Jost Bürgi
Jost Bürgi (according to his portrait also Jobst Bürgi; born February 28, 1552 in Lichtensteig / Toggenburg , † January 31, 1632 in Kassel ) was a Swiss watchmaker , instrument inventor, mathematician and astronomer .
introduction
For centuries, Jost Bürgi was primarily known as the builder of the first astronomical second clock, as the manufacturer of precise celestial globes , as a designer of scientific measuring devices and as a co-inventor of the logarithms . Now, a manuscript written by him in 1587/92, discovered by Menso Folkerts and commented on and edited by Dieter Launert, shows that he is also the inventor of the astronomical difference calculation, unique algebraic algorithms for determining sine and recursive polynomial table generation. Often mistakenly portrayed as an employee of Johannes Kepler, he was, in fact, hierarchically, as an imperial court watchmaker, on an equal footing with the imperial mathematician Kepler. During their eight years of joint employment in these functions from 1604 to 1612 at the imperial court of Rudolf II in Prague, Johannes Kepler benefited from Jost Bürgi's mathematical innovations, astronomical data and instruments, while Kepler edited the Coss algebra manuscript for him, also in silence.
Three phases shape the life of Jost Bürgi: the still largely undocumented phase of childhood, youth, training and waltzing of Jost Bürgi, who was born in Lichtensteig in Toggenburg, and which lasts until the age of 28; second, Jost Bürgi's activity as a court clockmaker at the royal court of Hesse-Kassel (1579–1604, employed by Landgrave Wilhelm IV of Hesse-Kassel ), where he created his authoritative works, for a good quarter of a century ; and thirdly another quarter of a century at the imperial court in Prague (1604–1630, employed by Emperor Rudolf II) during which he supported Johannes Kepler for eight years and from there returned to Kassel in 1631, a year before his death. The discovery of a hitherto unknown manuscript “Fundamentum Astronomiae” puts Jost Bürgi scientifically in line with his contemporaries Galileo Galilei and Johannes Kepler as well as Tycho Brahe , whose accuracy he exceeded.
On behalf of Landgrave Wilhelm IV, the watchmaker Bürgi also observed the stars at the Kassel observatory , one of the first permanent facilities of this type in Europe, from 1584 together with the court mathematician Christoph Rothmann . Even before he joined, Bürgi had to maintain the measuring instruments and, of his own accord, also improved their construction . The newly designed devices included clocks, models of the cosmos such as his lost planetary globes and famous celestial globes (as the predecessors of the planetarium ) as well as new measuring instruments such as the first metal sextant, a universal reduction circle, a triangular instrument and a device for drawing perspective.
What distinguishes Jost Bürgi from all other manufacturers of celestial globes and from all contemporaries is his ingenious mathematical and technical universality, which is unparalleled in the history of science, astronomy, mathematics and instruments. He collected the astronomical data himself and developed innovative instruments such as the metal sextant and the observatory clock accurate to the second for measuring celestial bodies using the horizontal method. Then he calculated the spherical positions of the celestial bodies from the observation data with mathematical methods of logarithm computation developed by himself and the algorithms he created for determining the sine and the difference computation with unmatched accuracy and efficiency. He transferred these data in the form of 1026 star positions with arc minute precision to his small, 14.2 cm diameter celestial globe from 1594, which showed its owner the current starry sky at any time of the day or night and also the position of the sun as well as the date, time, the weekday and church holiday names with automated leap year adjustment. Thanks to the slip clutch he invented, the user could also set any point in time of the past and future at any time and view and calculate the astronomical past and future constellations without influencing the current functions.
With his Artificium Kunstweg table, Bürgi's most important mathematical achievements include the invention of the difference calculation and the subsequent creation of a sine table progressing from 2 to 2 arc seconds ("Canon Sinuum", lost after 1592), as well as the world's first compilation of a logarithm table ("Arithmetic and geometric progress bars ... “, print 1620). In the manuscript “Fundamentum Astronomiae” (handed over to Emperor Rudolph II in 1592), Bürgi explains his “Kunstweg”, a completely new algebraic way of calculating sine values with a rapidly converging algorithm in which he only needs additions and halves; and it gives a sine table with a step size of 1´. Henry Briggs was familiar with Bürgi's method in Oxford around 1620. The discovery of logarithms is attributed to Bürgi independently of John Napier and, according to Kepler, took place many years before Napier. He published his discovery later than Napier.
