Jost Bürgi

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Jost Bürgi
Jost Bürgi Porträt.jpg
Jobst Burgius
Born 28 February 1552
Lichtensteig, Toggenburg
Died 31 January 1632
Kassel, Holy Roman Empire
Nationality Swiss
Fields Mathematician
Known for Logarithms
Mechanised Celestial Globe, made 1594 in Kassel, now at Schweizerisches Landesmuseum in Zurich
Jost Bürgi and Antonius Eisenhoit: Armillary sphere with astronomical clock, made 1585 in Kassel, now at Nordiska Museet in Stockholm
Medal issued on the 350th anniversary of his death

Jost Bürgi (also Joost, Jobst; Latinized surname Burgius or Byrgius; 28 February 1552 – 31 January 1632), active primarily at the courts in Kassel and Prague, was a Swiss clockmaker, a maker of astronomical instruments and a mathematician.


Bürgi was born in 1552 Lichtensteig, Toggenburg, at the time a subject territory of the Abbey of St. Gall (now part of the canton of St. Gallen, Switzerland). Not much is known about his life or education before his employment as astronomer and clockmaker at the court of William IV in Kassel in 1579; it has been theorized that he acquired his mathematical knowledge at Strasbourg, among others from Swiss mathematician Conrad Dasypodius, but there are no facts to support it.[1]

Even though he was an autodidact, was already during his lifetime considered as one of the most excellent mechanical engineers of his generation. His employer, William IV, Landgrave of Hesse-Kassel, in a letter to Tycho Brahe praised Bürgi as a "second Archimedes" ( quasi indagine Archimedes alter est).[2] Another autodidact, Nicolaus Reimers, in 1587 translated Copernicus' De Revolutionibus Orbium Coelestium into German for Bürgi. A copy of the translation survived in Graz, it is thus called "Grazer Handschrift".[3][4][5]

In 1604, he entered the service of emperor Rudolph II in Prague. Here, he befriended Johannes Kepler. Bürgi constructed a table of sines (Canon Sinuum), which was supposedly very accurate, but since the table itself is lost, it is difficult to be sure of its real accuracy (for instance, Otho's Opus Palatinum had parts which were not as accurate as it was claimed). An introduction to some of Buergi's methods survives in a copy by Kepler; it discusses the basics of Algebra (or Coss as it was known at the time), and of decimal fractions. Buergi has also constructed a table of antilogarithms, printed in 1620 (but perhaps not published), but he did not objectivate the notion of a logarithmic function and cannot therefore be considered as an independent inventor or discoverer of logarithms. More important than his written legacy is the engineering achievement contained in his innovative mechanical astronomical models.[6] During his years in Praha he worked closely with the astronomer Johannes Kepler at the court of Rudolf II.

Bürgi as a clockmaker[edit]

It is undocumented where he learned his clockmaking skills, but eventually he became the most innovative clock and scientific instrument maker of his time.[7][8] Among his major horological inventions were the cross-beat escapement, and the remontoire, two mechanisms which improved the accuracy of mechanical clocks of the time by orders of magnitude.[9] This allowed for the first time clocks to be used as scientific instruments, with enough accuracy to time the passing of stars (and other heavenly bodies) in the crosshairs of telescopes to start accurately charting stellar positions.

Working as an instrument maker for the court of William IV, Landgrave of Hesse-Kassel in Kassel[10] he played a pivotal role in developing the first astronomical charts. He invented logarithms as a working tool for himself for his astronomical calculations, but as a "craftsman/scholar" rather than a "book scholar" he failed to publish his invention for a long time.[6]

In 1592 Rudolf II, Holy Roman Emperor in Prague received from his uncle, the Landgrave of Hesse-Kassel, a Bürgi globe and insisted that Bürgi deliver it personally. From then on Bürgi commuted between Kassel and Prague, and finally entered the service of the emperor in 1604 to work for the imperial astronomer Johannes Kepler.[11]


The most significant artifacts designed and built by Burgi surviving in museums are:[12]

  • Several mechanized celestial globes (now in Paris [Conservatoire Arts et Metiers], Zuerich [Schweizerisches Landesmuseum], Kassel [Orangerie,2x,1580–1595] and Weimar [Herzogin Anna Amalia Bibliothek] )
  • Several clocks in Kassel, Dresden (Mathematisch Physikalischer Salon) and Vienna (Bergkristaluhr (incorporating a mechanised rock-crystal celestial globe) and a 'Planetenlaufuhr' at the Kunsthistorisches Museum)
  • Sextants made for Kepler (at the National Technical Museum in Prag)
  • The Mond-Anomalien-Uhr (a mechanical model of the irregularities of the motion of the Moon around the Earth)at the Orangerie in Kassel
  • Mechanized Armillary Sphere in Upsala (Sweden)

Bürgi as a mathematician[edit]

He constructed a table of what is now understood as antilogarithms[13] independently of John Napier, since his method is distinct from Napier's. Napier published his discovery in 1614, and this publication was widely disseminated in Europe by the time Bürgi published at the behest of Johannes Kepler. There is evidence[14] that Bürgi arrived at his invention as early as 1588, six years before Napier began work on the same idea. However, Buergi did not develop a clear notion of a logarithmic function and can therefore not be viewed as an inventor of logarithms.[15] Bürgi was also a major contributor to prosthaphaeresis, a technique for computing products quickly using trigonometric identities, which predated logarithms.

