Talk:Jost Bürgi

message: I believe it violates NPOV to state that Jost Bürgi invented logarithms "first". Since he did not publish until four years *after* John Napier, by which time Napier's work was widely known, de facto Bürgi does not deserve credit for being "first". In addition, it is not clear that Bürgi was first in any sense, since Napier worked on his version for 20 years before publishing. Is there documentary evidence that Bürgi started before 1594?
The neutral point of view is that Bürgi *independently* developed logarithms.
I have edited both the logarithm and Jost Bürgi Wiki articles to reflect this, giving Bürgi  credit for independently inventing logarthms, but not for being first.
Nwbeeson 18:28, 4 January 2007 (UTC)
replies: text: I have edited the opening paragraphs a bit.  There was a long quote with two different sources on it, so I figured it must not actually be a quote.  If it was, or part of it was, someone who can verify please fix it. Dicklyon 22:58, 4 January 2007 (UTC)
thread_title:  Jost Bürgi 

message: Jost Bürgi did much more than what I found in this article. For a start, I added a section on his work on trigonometry. By 1586, Bürgi was able to calculate sines at arbitrary precision, using an algorithm he called Artificium. He used it to calculate a table of 81,000 sines of values between 0 and 45 degrees in steps of 2 arc seconds. Such tables were extremely important for navigation at sea. Bürgi explained Artificium in his work «Fundamentum Astronomiae» which he presented to Emperor Rudolf II. in 1592. Folkerts et al. proved that this simple process converges indeed towards the true sines.Menso Folkerts, Dieter Launert, Andreas Thom (Oct 2015). "Jost Bürgi's Method for Calculating Sines." http://arxiv.org/abs/1510.03180 According to Folkerts, this was the first step towards difference calculus.
Mathpriest (talk) 17:05, 28 February 2016 (UTC)
thread_title:  Bürgi's work on trigonometry 

message: The article claims: "Bürgi 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." I think this claim is too strong and has to be changed, because:
1. A recent reference has the following to say about Bürgi's invention of logarithms:
Jost Bürgi is well-known  in the history of mathematics  because he invented logarithms independently of John Napier... It seems that Bürgi invented the logarithms in the 1580s, but he published his table of logarithms not before 1620.... In Kassel, Bürgi not only worked as an instrument maker but was also involved in astronomical observations and interpretations.... Wittich, who was in Kassel from 1584 to 1586, brought with him knowledge of prosthaphaeresis, a method by which multiplications and divisions can be replaced by additions and subtractions of trigonometrical values....  This procedure achieves the same as logarithms, which were invented some decades later.... Bürgi’s method was not entirely unknown:  Dieter Launert has found evidence that a trace of his work leads to England and to the mathematician Henry Briggs (1561-1630),  who is well known for his role in the history of logarithms:  A copy  of  Raimarus  Ursus’s Fundamentum  astronomicum, which is  kept  in the University Library of Leiden (The Netherlands), includes a folio, written about 1620, with numbers and calculations, a table similar to Bürgi’s diagram for calculating the sines, and a name which is most likely “H. Briggs”.  This proves that Briggs was acquainted with Bürgi’s method. Very  likely  Briggs  obtained  this  information  from  John  Dee  (1527-1608), who  was  in  contact  with  Rothmann,  when  he  visited  Kassel  in  1586  and 1589. It seems possible that the method of differences that Briggs used for the calculation of logarithms has some relation to Bürgi’s method of computing sines.
2. And another referenceMacTutor Article on Jost Bürgi: http://www-history.mcs.st-and.ac.uk/Biographies/Burgi.html has the following to say about Bürgi's invention of logarithms:
By the time Bürgi made his astronomical clock he was using his own version of logarithms, invented for his own use to aid him in his astronomical calculations. It is not clear precisely when he started using logarithms but most historians believe that he invented them around 1588... Bürgi's method is different from that of Napier and was clearly invented independently. Kepler wrote about Bürgi's logarithms in the introduction to his Rudolphine Tables (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. 
So I'll try to change this accordingly.
Mathpriest (talk) 17:42, 12 March 2016 (UTC)
thread_title:  Bürgi's work on logarithms 

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