In 1585, Bürgi constructed a clock with three hands for Landgrave Wilhelm IV in Kassel, which indicated hours, minutes and seconds. It is true that clocks with second hands existed earlier - by 1560 at the latest - but for the Kassel clock the detailed scientific use of these new clocks with high display accuracy is archivally tangible for the first time. In addition to this special clock and the many scientific instruments, Bürgi also manufactured other devices that were exhibited in the art and curiosity chamber of the Landgrave of Hesse. For example, there was a large copper celestial sphere and an astronomical clockwork set up according to the Ptolemaic worldview . The heliocentric Copernican view of the world is already shown in his moon and sun equation clock from 1591.
Since Bürgi had hardly any knowledge of Latin, Nicolaus Reimers ( Ursus ), a friend of Bürgi, prepared a German translation of Copernicus' De revolutionibus orbium coelestium for Bürgi between 1586 and 1587 at the court of Landgrave Wilhelm IV , which has been preserved as a so-called Graz manuscript . This is considered to be the first German translation of Copernicus' main work, three centuries before that of Menzzer, which was printed in 1879.
Life
Bürgi's career up to his employment as court clockmaker and astronomer of Landgrave Wilhelm IV of Hessen-Kassel is hardly known. We know almost nothing about Bürgi's youth and training. He probably learned the silversmith's craft from the gold and silversmith David Widiz, who moved from Augsburg to Lichtensteig in 1567/68, after which he probably received a watchmaker's training in Winterthur or Schaffhausen and learned more likely in Augsburg and certainly in Nuremberg. Bürgi did not attend any secondary school and was ignorant of Latin. It is doubted today that he worked with Josias and Isaak Habrecht in Strasbourg on the second Strasbourg cathedral clock . His as yet unknown talent was discovered by the astronomer-landgrave Wilhelm IV of Hessen-Kassel, who had studied in Strasbourg for a time. He acquired his mathematical knowledge partly self-taught, as others suspect in Strasbourg a. a. with the Swiss mathematician Konrad Dasypodius , as well as his technical and technical perfection probably on the rolling in Augsburg and Nuremberg . A stay in Italy in Milan , Florence or Cremona can not be ruled out .
Bürgi's appointment on July 25, 1579 in Kassel is the first document from his life that has been preserved. The coat of arms with which the 27-year-old sealed his appointment is astonishing . Opposite his family coat of arms, an owl, Bürgi independently added his initials, the half cogwheel as a symbol of his profession and two stars, as if he wanted to programmatically symbolize his inward turn to astronomy. In 1591 Bürgi was naturalized in the city of Kassel, where, according to a list of houses from 1605, he bought a house in Graben. In his first marriage he was married to the daughter of David Bramer, who was pastor in Felsberg near Kassel, in 1611 he married Catharina Braun. Both marriages remained childless. In 1591 he took his young orphaned brother-in-law Benjamin Bramer in as a foster son and trained him in mathematics. Bramer's surveying writings contain many valuable information about Bürgi's inventions.
In February 1592, Emperor Rudolf II in Prague asked his uncle in Kassel to personally deliver a mechanical Bürgi globe including planetary movements from the builder. Bürgi was able to hand over the special planetary globe in a personal audience with the emperor on July 4, 1592 (according to the old calendar) and a few weeks later to submit his book manuscript Fundamentum Astronomiae, which contains the solution to his artificium. When Bürgi returned to Kassel, the astronomer-landgrave Wilhelm the Wise had died on August 25, 1592, and Bürgi became his son and successor Moritz the Scholar on January 1, 1593 (old Julian calendar) on the same terms and with roughly the same wording newly ordered. In 1596 and 1604 Bürgi traveled again to Prague for repair work. On December 23, 1604, at the request of the emperor and with the consent of Landgrave Moritz, he entered the service of the emperor and was given a workshop with two assistants at Prague Castle. There he also worked for the imperial astronomer Kepler and made his novel mathematical methods such as logarithm and difference calculation and his much more accurate metal instruments available to him, as well as his much more accurate Mars planetary and fixed star data. In return, Johannes Kepler edited Bürgi's manuscript on Coss algebra, which was only edited and published in 1974. Bürgi, in turn, realized the prototype of the gear pump he had invented for Kepler , which is used for draining mine tunnels (and is still used in many ways today, e.g. in car engines). After the death of his first wife in 1609 as well as in 1614 and 1617, Bürgi was again in Kassel for a long time, where he had obviously only been on leave. He then went back to Prague, where, according to his own words, he made his most perfect clock in the years 1622–1627 with the crystal globe clock exhibited today in the Vienna Kunstkammer. In the middle of the Thirty Years' War he decided to finally return to Kassel around 1631. He died here on January 31, 1632.
