Köbel (or Kobel or Kobilin or Kiblin or Caballinus), Jacob

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Köbel (or Kobel or Kobilin or Kiblin or Caballinus), Jacob

(b Heidelberg, Germany, 1460/1465; d Oppenheim, Germany, 31 January 1533)

mathematics, law, publishing, municipal administration.

Köbel was the son of Klaus Köbel, a goldsmith. He began his studies at the University of Heidelberg on 20 February 14801 and earned his bachelor’s degree from the Faculty of Arts in July 1481. Concerning the following years it is known only that “Jacobus Kiblin” was active in the book trade in 1487. Simultaneously he studied law, receiving the bachelor’s degree on 16 May 1491. He appears to have gone then to Cracow, where he studied mathematics, a subject then flourishing at the Jagielloniamn University. He is also reported to have been a fellow student of Copernicus, who had enrolled there in 1491 under the rectorship of Mathias de Cobilyno (perhaps a relative of Köbel).2 In 1494 Köbel was in Oppenheim, where on 8 May 1494 he married Elisabeth von Gelthus, the daughter of an alderman. They are known to have had one son and two daughters. Köbel worked as town clerk and official surveyor, as well as manager of the municipal wine tavern. A scholar of manifold inte4rests, he wrote extensively and was also a printer and publisher. As a member of the Sodalitas Litteraria Rhenana he was friendly with many humanists.3 In the religious conflicts he stood with the Catholic reformers. He died after suffering greatly in his last years from gout and was buried in Oppenheim, in the Church of St. Katherine. A portrait of him can be found in his 1532 essay on the sundial.4

Between 1499 and 1532 Köbel published ninety-six works, at first those of others and then his own. Among the authors whose writings he published were Albertus Magnus, Virdung, and especially his friend Johann Stöffler.5 Köbel’s publishing activity decreased markedly after 1525, no doubt as a result of his poor health.

Köbel wrote three arithmetic books of varied content, all of which were well received. They appeared during the period in which the algorithm, with new numerals and methods—propagated especially through the writings of Sacrobosco—was gradually supplanting the traditional computation with the abacus and with Roman numerals (which Köbel called “German” numerals) Köbel’s first book was Rechenbüchlein vf den Linien mit Rechenpfenigen because such a book was the easiest sort for beginners, who had to know only the corresponding Roman letters. The book was widely read and went through many editions, most of them under altered titles, and was continually revised and enlarged. In it Köbel treated the manipulation of the abacus, computational operations (with duplication, mediation, and progression but without the roots, since they are “unsuitable for domestic use”), the rule of three, fractions (also with Roman numerals), and a few problems of recreational mathematics.

The next to appear was Eyn new geordent Vysirbuch (1515), which dealt with the calculation of the capacity of barrels. Köbel presented the new methods of calculation with Arabic numerals in Mit der Kryden oder Schreibfedern durch die Zeiferzal zu rechnen (1520).

Köbel’s writings were most widely disseminated in a collection that he himself had prepared, ZweyRechenbüchlin: Uff der Linien und Zipher. Mit eym angehenckten Visirbuch (1573). It contained almost verbatim the line arithmetic book of 1525 (now without Roman numerals), as well as the Vysirbuch and Mit der Kryden order Schreibfedern. In the editions after 1544 a chapter was added on the commercially important measures and coins of many foreign lands.

A Geometrei appeared posthumously (1535) and was in print until 1616. This work consisted of three papers by Köbel: “Von vrsprung der Teilung …” (1522), which contained formulas for the surveyor;6 an essay on the Jacob’s staff, written in February and May 1531,7 and “Feldmessung durch Spiegel,” which was first published in the Geometrei.

As an astronomer Köbel was concerned with the astrolabe and with the publication of numerous popular calendars. His Astrolabii declarations (1532) went through several editions. He also published a treatise entitled Eyn Künstliche son-Uhr inn eyenes yeden menschen Lincken handt gleicht wie in eynem Compass zu erlerenn … (1532), which later appeared under the titles Baure Compass and LeyenCompas.8

Besides informative handbooks and many poems, Köbel wrote works on law—for example, on inheritance cases and rules of the court. He also wrote on imperial history and continued the chronicle of Steinhöwel from the time of Frederick III to his own day.

The high esteem accorded to Köbel’s writings is reflected in the numerous editions that appeared until the beginning of the seventeenth century. Today his importance lies principally in his dissemination of mathematical knowledge, especially of the new Hindu numerals and methods, among broad segments of the population. He accomplished this through the use of German in his work, a practice he was the first to adopt since the publication of the arithmetic books of Bamberg (1482, 1483) and Widmann (1489)—which, moreover, were basially collections of problems. Adam Ries, who replaced Köbel as teacher of the nation, used his books, having become acquainted with them while in Erfurt (1518—1522) through the humanist George Sturtz.9


1. The printed register of Heidelberg, University, I 367, gives the name Johannes Köbel; the original has the correct form.

