Jost Bürgi, or Joost, or Jobst Bürgi (February 28, 1552, Lichtensteig, Switzerland – January 31, 1632), active primarily at the courts in Kassel and Prague, was a Swiss clockmaker, a maker of astronomical instruments and a mathematician.
Jost Bürgi is widely considered one of the most innovative and most skillful 'mechanics' of his era. It has been suggested that he should also be counted among the leading astronomers of his time because his unprecedented ability to design and construct mechanical models of the movement of heavenly bodies proves an advanced level of insight into celestial mechanics. His classification as a scholar is controversial because he lacked a formal education and did not know Latin, the only language of scholarly publications at the time. 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".
He left few written records of his work. However other historians of science claim that Bürgi's legacy of many unique and innovative mechanical astronomical models should be considered an unorthodox method of 'publishing' astronomical insights. During his years in Praha he worked closely with the astronomer Johannes Kepler at the court of Rudolf II.
Bürgi as a clockmaker
It is undocumented where he learned his clockmaking skills, but eventually he became the most innovative clock and scientific instrument maker of his time. 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. 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 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.
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.
The most significant artifacts designed and built by Burgi surviving in museums are:
- Several mechanized celestial globes (now in Paris, Zuerich (Schweizerisches Landesmuseum), Stuttgart (Wurttembergisches Landesmuseum) and Kassel (Orangerie,2x,1580–1595) )
- Several clocks in Kassel, Dresden (Mathematisch Physikalischer Salon) and Vienna (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)
Bürgi as a mathematician
He invented logarithms 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 that Bürgi arrived at his invention as early as 1588, six years before Napier began work on the same idea. By delaying the publication of his work to 1620, Bürgi lost his claim for priority in historic discovery. Bürgi was also a major contributor to prosthaphaeresis, a technique for computing products quickly using trigonometric identities, which predated logarithms.
- UB-Graz / Handschriftenkatalog / Katalogisat Nr.:560
- Nicolaus Copernicus Gesamtausgabe: De revolutionibus: die erste deutsche Übersetzung in der Grazer Handschrift 
- 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
- Jost Bürgi; by Ludwig Oechslin; Publisher: Verlag Ineichen, Luzern, 2001, 108 p.
- Jost Bürgi als Künstler der Mechanik, Separatum Toggenburgerblätter für Heimatkunde 1982/Heft 34; by Johann Wenzel; Publisher: Toggenburgerblaetter
- 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
- Lance Day and Ian McNeil, ed. (1996). online preview: Biographical dictionary of the history of technology. Routledge (Routledge Reference). p. 116. ISBN 0-415-06042-7.
- 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
- Ralf Kern. Wissenschaftliche Instrumente in ihrer Zeit/Vol. 1: Vom Astrolab zum mathematischen Besteck. Cologne, 2010. p. 393. ISBN 978-3-86560-865-9
- 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)
- e:The story of a Number, by Eli Maor. page 14. Princeton University Press (Princeton, New Jersey) (1994) ISBN 0-691-05854-7
- Bürgi, Jost from Oliver Knill History pages
- Bürgi's Progress Tabulen (1620): logarithmic tables without logarithms from LOCOMAT The Loria Collection of Mathematical Tables
- Jost Bürgi from the MacTutor History of Mathematics archive