Priority, parallel discovery, and pre-eminence Napier, Bürgi and the early history of the logarithm relation

Kathleen M. Clark; Clemency Montelle

Revue d'histoire des mathématiques (2012)

  • Volume: 18, Issue: 2, page 223-270
  • ISSN: 1262-022X

Abstract

top
There has never been any doubt as to the importance of the logarithm, a mathematical relation whose usefulness has persisted in different aspects to the present day. Within years of their introduction, logarithms became indispensable for mathematicians, astronomers, navigators, and geographers alike. The question of their origins, however, is more contentious. At least two scholars, the Scottish nobleman John Napier and the Swiss craftsman Jost Bürgi, simultaneously and independently produced proposals which embodied the logarithmic relation and, within years of one another, produced tables for its use. In light of this parallel discovery, we read, analyzed, and interpreted the texts of Napier and Bürgi to better understand and contextualize the two distinctly different approaches. As a result, here we compare and contrast the salient features of Napier’s and Bürgi’s endeavors and the construction of each man’s tables of logarithms. Through these details, we will query the focus on the issue of priority and pre-eminence when discussing the historical development of logarithms, and pose critical questions about the phenomenon of parallel insights and what they can reveal about the mathematical environment at the time they arose.

How to cite

top

Clark, Kathleen M., and Montelle, Clemency. "Priority, parallel discovery, and pre-eminence Napier, Bürgi and the early history of the logarithm relation." Revue d'histoire des mathématiques 18.2 (2012): 223-270. <http://eudml.org/doc/274957>.

@article{Clark2012,
abstract = {There has never been any doubt as to the importance of the logarithm, a mathematical relation whose usefulness has persisted in different aspects to the present day. Within years of their introduction, logarithms became indispensable for mathematicians, astronomers, navigators, and geographers alike. The question of their origins, however, is more contentious. At least two scholars, the Scottish nobleman John Napier and the Swiss craftsman Jost Bürgi, simultaneously and independently produced proposals which embodied the logarithmic relation and, within years of one another, produced tables for its use. In light of this parallel discovery, we read, analyzed, and interpreted the texts of Napier and Bürgi to better understand and contextualize the two distinctly different approaches. As a result, here we compare and contrast the salient features of Napier’s and Bürgi’s endeavors and the construction of each man’s tables of logarithms. Through these details, we will query the focus on the issue of priority and pre-eminence when discussing the historical development of logarithms, and pose critical questions about the phenomenon of parallel insights and what they can reveal about the mathematical environment at the time they arose.},
author = {Clark, Kathleen M., Montelle, Clemency},
journal = {Revue d'histoire des mathématiques},
keywords = {logarithms; Napier; Bürgi; renaissance; priority},
language = {eng},
number = {2},
pages = {223-270},
publisher = {Société mathématique de France},
title = {Priority, parallel discovery, and pre-eminence Napier, Bürgi and the early history of the logarithm relation},
url = {http://eudml.org/doc/274957},
volume = {18},
year = {2012},
}

TY - JOUR
AU - Clark, Kathleen M.
AU - Montelle, Clemency
TI - Priority, parallel discovery, and pre-eminence Napier, Bürgi and the early history of the logarithm relation
JO - Revue d'histoire des mathématiques
PY - 2012
PB - Société mathématique de France
VL - 18
IS - 2
SP - 223
EP - 270
AB - There has never been any doubt as to the importance of the logarithm, a mathematical relation whose usefulness has persisted in different aspects to the present day. Within years of their introduction, logarithms became indispensable for mathematicians, astronomers, navigators, and geographers alike. The question of their origins, however, is more contentious. At least two scholars, the Scottish nobleman John Napier and the Swiss craftsman Jost Bürgi, simultaneously and independently produced proposals which embodied the logarithmic relation and, within years of one another, produced tables for its use. In light of this parallel discovery, we read, analyzed, and interpreted the texts of Napier and Bürgi to better understand and contextualize the two distinctly different approaches. As a result, here we compare and contrast the salient features of Napier’s and Bürgi’s endeavors and the construction of each man’s tables of logarithms. Through these details, we will query the focus on the issue of priority and pre-eminence when discussing the historical development of logarithms, and pose critical questions about the phenomenon of parallel insights and what they can reveal about the mathematical environment at the time they arose.
LA - eng
KW - logarithms; Napier; Bürgi; renaissance; priority
UR - http://eudml.org/doc/274957
ER -