2. Starowolsky, Scriptorym Polonicorum …, p. 88; in it Köbel is cited as Cobilinius in Catalogus illustrium Poloniae scriptorum (p. 133). Benzing, in Jakob Köbel zu Oppenheim, 1494—1533, p. 8, remarks that we have no proof that Köbel studied at Cracow.

3. Vigilius, who was a guest of Köbel 9Caballinus), reports in a letter to Conradus Celtis (Heidelberg, 19 Apr. 1496) that Köbel was estranged from Johann von Dalberg because Köbel had, without permission, given Celtis a book he had borrowed from Dalberg. See Rupprich, Der Briefwechsel des Konrad Celtis, pp. 178–227 ff.; and Morneweg, Johann von Dalberg, pp. 196 ff.

4. The portrait can be found in Benzing, op, cit., p. 6.

5. For example, Stöffler’s Calendarium Romanorum magnum (1518); Der newe grosz Römisch Calender (1522); and Elucidatio fabricae ususque astrolabii (1513).

6. With regard to the errors criticized by Kaestner (Geschichte der Mathematik, I [1796], 655), it should he said that Köbel intended to provide the surveyor only with formulas, such as the ancient Egyptian approximation formula for quadrangles.

7. Köbel explained this work by stating that he himself was now obliged to use a staff.

8. See Benzing, op. cit., pp. 79. ff.

9. Köbel never realized his intention to write on algebra. See Unger, Die Methodik der praktischen Arithmetik, p. 45.


I. Original Works. A list of all of Köbel’s writings, with full titles, subsequent eds., and presnet locations, is in Joseph Benzing, Jakob Köbel zu Oppenheim, 1494–1533. Bibliographie seiner Druke und Scriften (Wiesbaden, 1962). Most of his works were published “under such varied titles and in such different combinations with his other books, that it is difficult to say whether a given edition is a new work or merely a revision” (Smith, Rara Arithmetica, p. 102). Among them are, Rechenbüchlein vf den Linien mit Rechenpfenigen (Oppenheim—Augsburg, 1514; 2nded., 1517; 3rd ed., 1518); Eyn new geordent Vysirbuch (1515l; 1527), later issued with line arithmetic book (also with square and cube roots) (1531; 1532); über die Pestilenz (1519); Was Tugend und Geschicklichkeit ein Oberster regirer an ynn haben soll (1519), an exhortation to Charles V; Mit der Kryden oder Schreibfedern durch die Zeiferzal zu rechnen (1520); the line arithmetic book, Eyn new Rechenbüchlin Jacob Köbels Stadtschreiber zu Oppenheym auff den Linien vnd Spacien gantz leichtlich zu lernen mit Vyelen zusetzen (oppenheim, 1525); Astrolabii declaratio (1532), also published with Stöffler’s Elucidatio and later trans, into German as Von gerechter Zubereitung des Astrolabiums … (1536); Eyn künstliche sonnUhr inn eynes yeden menschen Lincken handt gleicht wie in eynem Compass zu erlernen … (1536); Geometrei (1535; 1550; 1570; 1584; 1598; 1616), with a treatise on the quadrant by Johann Dryander, who also published a work on the Nachtuhr begun by Köbel (1535); and Zwey Rechenbüchlin: Uff der Linien und Zipher. Mit eym angehenckten Visirbuch (1537; 1543; 1564; 1584).

II. Secondary Literature. On Köbel or his work, see Allgemeine deutsche Biographie, XVI, 345–349, and XIX, 1827; M. Cantor, Vorlesungen üer Gaschichte der Mathematik, 2nd ed., II (Leipzig, 1913), 419 f.; S. Günther, Geschichte des mathematischen Unterrichts im deutschen Mittelater bis zum Jahre 1525 (Berlin, 1887), p. 386; K. Haas, “Der Rechenmeister Jakob Köbel,” in Festschrift zum 125-jährigen Jubiläum des Helmholtz-Gymnasiums in Heidelberg (Heidelberg, 1960), pp. 151–155; K. Morneweg, Johann von Dalberg (Heidelberg, 1887); F. W. E. Roth, “Jakob Köbel, Verleger zu Heidelberg, Buchdrucker und Stadtschreiber zu Oppenheim am Rhein 1489-1533, “in Neues Archiv zur Geschichte der Stadt Heidelberg, 4 (1901), 147-179; H. Rupprich, Der Briefwechsel des Konrad Celtis (Munich, 1934); D. E. Smith, Rara arithmetica (Boston-London, 1908), pp. 100-114; Szymon Starowolsky, Scriptorum Polonicorum ‘EKATONTÀΣ (Frankfurt, 1625); and F. Unger, Die Methodik der praktischen Arithmetik (Leipzig, 1888), pp. 44-46.

Kurt Vogel