Johannes Widmann (mathematician)

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Johannes Widmann (also: Johannes Weidemann , Weideman , Widman , Wideman ; * around 1460 in Eger , Bohemia ; † after 1498 in Leipzig ) was a lecturer at the University of Leipzig .

In the winter semester of 1480, Widmann was entered in the register of the University of Leipzig (as Iohannes Weideman de Egra ). For the degrees as Baccalaureus 1482 and Magister 1485, he was waived the fees because he was penniless.

Widmann became famous for his book Mercantile Arithmetic or Behende und hüpsche Rechenung auff allen Kauffmanschienste , published in Leipzig in 1489 . For the first time, the symbols + and - are used to indicate excess and deficiency, but not yet in the modern sense as plus and minus signs for the arithmetic operations of addition and subtraction ; this meaning was only to be introduced in 1518 by Heinrich Schreiber .

Mercantile Arithmetic (1489)

Its arithmetic book 1489 (printed in Leipzig at Konrad tiled stove) is the second oldest printed in Germany computing book after Bamberger arithmetic book by Ulrich Wagner (1482/83), and the third oldest printed arithmetic book at all. It was dedicated to Siegismund Altmann. Widmann's book was widely distributed and was reprinted in Pforzheim , Hagenau and Augsburg , among others, until 1526 . It was then overtaken by other arithmetic books such as those by Adam Ries and Jakob Köbel . According to Kurt Vogel, it surpassed its predecessors by far in terms of the number and breadth of calculation examples. As a source he used the Bamberg arithmetic book and the algorism Ratisbonensis , an arithmetic book that was created around 1450 in the Benedictine monastery of St. Emmeran in Regensburg.

His lecture on algebra 1486 is the first algebra lecture in Germany. Their content is known from student notes (obtained in manuscripts in Dresden, Vienna, Munich). There is also a manuscript in the possession of the Dresden State Library from Widmann's possession (Codex Dresdensis C 80), which contains texts on algebra, including a German algebra from 1471 and a Latin algebra, which served as the basis for his lecture. The lecture dealt with the 24 types of equations customary for the Cossists (algebra experts) at the time , but also as preparation for fractions and ratios.

Adam Ries got to know Widmann's book (and the Dresden manuscript with algebra texts from Widmann's possession, today Dresden State Library) in Georg Sturtz's library in Erfurt, where Ries was between 1518 and 1522. Ries took from the manuscript examples of his Coss (his algebra manuscript), but apparently (Kurt Vogel) did not know the identity of the author of the manuscript.

According to Kurt Vogel, in addition to his arithmetic book, he anonymously published Algorithmus integrorum cum probis annexis , Algorithmus linealis , Algorithmus minutiarum phisicarum , Algorithmus minutiarum vulgarium , Regula falsi apud philosophantes augmenti et decrementi appellata and Tractatus proportionum plusquam aureus . The writings probably appeared in Leipzig around 1495.


  • Moritz CantorWidmann: Johannes W. von Eger . In: Allgemeine Deutsche Biographie (ADB). Volume 42, Duncker & Humblot, Leipzig 1897, p. 355.
  • Barbara Gärtner: Johannes Widmann's “Agile and pretty calculation”. The text type "arithmetic book" in the early modern period , Tübingen 2000. (German Linguistics. 222.)
  • Karl Röttel : Johannes Widmann - At the turning point in the history of mathematics . In: Treasury of arithmetic . Annaberg-Buchholz 2008 (with details of further literature).
  • Franz Xaver Wilhelm: On the biography of the mathematician Johann Widmann von Eger . In: Communications of the Association for the History of Germans in Böhmen, Volume 45 (1907), pp. 429-430.
  • Ina Prinz Arithmetic like a master: the arithmetic books by Johannes Widmann, Adam Ries, Christoph Rudolff and Johann Albrecht , Berlin, Nicolai 2009
  • Kurt Vogel : Widman (or Wiedeman or Wideman), Johannes . In: Charles Coulston Gillispie (Ed.): Dictionary of Scientific Biography . tape 14 : Addison Emery Verrill - Johann Zwelfer . Charles Scribner's Sons, New York 1976, p. 325-326 .
  • Wolfgang Kaunzner About Johannes Widmann von Eger. A contribution to the history of arithmetic in the late Middle Ages , publications by the research institute of the German Museum for the History of Natural Sciences and Technology, Series C, No. 4, 1968
  • W. Kaunzner German mathematicians of the 15th and 16th centuries and their symbolism , publications by the Research Institute of the German Museum for the History of Natural Sciences and Technology, Series A, No. 90, 1971

Web links

Individual evidence

  1. Ina Prinz, Mitteilungen DMV, Volume 19, 2011, p. 105 gives 1505 as the date of death and 1460/65 as the date of birth
  2. Born around 1450 in Schmidtmühlen. Jurist. 1504 Rector of the University of Leipzig. Also as Dr. Smidemol known. Koebler, historical persons at the Leipzig Faculty of Law
  3. ^ Digitized edition of the Augsburg 1526 and Pforzheim 1508 editions in the Bavarian State Library
  4. The editions are listed by David Eugene Smith Rara Arithmetica , Boston, London 1908
  5. Article Widman in Dictionary of Scientific Biography. It refers to E. Wappler's contribution to the history of mathematics , Treatises on the history of mathematics, Volume 5, 1890, pp. 147-169