499:, through a method 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. Bürgi may have constructed his table of progressions around 1600, but Bürgi's work is not a theoretical basis for logarithms, although his table serves the same purpose as Napier's. One source claims that Bürgi did not develop a clear notion of a logarithmic function and can therefore not be viewed as an inventor of logarithms. Bürgi's method is different from that of Napier and was clearly invented independently.
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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
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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.
314:, 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
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of sines are obtained after few iterations. Only recently, Folkerts et al. proved that this simple process converges indeed towards the true sines. Another of Buergi's algorithms uses differences in order to build up a table, and this was an anticipation of the famous
507:(1627): "... as aids to calculation Justus Byrgius was led to these very logarithms many years before Napier's system appeared; but being an indolent man, and very uncommunicative, instead of rearing up his child for the public benefit he deserted it at birth."
221:, 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
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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
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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,
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Jost Bürgi – Kepler und der Kaiser – Instrumentenbauer, Astronom, Mathematiker 1552-1632 – Jost Bürgi – Kepler and the
Emperor – Clockmaker, Astronomer, Mathematician 1552–1632 (in German)
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753:; 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
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had parts which were not as accurate as it was claimed). An introduction to some of Bürgi's methods survives in a copy by Kepler; it discusses the basics of
Algebra (or
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453:. Nothing more is known on this table, and some authors have speculated that its range was only over 45 degrees. Such tables were extremely important for
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Although an autodidact, he was already during his lifetime considered as one of the most excellent mechanical engineers of his generation. His employer,
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Die astronomischen
Forschungen in Kassel unter Wilhelm IV. Mit einer wissenschaftlichen Teiledition der Übersetzung des Hauptwerkes von Copernicus 1586
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474:. The final cell's value is divided by two, and the next iteration starts. Finally, the values of the last column get normalized. Rather accurate
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Iterative table calculation through Bürgi's algorithm essentially works as follows: cells sum up the values of the two previous cells in the same
273:), which was supposedly very accurate, but since the table itself is lost, it is difficult to be sure of its real accuracy (for instance,
289:. His legacy also includes the engineering achievement contained in his innovative mechanical astronomical models. During his years in
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at sea. Johannes Kepler called the Canon Sinuum the most precise known table of sines. Bürgi explained his algorithms in his work
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Ralf Kern. Wissenschaftliche
Instrumente in ihrer Zeit/Vol. 1: Vom Astrolab zum mathematischen Besteck. Cologne, 2010. p. 393.
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as it was known at the time), and of decimal fractions. Some authors consider Bürgi as one of the inventors of
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652:(Acta Historica Astronomiae; Vol. 2) Thun; Frankfurt : Deutsch, 1998; 2., korr. Aufl. 2002, 175 S.,
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Menso
Folkerts, Dieter Launert, Andreas Thom (Oct 2015). "Jost Bürgi's Method for Calculating Sines."
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660:(1. Aufl.), 3-8171-1690-X (2. Aufl.), Abb., 15 x 21 cm, kartoniert EUR 14,80 / sFr 23,10. Inhalt:
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Jost Bürgi als Künstler der
Mechanik, Separatum Toggenburgerblätter für Heimatkunde 1982/Heft 34
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Die erste
Sternwarte Europas, mit Ihren Uhren und Instrumenten, 400 Jahre Jost Buergi in Kassel
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Mechanised Celestial Globe, made 1594 in Kassel, now at Schweizerisches Landesmuseum in Zurich
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Williams, Mike (1980). "Invention of logarithm tables eased the workload in computation".
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A mechanical model of the irregularities of the motion of the Moon around the Earth (
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in Vienna including one that incorporates a mechanised celestial globe made of
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Staudacher, F., 2014. Jost Bürgi, Kepler und der Kaiser. Verlag NZZ, Zürich.
