Talk:Jost Bürgi

Jost Bürgi
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)


 * 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)

Bürgi's work on trigonometry
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. According to Folkerts, this was the first step towards difference calculus.

Mathpriest (talk) 17:05, 28 February 2016 (UTC)

Bürgi's work on logarithms
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 reference 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)

Hello, thanks for your efforts in correcting the history, but are you sure that your interpretation is the right one? Folkerts et al. have not proven in any way that Briggs knew about the details of Buergi's work or used it. The name that they read as Briggs could well be read as Buergi, in fact. Btw, Buergi's iterative method is not related to difference calculus, and it can't be used to compute the table that Buergi is supposed to have computed. There is a confusion between several algorithms used by Buergi.

Concerning the discovery/invention of logarithms, the truth is not obtained by taking the average of all the opinions, but by having a critical approach. For instance, before deciding who invented some notion, that notion should be defined. Please, give a definition of 1) logarithms and 2) inventing logarithms. Since nobody does that, everybody in fact twists the meanings of the words. I myself have a lot of admiration for Buergi, and I consider him well ahead of his time in many things, but I don't see anything to support the claim that he invented or discovered logarithms, even if his table of progressions was constructed in the 1580s. Best.Schwilgue (talk) 16:16, 14 March 2016 (UTC)

Hello, thanks to you. In the revision history of the article you wrote that you "removed the reference to Folkerts (not on logarithms)" but this reference actually does have comments not only on sines but also on the invention of logarithms (see above), so I felt it's a reasonable source. But feel free to correct this by adding contrarian sources. Mathpriest (talk) 20:08, 20 March 2016 (UTC)

Folkerts et al. only mention the logarithms in passing, as part of their introduction. The article is not at all about that topic. Moreover, they don't give any references. Now, if someone just mentions that "something is well known", does that make it a reference to cite? I don't think so. More generally, there is a group of people who want to make Buergi the inventor of everything, including logarithms, but also many other things, without any critical approach. Many of these people have not studied the work of Napier, and confuse discovering/inventing logarithms and making a tables of logarithms. These are two different things. Wikipedia should at least reflect that there is a debate, and that the debate is not just about the date of publication, but goes deeper.Schwilgue (talk) 12:41, 21 March 2016 (UTC)

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