The following entry can be found in the Martinskirche's book of the dead :
"Anno domini 1632. Jost Burgi von Liechsteig from Switzerland, a clockmaker in his art, but in experience [according to] a famous (at the imperial court and princely court) astronomer and godly man, aetis 81 anno."
Factory as an instrument maker
When Bürgi came to Kassel, the very important clockmaker Ebert Baldewein had been working there for about 20 years , who had built two mechanically very important planetary clocks (the one completed in 1561 is still in the Astronomical-Physical Cabinet in Kassel), the one from 1568 for Elector August von Sachsen, today in the Mathematisch-Physikalischer Salon Dresden . In addition, Baldewein produced a large, stand-alone celestial globe in 1575, which was the first of its kind to be operated by a clock mechanism located inside the globe. When Bürgi began his activity in Kassel in 1579, the status of watchmaking was already astonishingly high if you compare it with that of 100 years earlier.
If one compares the Bürgi globes with those of Baldewein, the latter can undoubtedly be recognized as the essential starting point for the Bürgi globes, but at the same time, very strong progress can be seen immediately. Bürgi did not only gradually grow into the high art of watchmaking and mechanics at Baldewein, but entered with considerable experience and strong own ideas. It can therefore be assumed that the young Bürgi was inspired by the best watchmakers of his time, such as B. from Nuremberg's Christian Heiden and Gianello Torriano (1500–1585) from Cremona. As the latest research shows, he was in Nuremberg in 1576 to complete the gilded terrestrial and celestial globe of the recently deceased Christoph Heiden.
The first clock from 1585 built entirely by Bürgi therefore already has many peculiarities: in terms of the design of the iron movement, as well as in the shape and finally in the execution, little can be compared to what was otherwise common in southern and central Germany at the time Determine the construction. It is something different from the works of the smaller and larger table clocks that were built in the second half of the 16th century by Baldewein, Habrecht in Strasbourg, Imbser in Tübingen, Gruber in Nuremberg or Fobis in Lyon. What is particularly noticeable are the very unusual movement body and the uniquely large, particularly delicate, iron gears of the movement . This shows a unique, new engineering conception of the transmission: Reduction of the wheel mass, regularity of the tooth pitch and shape, furthermore the best centering and balancing. But Bürgi's watches have other special features: an intermediate winding device (remontoir d'égalité), which makes it possible to completely compensate for the unequal driving effect of the spring, spring drive for three months, ordinary-beat escapement , seconds hand. With his designs, Bürgi was 100 to 150 years ahead of his time.
In addition to celestial globes and clocks, Bürgi also built various interesting new and improved types of instruments. With them and with special surveying instruments , he displayed a wealth of inventiveness and precision that made his products far beyond the standard of his time.
For example, he is considered to be the rediscoverer of the reduction circle already used in antiquity . The reduction circle , further developed by Fabrizio Mordente , Federigo Commandino and Galileo Galilei into the proportional circle, is used to divide, enlarge or reduce distances in a certain ratio . It can also be used to divide the circumference into equal parts. In addition, various special constructions can be made, such as the division of a line according to the golden ratio or the " squaring of the circle " (ie the construction of a square that is equal in area to a given circle).
The reducer consists of two legs that are connected by a movable adjusting screw (usually with a vernier ). It has two points at each end. One pair is used to pick up the initial dimension, the second to knock off the size to be constructed. With precisely manufactured devices, an accuracy of ± 0.1 mm can be achieved.
