Frankfurt am Main 1574; Reprint 1954.

Transfers into New High German

  • Kai Brodersen , Christiane Brodersen: Adam Ries, The first arithmetic book (Erfurt 1525). Speyer 2018 ISBN 978-3-939526-38-4
  • Stefan Deschauer: The second arithmetic book by Adam Ries: a modern text version with commentary and metrological appendix and an introduction to the life and work of the arithmetic master . Braunschweig u. a. 1992, ISBN 3-528-06412-9 .

Digital copies available online

Manuscripts

  • Bamberg mathematical manuscript . Nuremberg? circa 1460.
  • Andreas Reinhard : Three registers arithmetic ahnfeng for Practic . Snow mountain 1599.
  • Johann Friedrich Rosenzweig the Younger : Arithmetic book of the Bamberg court engineer Johann Friedrich Rosenzweig . Bamberg 1721.

Prints

literature

Tools

  • David Eugene Smith: Rara Arithmetica: a catalog of the arithmetics written before the year 1601 with a description of those in the library of George Arthur Plimpton of New York . Boston et al. a. 1908.

Representations

  • Walther L. Fischer: The Jinko-ki by Mitsuyoshi Yoshida (1627). The most famous Japanese arithmetic book of the Edo period . University of Erlangen-Nürnberg, Nürnberg 1996 ( work reports and reprints , No. 2, 1996.).
  • Menso Folkerts , Erwin Neuenschwander: The art and methods of arithmetic, arithmetic books . In: Lexicon of the Middle Ages . Volume 7, Munich a. a. 1995, ISBN 3-7608-8907-7 , pp. 502-508 (there also information on further literature).
  • Barbara Gärtner: Johannes Widmann's “Behende vnd pretty calculation”. The text type "arithmetic book" in the early modern period . Tübingen 2000, ISBN 3-484-31222-X (contains among other things the edition of Johannes Widmann's arithmetic book published in Leipzig in 1489).
  • Rainer Gebhardt , Helmuth Albrecht (Hrsg.): Arithmetic masters and cossists of the early modern times. Contribution to the scientific colloquium on September 21, 1996 in Annaberg-Buchholz . Freiberg 1996, ISBN 3-930430-05-3 .
  • Hugo Grosse: Historical arithmetic books of the 16th and 17th centuries and the development of their basic ideas up to modern times. A contribution to the history of the methodology of arithmetic instruction . Reprint of the Leipzig 1901 edition, Wiesbaden 1965.
  • Wolfgang Kaunzner , Karl Röttel: Christoff Rudolff from Jauer - facsimiles of the Coss and the two arithmetic books as well as detailed descriptions. For the 500th birthday of the Silesian mathematician Rudolff . Eichstätt 2006, ISBN 3-928671-39-1 .
  • Friedrich Unger: The method of practical arithmetic in historical development from the beginning of the Middle Ages to the present . Leipzig 1888.

Web links

Wikisource: Arithmetic books  - sources and full texts
Commons : Arithmetic books  - collection of pictures, videos and audio files

Individual evidence

  1. ^ Kai Brodersen , Christiane Brodersen: Planudes, Rechenbuch , Greek and German. Berlin 2020 (= Tusculum Collection ), ISBN 978-3-11-071192-9 .
  2. ↑ Monika Zimmermann: Bamberger Rechenbuch 1483. In: Burghart Wachinger u. a. (Ed.): The German literature of the Middle Ages. Author Lexicon . Volume 1: 'A solis ortus cardine' - Colmar Dominican chronicler. 2nd, completely revised edition. de Gruyter, Berlin / New York 1978, ISBN 3-11-007264-5 , column 596-599.
  3. ↑ online via the Bamberg State Library.
  4. ^ Digital full-text edition of the copy from the Historical High School Library Christianeum Hamburg in Wikisource ( digital copy on Wikimedia Commons , accompanying project on Wikiversity ).
  5. ↑ urn : nbn: de: bvb: 22-dtl-0000000478 via the Bamberg State Library.
  6. ↑ online via the Herzog August Library Wolfenbüttel.
  7. ↑ online about the Albert Ritzaeus Hardenberg collection of the Johannes a Lasco Library Emden.
  8. ^ De Adam Risen arithmetic book . Wikimedia Commons
  9. ↑ online via the Bielefeld University Library.