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De revolutionibus: die erste deutsche Übersetzung in der Grazer Handschrift
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599:(in German), vol. 3, Leipzig: Duncker & Humblot, pp. 604–606
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Justus Byrg als Mathematiker, und dessen Einleitung zu seinen Logarithmen
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The most significant artifacts designed and built by Bürgi surviving in
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Clark, Kathleen (2015). "A Brief Biography of Jost Bürgi (1552–1632)".
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Bürgi's Progress Tabulen (1620): logarithmic tables without logarithms
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Lorraine Research Laboratory in Computer Science and its Applications
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Bürgi constructed a table of progressions what is now understood as
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Jost Bürgi's Aritmetische und Geometrische Progreß Tabulen (1620)
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Jost Burgi 1552-1632, Horloger, Astronome & Mathematicien
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into German for Bürgi. A copy of the translation survived in
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wrote about Bürgi's logarithms in the introduction to his
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946:. Canadian Information Processing Society. p. 18.
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Biographical dictionary of the history of technology
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UB-Graz / Handschriftenkatalog / Katalogisat Nr.:560
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LOCOMAT The Loria Collection of Mathematical Tables
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158:Medal issued on the 350th anniversary of his death
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318:to start accurately charting stellar positions.
893:Arithmetische und Geometrische Progress Tabulen
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369:Several clocks at the Orangerie in Kassel, the
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261:In 1604, he entered the service of emperor
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258:, it is thus called "Grazer Handschrift".
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240:praised Bürgi as a "second Archimedes" (
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763:Lance Day and Ian McNeil, ed. (1996).
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362:in Kassel (2 pcs., 1580–1595) and the
269:. Bürgi constructed a table of sines (
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433:By 1586, Bürgi was able to calculate
234:William IV, Landgrave of Hesse-Kassel
773:(Routledge Reference). p. 116.
573:Historical Dictionary of Switzerland
251:De Revolutionibus Orbium Coelestium
242:quasi indagine Archimedes alter est
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1055:17th-century Swiss mathematicians
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858:Roegel, Denis (10 January 2013).
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371:Mathematisch-Physikalischer Salon
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429:Bürgi's work on trigonometry
412:) at the Orangerie in Kassel
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716:10.1007/978-1-4939-3161-3_1
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364:Duchess Anna Amalia Library
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52:Lichtensteig, Toggenburg
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977:Quotations related to
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373:in Dresden and the
346:Several mechanized
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481:Tables du cadastre
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725:978-1-4939-3160-6
505:Rudolphine Tables
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150:in Stockholm
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943:CIPS Review
873:. p. 7
550:Bürgi, Jost
497:John Napier
451:arc seconds
415:Mechanized
238:Tycho Brahe
111:mathematics
1029:Categories
979:Jost Bürgi
967:Jost Bürgi
877:30 January
694:Jost Bürgi
455:navigation
439:algorithms
316:telescopes
312:remontoire
310:, and the
295:astronomer
287:logarithms
223:Strasbourg
211:Toggenburg
191:clockmaker
163:Jost Bürgi
90:Logarithms
67:1632-02-01
45:1552-02-28
23:Jost Bürgi
771:Routledge
589:(1876), "
467:in 1592.
465:Rudolf II
403:in Prague
366:in Weimar
360:Orangerie
325:In 1592,
263:Rudolf II
171:Latinized
921:Eli Maor
613:Archived
443:Kunstweg
397:Sextants
173:surname
107:Horology
567:Italian
523:Byrgius
340:museums
179:Byrgius
175:Burgius
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379:quartz
291:Prague
187:Prague
183:Kassel
165:(also
103:Fields
75:Kassel
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987:from
919:, by
863:(PDF)
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529:Notes
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435:sines
342:are:
334:Works
142:with
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879:2018
834:ISBN
818:ISBN
802:ISBN
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662:HTML
654:ISBN
564:and
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515:The
283:Coss
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201:Life
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60:Died
38:Born
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