For a triangular instrument (range finder) from 1592 he received a patent in 1602. The use of this instrument was not published until 1648 by his brother-in-law Benjamin Bramer. The use of the triangular instrument to find inaccessible locations N of the enemy: In an easily accessible place, insert the instrument and point the movable side D on the left towards N. Then move the device to the right so that AB remains in the same line as before and then also set the right side with the Bussole to N, and get the triangle AEV in the device, which is similar to the large triangle with N as the vertex. The distance you are looking for results immediately from the measured distance between the two observation points.
Another, different kind of instrument, a perspective drawing device, is preserved in Kassel and in the Kunsthistorisches Museum in Vienna (fragments). In the art chamber of this museum, near the bronze bust of Emperor Rudolf II von de Vries, two of his clocks made in Prague are exhibited: in addition to the planet clock from 1605, his rock crystal clock containing the smallest celestial globe, which he himself considered to be his masterpiece. Jost Bürgi was not only a watchmaker and instrument maker at the Kassel observatory, but also grew more and more into the role of astronomer and mathematician, a role that Bürgi already had , in his own studies and in cooperation with Nicolaus Reimers as well as in competition with the actual court mathematician Rothmann In 1586/87 he invented the first difference calculation with his Artificium (Kunstweg) . Apparently there had been jealous rivalries between these two particularly favored employees of the sovereign, so that Rothmann did not return to Kassel after a visit to Tycho Brahe in 1590, and Buergi's biographer Fritz Staudacher suspected the disclosure of confidential Bürgi information as the main reason. Ultimately, Bürgi also introduced himself to the history of astronomy as an observer with his own series of measurements of the moon, sun and Mars and through the discovery of new stars, which shows the universality of the great engineer Bürgi in all its breadth.
There are several treatises on his work :
- The mechanical instruments collated by the geographer and mathematician Levinus Hulsius
- In 1648, Bürgi's brother-in-law , the mathematician Benjamin Bramer, published a "Report by M. Jobsten Burgi Geometric Triangular Instrument" as an appendix to his work "Apollonius Cattus or Kern der gantzen Geometria". Bürgi received a patent in 1592 for this invention , which expanded triangulation to include a distance measurement .
- The third treatise "The Mechanical Instruments" by Levinus Hulsius (1604/5) introduces the use of Bürgi's reduction circles . It is used to enlarge or reduce constructions or maps by using route conditions, as the pantograph did later (somewhat more economically) .
Mathematical work
As an abstract scientist, Napier is entitled to set up one of the first logarithm tables (more precisely an antilogarithm table). For calculations of his models and astronomical measurements, Bürgi first created very precise sine tables according to Kepler following Peuerbach , which according to Bramer progressed at intervals of 2 arc seconds, but has not been preserved (apart from a foreword in Kepler's estate), and he developed like others In the mid-1580s, contemporary mathematicians continued to use a method called prostaphairesis to facilitate multiplication based on trigonometric identities. He developed his logarithm tables after Kepler's (in a remark in his Rudolfinische Tafeln from 1627) and Bramer's testimony before 1610, i.e. before Napier's first publication (1614). Sometimes the discovery is dated to 1588 after a remark by Reimarus (Ursus) that Bürgi had a method to simplify calculations.
Napier had made his logarithm method known through the publication of a manual (1614) and became famous as the "inventor of the logarithms". Jost Bürgi, on the other hand, had "put his light under a bushel" and not published it for a long time, although Kepler urged him to do so. When he finally did so in 1620 (“Arithmetic and Geometric Progress Tabules, sambt thorough instruction how such should be used and understood useful in all sorts of calculations”), he published only the tables without instructions (this only appeared in 1856) and the few in Copies printed in Prague were also largely victims of the beginning Thirty Years' War. Kepler, who had known Bürgi's logarithms since 1603, but had to remain silent about them, enthusiastically received Napier's logarithms when they became known to him in 1617 and dedicated his ephemeris from 1620 to him. The reason for Bürgi's hesitant attitude to publications is believed to be that He was considered uneducated by the standards of his time due to a lack of knowledge of the scientific language of the time, Latin, and was therefore insecure. Bürgi was a mechanic, a practitioner who converted his mathematical and astronomical knowledge into practical calculation methods (logarithms) or into highly complex mechanical models (for astronomical knowledge) and not into books.
