More about Jost Bürgi (1552-1632)

Update of August 11, 2018: The book of Fritz Staudacher appears soon in an extended forth edition (2018).
Staudacher. Fritz: Jost Bürgi, Kepler und der Kaiser. 
Uhrmacher, Astronom, Mathematiker, Instrumentenbauer, 
Erz-Metallurgist (1552-1632). 4., überarbeitete und 
erweiterte Auflage, mit einem Beitrag des 
Artificium-Entdeckers Menso Folkerts, 
320 Seiten, 279 Abbildungen. 
Verlag NZZ Libro, Zürich 2018. ISBN 978-3-03810-345-5.
It will be available in the 4th edition soon.

Update of December 17, 2017: A book review of the book of Fritz Staudacher about Buergi. Here is a cleaned out Google translation:

Not only is this the best information source about Buergi, it is also the best biography I've seen about this mathematician. The book is well researched (there are many original sources and not just secondary literature), it is clearly and well written and also beautifully printed. Jost Buergi is a very interesting Renaissance personality, an universal talent that is even today vastly underestimated. For example, it has only been realized recently that the logarithms of Buergi were not only found long before Napier, but that they were also introduced in a more modern and clearer manner than those of Napier. Also, the enormous influence of Buergi on Kepler is made clear in the book. Without the logarithms of Buergi, the latter would hardly have found the Kepler laws. While other cases of unusual geniuses have been documented extensively (examples are Archimedes, who was also an engineer and inventor, George Green, who was a miller, Albert Einstein who was a patent employee, Srinivasa Ramanujan, who was an autodidact, Fritz Zwicky, a rocket man), so is the case Buergi much less well known. This book will help to give the necessary attention to one of the best and most creative mathematicians of the renaissance. On the structure of the book: the first chapter describes the origin of Buergi (Lichtensteig in Toggenburg). The author built in a lot of historical background here. The second chapter shows the professional career (locksmith, silversmith, watchmaker apprentice, etc.) It is exciting that there is a great deal of uncertainty: did Jost learn the watchmaking profession in Winterthur, or with the Habrecht family in Schaffhausen? Also, one does not know exactly, where Buergi spent his apprentice years: Nuernberg is the almost certain guess. Chapter 3 describes clocks built by Buergi, including observation clocks having an accuracy not surpassed at gthat time: Buergi was seven decades ahead of Huygens pendulum clock, of course, accurate astronomical data were extremely important. Kepler would not have found the elliptical shape without a precise timekeeping device. The book rightly refers to the Antikythera, a calendar mechanism that could have been built by Archimedes. In Chapter 4, instruments built by Buergi are introduced like (astrolabes, proportional compass, caliber rod, triangulation instruments or sextants.) Kepler has determined the Mars orbital ellipse with a Buergi sextant. Chapter 5 is dedicated to count Wilhelm IV of Hessel-Kassel. The kurfurstliche castle was the workplace of Buergi for 25 years. Tycho Brahe called it the count the most important astronomer in Europe. Buergi was responsible for the instruments. The fact that the accuracy of the Kasseler star measurements is twice as good as that of Tycho Brahe, is the merit of Buergi. Chapter 6 is about the celectial globes. Finally, Chapter 7 is devoted to mathematics. Buergi turns out to be more talented than the court mathematician Rothmann, who called the only Swiss-German-speaking Buergi read "the Illiteratus" (the unread) or "Horlogiopaeus" (the watchmaker). For the moment, Buergi has a friend in Reimers Baer, who also comes from simple circumstances, but can translate the Kopernikus for Buergi. The book notes that "along with Viete, Clavius and Stevin, Buergi is one of the pioneers of decimals and spelling" and "For Johannes Kepler it is not a question that it is Jost Buergi who invented the decimal fraction." Another central statement, which I have confirmed with my own humble research on writing an encyclopedia article on Buergi, is on page 179 of the book: "Buergi's logarithm pegs are not only developed earlier in time than Napier's, but from today's perspective also a qualitatively more modern one mathematical concept. "The whole chapter is exciting, showing that Buergi himself is not far from his own calculating machine and with an "art path algorithm" that anticipated matrix multiplication. Chapter 8 addresses the question of why Buergi remains so much obscured still today. Negative experiences played a role, and Kepler's secrecy clause is also essential. Buergi who was "beyond university and Latin" had to work hard to invent any invention, not just unprejudiced and unpunished copied. Fatal was that it was prohibited to Kepler due to objections by Brahe heirs, to mention only Brahe and his assistants. The logarithmic publication was also carried away in the turmoil of the Thirty Years' War. An interesting paradox is mentioned at the end of the chapter: "It's a paradox: Kepler sees badly, Brahe does not like to calculate, Buergi does not understand Latin, and yet revolutionizes this European triumvirate of a German mathematician, a Danish Astronomen and a Swiss clock maker in the Chech-Bohemian Prag in Austrian-Habsburg Aegide the knowledge of the world, because of extraordinary individual competences in their complementary areas of expertice." Chapter 9 illustrates the contributions of Buergi to the astronomy of Keplers, Chapterl 10, the return from Prague to Kassel, where also the family circumstances of Buergi are explained. chapter 12 is an epiloge to this extraordinary bibliography. A quote from the end of the book: "Jost Buergi is is the reason why the modern age ticks".
It is an important historical question, whether it was Bürgi or Napier who "invented logarithms". The evidence is overwhelming that Bürgi and Napier developed the concept independently, that Buergi knew it first, but that Napier published it first. The literature sources
are added here due to special interest in the sentence I have written
"Indications that Bürgi knew about Logarithms earlier in 1588 come from a letter of the astronomer Reimarus Ursus Dithmarus, who explains that Bürgi had a method to simplify his calculations using logarithms."
in the entry [PDF] about Büri to the book Biographical Encyclopedia of Astronomers:

By the way, the Prize Committee of the Historical Astronomy Division of the American Astronomical Society has awarded to Thomas Hockey and all the authors of individual entries of that book the 2017 "The Donald E. Osterbrock Book Prize for Historical Astronomy" for the Biographical Encyclopedia of Astronomers.
It is nice that they sent out award cards for all the 430 authors of the book

Source: Wikipedia


Here is the historiography I had used when writing that encyclopedia article. As custom, the article had been shortened considerably by the editors and only a small part of the literature has been included: here is the full list of references, I had used when composing the article:
1) J.V. Field, Büurgi, Mac-tutor Bibliography entry
2) R. V. Caffarelli, Il Compasso Geometrico e miltare
3) L. Novy, Joost Büurgi, in Biography in Dictionary of Scientific Biography
   (New York 1970-1990).
4) E. Neuenschwander, Büurgi Jost, Historisches Lexikon der Schweiz
5) ETH library, Portrait on Jost Büurgi honoring his 450'th birthday:
6) R. S. Westfall, Jost Büurgi, Catalogue of Scientific Community at
   Rice University
7) Voellmy, E.  Jost Büurgi und die Logarithmen. Elemente der Math. Beiheft no. 5
    Verlag Birkhüauser, Basel, 1948.
8) D. Gronau, Johannes Kepler und die Logarithmen, Reports of the
   Mathematical Statistical Section of the Research Society Joanneum, 284, 1987
9) V. Thoren, Prosthaphaeresis revisited, Historia Math. 15, 32-39, 1988
10) J H Leopold, Der kleine Himmelsglobus 1594 von Jost Burgi (Lucern, 1977).
11) E M Bruins, On the history of logarithms : Büurgi, Napier, Briggs,
    de Decker, Vlacq, Huygens, Janus 67 (4) (1980), 241-260.
12) O Gingerich, Jost Büurgi at Kassel, Journal for the history of
   astronomy 11 (1980), 212-213.
13) E R Kiely, Surveying Instruments (New York, 1947), 224.
14) M List and V Bialas (eds.), Die Coss von Jost Büurgi in der
    Redaktion von Johannes Kepler. Ein Beitrag zur früuhen Algebra,
    Akad. Wiss. Math.-Natur. Kl. Abh. (N.F.) 154 (1973).
15) H. Loeffel, Das mathematische Werk von Jost Büurgi (1552-1632),
    Mitt. Verein. Schweiz. Versicherungsmath. (1) (1982), 25-41.
16) G Pajares, Emilio Büurgi. (Spanish) Gaceta Mat. (1) 4, (1952).
17)  E. Voellmy, Jost Büurgi und die Logarithmen, Zweite Auflage, Kurze
    Mathematiker-Biographien. Elem. Math. Beiheft 5 (Basel, 1974).
18) L. von Mackensen, Erfindung und Bedeutung des universalen
    Reduktionszirkels von Jost Büurgi, in Mathemata, Boethius : Texte
    Abh. Gesch. Exakt. Wissensch. XII (Wiesbaden, 1985), 317-326.
19) Folti, Jaroslav, and Lubos Novy, "Zu Bürgis Anleitung zu den
    Logarithmentaflen," Acta Hist. Rerum Nat. Tech., 4 (1968), 97- 126.
20) Groetzsch, H., "Die Kreuzschlaguhr und Globusuhr von Jost Bürgi
    - Wissenschaftliche Instrumente aus dem Arbeitsgebiet von
    Johannes Kepler," Actes XIIIe Cong. Int. Hist. Sci., 1971, 6
    (1974), 246-250.
21) Mackensen, Ludolf von, "Erfindung und Bedeutung des universalen
    Reduktionszirkels von Jost Buergi," in M. Folkerts, and U. Lindgren,
    eds., Mathemata: Festschrift für Helmuth Gericke (Stuttgart: Steiner, 1985).
22) Jost Büurgi's "Progress-Tabulen" (Logarithmen), nachgerechnet und
    kommentiert von H. Lutstorf, M. Walter, 1992.
Added in Proof:
  • Jost Bürgi's "Progress-Tabulen" (Logarithmen) Quelle: Schriftenreihe der ETH Bibliothek