The lunar crater Byrgius is named in his honor.


  1. ^ Bürgi, Jost in German, French and Italian in the online Historical Dictionary of Switzerland.
  2. ^ Moritz Cantor (1876), "Burgi, Jobst", Allgemeine Deutsche Biographie (ADB) (in German) 3, Leipzig: Duncker & Humblot, pp. 604–606 
  3. ^ UB-Graz / Handschriftenkatalog / Katalogisat Nr.:560
  4. ^ Nicolaus Copernicus Gesamtausgabe: De revolutionibus: die erste deutsche Übersetzung in der Grazer Handschrift [1]
  5. ^ Jürgen Hamel: Die astronomischen Forschungen in Kassel unter Wilhelm IV. Mit einer wissenschaftlichen Teiledition der Übersetzung des Hauptwerkes von Copernicus 1586 (Acta Historica Astronomiae ; Vol. 2) Thun ; Frankfurt am Main : Deutsch, 1998; 2., korr. Aufl. 2002, 175 S., ISBN 3-8171-1569-5 (1. Aufl.), 3-8171-1690-X (2. Aufl.), Abb., 15 x 21 cm, kartoniert EUR 14,80 / sFr 23,10. Inhalt: HTML PDF
  6. ^ a b Jost Bürgi; by Ludwig Oechslin; Publisher: Verlag Ineichen, Luzern, 2001, 108 p.
  7. ^ Jost Bürgi als Künstler der Mechanik, Separatum Toggenburgerblätter für Heimatkunde 1982/Heft 34; by Johann Wenzel; Publisher: Toggenburgerblaetter
  8. ^ Jost Burgi 1552-1632, Horloger, Astronome & Mathematicien; by M.L. Defossez; Publisher: SSC, separate offprint of a 20 page biographic article on Jost Bürgi, first published in the 1943 Annual Bulletin of the Societe Suisse de Chronometrie
  9. ^ Lance Day and Ian McNeil, ed. (1996). Biographical dictionary of the history of technology. Routledge (Routledge Reference). p. 116. ISBN 0-415-06042-7. 
  10. ^ Die erste Sternwarte Europas,mit Ihren Uhren und Instrumenten, 400 Jahre Jost Buergi in Kassel, by Ludolf von Mackensen, Hans von Bertele & John H. Leopold; Publisher: Callwey Verlag; ISBN 3-7667-0875-9
  11. ^ Ralf Kern. Wissenschaftliche Instrumente in ihrer Zeit/Vol. 1: Vom Astrolab zum mathematischen Besteck. Cologne, 2010. p. 393. ISBN 978-3-86560-865-9
  12. ^ Jost Buergi - Kepler und der Kaiser - Instrumentenbauer, Astronom, Mathematiker 1552-1632 -- Jost Buergi - Kepler and the Emporer- Clockmaker, Astronomer, Mathematician 1552-1632 (in German) ISBN 978 3 03823 898 0 -- (Jost Buergi - Kepler and the Emporer- Clockmaker, Astronomer, Mathematician 1552-1632)
  13. ^ Jost Bürgi, Arithmetische und Geometrische Progress Tabulen … [Arithmetic and Geometric Progression Tables … ], (Prague, (Czech Republic): University [of Prague] Press, 1620). Available on-line at: Bavarian State Library, Germany
    Unfortunately, Bürgi did not include, with his table, instructions for using the table. That was published separately. The contents of that publication were reproduced in: Hermann Robert Gieswald, Justus Byrg als Mathematiker, und dessen Einleitung zu seinen Logarithmen [Justus Byrg as a mathematician, and an introduction to his logarithms] (Danzig, Prussia: St. Johannisschule, 1856), pages 26 ff.
  14. ^ Florian Cajori, "Algebra in Napier's Day and Alleged Prior Inventions of Logarithms," p. 93 of Napier Tercentenary Memorial Volume, ed. Cargill Gilston Kontt. Longmans, Green and Company (London) (1915)
  15. ^ e:The story of a Number, by Eli Maor. page 14. Princeton University Press (Princeton, New Jersey) (1994) ISBN 0-691-05854-7

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