Bürgi did not have a special name for the logarithms, which he represented consistently as red numbers, in contrast to the black numbers for the associated number. In the construction of the panels he proceeded similarly to Napier. The starting point was the comparison of geometrical and arithmetic sequences, known since Michael Stifel and others, which had to be done much more precisely for practical applications in the tables. The number belonging to the nth digit of the arithmetic sequence (the logarithm) resulted as:
a large prefactor was chosen to avoid decimal places. Voellmy points out that this implicitly leads to a base that is close to Euler's number , the base of the natural logarithms. In his table there were 23,030 entries on 58 pages with the logarithms n of the numbers (the value corresponded to the unit and thus n = 0) to . The logarithms were plotted on the edge (red numbers, each with a factor of 10), the associated numbers (black numbers) in the rows and columns, each with eight significant digits for the numbers. The arrangement is therefore the reverse of conventional logarithm tables. In a text that was printed much later, he also gave explanations on interpolation and use, for example how to pull cube roots with the blackboard.
As a calculator and an innovative mathematician, he introduced a decimal point and handled decimal fractions. Not only did the imperial mathematician Nicolaus Reimers call him a combination of Archimedes and Euclid and his teacher, but Jost Bürgi was also held in high regard by Kepler. Apart from Bürgi's foster son Benjamin Bramer, both were the only ones who saw Jost Bürgi's mathematical methods and were able to use them, bound by a vow of silence. That he published only one of his four works on mathematics late and without printed instructions for use in the midst of the war raging in Prague (1620: "Progresstabulen"), but not the other three manuscripts, is not so much of a concern for Bürgi's biographer Fritz Staudacher Dyslexia and the brief visit to the Lichtensteiger village school, but rather to the omnipresence of the noble, highly educated Tycho Brahe, who was very conscious of his ancestry. Brahe was known to be contentious and irascible, but enjoyed imperial protection in Prague because he himself censored Kepler's major works through his heirs. He had also fallen out with Bürgi's friend Nicolaus Reimers, which put a strain on his last years. The three manuscripts written by Jost Bürgi but kept secret from Brahe are: the Canon Sinuum of 2 ″ increments with eight digits, which has been lost to this day but has been attested by Kepler and Bramer; the "Bürgi Coss" found in Kepler's estate and edited by him in 1603, a guide to algebra (Coss) by Bürgi, which was only published in 1973; and thirdly, the “Fundamentum astronomiae” with the first astronomical difference calculus, the Sinus Art Path for algebraic, very efficient and precise determination of the sine, as well as the one written by Jost Bürgi in 1586/92, only discovered by Menso Folkerts in 2013 and transcribed, annotated and edited by Dieter Launert in 2016 recursive polynomial generation and interpolation of tables, the Henry Briggs methods and, according to Denis Roegel, the methods of Isaac Newton , de Prony and Charles Babbage anticipate decades and even centuries. In the third and fourth editions of his Bürgi biography, Staudacher discusses whether and how these Bürgi methods and algorithms, which have not become known on the continent, were brought to the knowledge of Henry Briggs and has not been conclusively clarified. At the 2nd International Jost-Bürgi-Symposium 2018 in Lichtensteig, Jürgen Hamel presented another manuscript, which Jost Bürgi had signed for Count Simon zur Lippe in 1598 and which identifies him as a metallurgist and on his training as a goldsmith or silversmith closes.
Honor
The lunar crater Byrgius and the asteroid (2481) Bürgi are named after him. In Kassel the Bürgistraße in the Wesertor district is named after him, in Berlin-Lichterfelde the Bürgipfad. In his home town of Lichtensteig, the Bürgistrasse is also named after him.
literature
- Volker Bialas , Martha List : Die Coss by Jost Bürgi in the editorial department of Johannes Kepler, A contribution to early algebra , Nova Kepleriana, Neue Reihe, Heft 5, Verlag der Bayerischen Akademie der Wissenschaften, 1973
- Moritz Cantor : Burgi: Jobst B. In: General German Biography (ADB). Volume 3, Duncker & Humblot, Leipzig 1876, pp. 604-606.
