Johann Scheubel

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Johann Scheubel (born August 18, 1494 in Kirchheim unter Teck , † February 20, 1570 in Tübingen ) was a German mathematician . Scheubel is regarded as a pioneer of algebra in Europe.

life and work

Significant innovations in solving quadratic equations go back to him. He wrote a total of six books on arithmetic and algebra as well as numerous manuscripts on mathematical and astronomical topics. Since 1535 at the University of Tübingen , he was there in 1540 Magister and 1550 Professor. In 1559 he also designed the oldest map of the Duchy of Württemberg . The woodcut round map on a scale of about 1: 600,000 names 122 places. The book collection of 200 volumes in his estate is now part of the old holdings of the Tübingen University Library .

In 1555 Johann Scheubel published the next two perfect numbers 2 16 · (2 17 -1) = 65536 · 131071 = 8589869056 and 2 18 · (2 19 -1) = 262144 · 524287 in his German translation of Books VII-IX of Euclid's Elements = 137438691328. The second factors are the Mersenne prime numbers M 17 and M 19 . However, he did not recognize both 2 11 -1 = 2047 = 23 · 89 and 2 15 -1 = 32767 = 7 · 31 · 151 as composite, but instead 2 21 -1 = 2097151 = 7 2 · 127 · 337. (Die However, he does not give decompositions at this point.) In his work, he incorrectly receives nine instead of the correct seven perfect numbers.

He wrote the first German translation of the elements, but it was incomplete (only books 7 to 9). He published books 1 to 6 of the elements as early as 1550 in a Greco-Latin edition. Extensive manuscripts by him on Euclid's elements are in Tübingen, in the Vatican Library and at Columbia University.

With his introduction to algebra from his Latin Euclid edition of 1550 (and printed separately in Paris) he belonged to the German Cossists (Coss was called algebra at the time) and still used algebraic symbols such as for plus and minus, as well as Michael Stifel and Christoph Rudolff (on whom he builds) and other German Cossists, but also has its own notation. For example, depending on the position of the number before or after the symbol , the use of ra means a root or multiplication by an unknown, but he also mentions the root symbol that is used today. Robert Recorde in England used it as a source alongside Stifel. However, he uses different symbols for plus and minus in his arithmetic than in his algebra. In his Euclid edition he uses algebraic symbols to represent examples to illustrate Euclid's theorems.

Private

After the death of his first wife in 1554, he remarried two years later (Anna Stöfflin, died 1573).

Fonts

  • De numeris et diversis rationibus seu regulis computationum opusculum , Leipzig 1545, 1557
  • Compendium arithmeticae artis , Basel 1549, 1560
  • Euclidis Megarensis […] sex libri priores , Basel 1550, 1590
    • The Brevis Regularum Algebrae Descriptio (an introduction to algebra of 76 pages) contained therein, which precedes the description of Euclid's first six books, was printed separately in Paris in 1551 and 1552: Algebrae compendiosa facilisque descriptio
  • The sibend, eight and ninth books by the famous Mathematici Euclidis Megarensis , Augsburg 1555
  • A thorough and thorough description of the laudable principality of Würtemberg , 1559 (map)
  • Jacobi Fabri Stapulensis in Arithmetica Boëthi epitome , 1553

literature

  • Hermann Staigmüller: Johannes Scheubel, a German algebraic of the 16th century , in: Abhandlungen zur Geschichte der Mathematik, Volume 9, 1899, pp. 431–469
  • Mary S. Day: Scheubel as an algebraist , New York 1926
  • Ulrich Reich: Johann Scheubel (1494 - 1570), pioneer of algebra in Europe , in: Rainer Gebhardt u. a. Arithmetic masters and cossists of the early modern period , writings of the Adam-Ries-Bund, Volume 7, Annaberg-Buchholz 1996, pp. 173–190
  • Ulrich Reich Johann Scheubel and the oldest map of Württemberg , Karlsruhe Geoscientific Writings, Series C, 14, Karlsruhe University of Applied Sciences, Geoinformation Center, 2000
  • Ulrich Reich 500 years of Johann Scheubel , in the series of publications by the city of Kirchheim unter Teck, Volume 18, 1994, pp. 59–90
  • Florian Cajori A history of mathematical notations , Dover
  • Ulrich Reich:  Scheubel (ius), Johann (es). In: New German Biography (NDB). Volume 22, Duncker & Humblot, Berlin 2005, ISBN 3-428-11203-2 , p. 709 f. ( Digitized version ).

Individual evidence

  1. ^ To his library: BB Hughes The private library of J. Scheubel, sixteenth-century mathematician , VIATOR, medieval and renaissance studies, Vol. 3, 1972, pp. 417-432
  2. ^ Mersenne prime # history
  3. ↑ See Thomas Heath The thirteen books of Euclid's Elements , Cambridge 1908, Dover, Volume 1
  4. ↑ Alten, Wussing a. a. 4000 years of algebra , Springer Verlag 2008
personal data
SURNAME Scheubel, Johann
BRIEF DESCRIPTION German mathematician
DATE OF BIRTH August 18, 1494
PLACE OF BIRTH Kirchheim unter Teck
DATE OF DEATH February 20, 1570
Place of death Tübingen