- Kathleen Clark: Jost Bürgi's Aritmetic and Geometric Progreß Tabulen (1620). Edition and Commentary , Birkhäuser 2015
- Menso Folkerts / Dieter Launert / Andreas Thom : Jost Bürgi's method for calculating sines. Historia Mathematica 43, 2016, pp. 133-147.
- Jürgen Hamel : Not just the stars. The discovery of completely new facets. Jost Bürgi: From probing and melting of metals (1598) , 2. Intern. Jost Bürgi Symposium, Lichtensteig, April 14, 2018
- Dieter Launert: Sinus table rediscovered - Bürgi's “Art Path” deciphered . In: Mitteilungen der DMV , Volume 24, 2/2016, pp. 89–94.
- Dieter Launert: Bürgis Kunstweg in the Fundamentum Astronomiae - deciphering his riddle. Nova Kepleriana New Episode 141, Munich 2015.
- Hans Loeffel, Johann Wenzel, Armin Müller: The mathematical work of Jost Bürgis . In: Jost Bürgi, 1552–1632 , presentations at an evening party at the St. Gallen University of Economics and Social Sciences on January 21, 1982 (= Toggenburger Blätter für Heimatkunde, issue 34), Wattwil 1985, OCLC 782061377 .
- Heinz Lutstorf: The logarithm table Jost Bürgis , Series A (History of Science) of the ETH Library, Volume 3, 2005
- Heinz Lutstorf, Max Walter: Jost Bürgis Progress-Tabulen (logarithms) , publication series of the ETH-Bibliothek, volume 28, 1992.
- Ludolf von Mackensen: The first observatory in Europe with its instruments and clocks. 400 years of Jost Bürgi in Kassel , Callwey Verlag, Munich 1979 (exhibition catalog)
- Erwin Neuenschwander : Bürgi, Jost. In: Historical Lexicon of Switzerland .
- Luboš Nový: Bürgi, Joost . In: Charles Coulston Gillispie (Ed.): Dictionary of Scientific Biography . tape 2 : Hans Berger - Christoph Buys Ballot . Charles Scribner's Sons, New York 1970, p. 602-603 .
- Ludwig Oechslin: Jost Bürgi , biography, Ineichen, Luzern 2001, OCLC 80426641
- Denis Roegel: A preliminary note on Bürgi's computation of the sine of the first minute . 2016 ( online ).
- Helmut Stalder: Jost Bürgi. With him the modern age begins to tick. In: Helmut Stalder, Misunderstood Visionaries. 24 Swiss life stories , NZZ Libro , Zurich 2011, ISBN 978-3-03823-715-0 , pp. 193–199.
- Fritz Staudacher: Jost Bürgi, Kepler and the Kaiser. Watchmaker, instrument maker, astronomer, mathematician, ore metallurgist (1552–1632) . Biography. 1st edition 2013. 4th revised and expanded edition with a contribution by the Artificium discoverer Menso Folkerts. 320 pages. NZZ Libro, Zurich 2018, ISBN 978-3-03810-345-5 .
- Fritz Staudacher: The Bürgi-007-Paradox . In: Toggenburger Jahrbuch 2017. pp. 115–130. Toggenburger Verlag Schwellbrunn 2016.
- Fritz Staudacher: Most important mathematician of the early modern period . VSMP Bulletin, September 2016, pp. 34-39.
- Erwin Voellmy: Jost Bürgi and the logarithms , in: Supplements to the journal "Elements of Mathematics" , Volume 5 (1948) digitized
- Jörg Waldvogel: Jost Bürgi and the discovery of the logarithms (= elements of mathematics , volume 69) (2014), pp. 89–117.
- Ernst Zinner : Bürgi (Burgi, Borgen, Byrgius), Jost (Justus). In: New German Biography (NDB). Volume 2, Duncker & Humblot, Berlin 1955, ISBN 3-428-00183-4 , p. 747 ( digitized version ).
Web links
- Publications by and about Jost Bürgi in the Helveticat catalog of the Swiss National Library
- Literature by and about Jost Bürgi in the catalog of the German National Library
- Brief portrait of Jost Bürgi of the ETH-Bibliothek, with an illustration of the reduction circle
- Fritz Staudacher: Jost Bürgi didn't just invent the second . Swiss Physical Society
- Table clock , Staatliche Kunstsammlungen Dresden
- Triangular instrument from 1609 in the Astronomical-Physical Cabinet Kassel
- George Szpiro: An “artificial way” for calculating sine values . In: NZZ , January 29, 2016, p. 40; accessed on February 3, 2016; There also comments and on February 26th as a letter to the editor from Johannes Thomann a reference to the sine calculation by Ghiyath ad-Din al-Kashi, † 1429 .
- Websites from Staudacher zu Bürgi
- Jost Bürgi Symposium, Lichtensteig 2018
- Spektrum.de: Jost Bürgi (1552–1632) January 1, 2017
Individual evidence
- ↑ Ralf Kern: Scientific instruments in their time . Volume 1: From astrolabe to mathematical cutlery . Walther König, Cologne 2010. p. 384.
- ^ UB-Graz / manuscript catalog / catalog number: 560
- ↑ Nicolaus Copernicus Complete Edition : De revolutionibus: the first German translation in the Grazer handwriting ( limited preview in the Google book search)
- ↑ Jürgen Hamel : The astronomical research in Kassel under Wilhelm IV. With a scientific partial edition of the translation of the main work of Copernicus 1586 (Acta Historica Astronomiae; Vol. 2) Thun; Frankfurt am Main: German, 1998; 2., corr. Edition 2002, ISBN 3-8171-1569-5 (1st edition), 3-8171-1690-X (2nd edition), 175 pages, illustrations, 15 × 21 cm, paperback. Content: HTML DNB (PDF)
- ^ Fritz Staudacher: Jost Bürgi, Kepler and the Kaiser . Zurich 2016, p. 55.
- ^ Ludolf von Mackensen : Europe's first observatory with its instruments and clocks: 400 years of Jost Bürgi in Kassel . Callwey, Munich 1988, ISBN 978-3-7667-0875-5 .
- ↑ Voellmy, Bürgi and the Logarithms, Elements of Mathematics, p. 13
- ↑ HR Gieswald: Justus Byrg as a mathematician and its introduction to its logarithms , Danzig in 1856, according to one obtained in Danzig manuscript. On-line
- ^ Ludwig Oechslin: Jost Bürgi. Ineichen, Luzern, 2001. p. 108
- ↑ z. B. Kathleen Clark, Clemency Montelle: Logarithms: The Early History of a Familiar Function - Joost Bürgi Introduces Logarithms . MAA
- ^ Voellmy, Bürger und die Logarithmen, p. 17
- ^ Fritz Staudacher: Jost Bürgi. Biography 4th edition, p. 23. Ed .: NZZ Libro.
- ↑ According to Kepler, he surpassed many professors in mathematical knowledge and ingenuity, cited by Voellmy: Bürgi and the logarithms . In: Elements of Mathematics , p. 13
- ↑ Martha List, Volker Bialas : The Coss by Jost Bürgi in the editorial office of Johannes Kepler . In: Nova Kepleriana , New Series, Volume 5, 1963, Bavarian Academy of Sciences
- ↑ see the map of Kassel in Google Maps maps.google.de
- ↑ Bürgipfad. In: Street name lexicon of the Luisenstädtischer Bildungsverein (near Kaupert )
- ↑ Refers to Jost Bürgi: Dem Wolgebornen Herr Herr Simon, Graffen and Noble Herr zur Lippe: Zur Erz-, Metall- und Münzprüfung (1598). Sign. Mscr. 86.4 °, Lippische Landesbibliothek, Detmold.
personal data | |
---|---|
SURNAME | Bürgi, Jost |
ALTERNATIVE NAMES | Bürgi, Jobst |
BRIEF DESCRIPTION | Swiss watchmaker, instrument maker and astronomer |
DATE OF BIRTH | February 28, 1552 |
PLACE OF BIRTH | Lichtensteig |
DATE OF DEATH | January 31, 1632 |
Place of death | kassel |