References

top
  1. [Baron 1974] Baron ( Margaret E.) – Napier, John, in Dictionary of Scientific Biography, New York: Scribners, 1974. 
  2. [Berggren 2003] Berggren ( John Lennart) – Episodes in the Mathematics of Medieval Islam, New York: Springer, 2003. Zbl0626.01001MR868081
  3. [Boyer & Merzbach 1991] Boyer ( Carl B.) & Merzbach ( Uta C.) – A History of Mathematics, New York: John Wiley and Sons, 1991. Zbl0733.01001MR1094813
  4. [Boyer & Merzbach 2011] Boyer ( Carl B.) & Merzbach ( Uta C.) – A History of Mathematics, Hoboken, NJ: John Wiley and Sons, 2011. Zbl0698.01001
  5. [Bretelle-Establet 2010] Bretelle-Establet ( Florence) – Looking at it from Asia: The Processes that Shaped the Sources of History of Science, Boston Studies in the Philosophy of Science, vol. 265, New York: Springer, 2010. 
  6. [Bruins 1980] Bruins ( Evert M.) – On the History of Logarithms: Bürgi, Napier, Briggs, De Decker, Vlacq, Huygens, Janus, 67 (1980), p. 241–261. Zbl0471.01006MR631322
  7. [Bürgi 1620] Bürgi ( Jost) – Arithmetische und Geometrische Progress Tabulen/sambt gründlichem unterricht/wie solche nützlich in allerley Rechnungen zu gebrauchen/und verstanden werden sol, Prag: Paul Sessen, 1620. 
  8. [Calinger 1999] Calinger ( Ronald) – A Contextual History of Mathematics, Upper Saddle River, NJ: Prentice Hall, 1999. Zbl0986.01002MR1880620
  9. [Calinger 1995] Calinger ( Ronald) – Classics in Mathematics, Englewood Cliffs, NJ: Prentice Hall, 1995. MR1344452
  10. [Cajori 1915] Cajori ( Florian) – Algebra in Napier’s day and alleged prior inventions of logarithms, in Knott (C. G.), ed., Napier Tercentenary Memorial Volume, London: Longmans, Green and Company, 1915, p. 93–109. 
  11. [Cantor 1900] Cantor ( Moritz) – Vorlesungen über Geschichte der Mathematik: Zweiter Band von 1200–1668, Leipzig: Teubner, 1900. JFM24.0001.01
  12. [Folta & Nový 1968] Folta ( Jaroslav) & Nový ( Luboš) – Zu Bürgi’s Anleitung zu den Logarithmentafeln, Acta historiae rerum naturalium necnon technicarum, special issue 4 (1968), p. 97–126. Zbl0209.29801
  13. [Gieswald 1856] Gieswald ( Hermann R.) – Justus Byrg als Mathematiker und dessen Einleitung in seine Logarithmen, Bericht über die St. Johannis-Schule, 35 (1856), p. 1–36. 
  14. [González-Velasco 2011] González-Velasco ( Enrique A.) – Journey through Mathematics Creative Episodes in Its History, New York: Springer, 2011. Zbl1243.01002MR2848120
  15. [Grattan-Guinness 1997] Grattan-Guinness ( Ivor) – The Rainbow of Mathematics A History of the Mathematical Sciences, New York: W. W. Norton and Company, 1997. Zbl0949.01002MR1682977
  16. [Gridgeman 1973] Gridgeman ( Norman T.) – John Napier and the history of logarithms, Scripta Mathematica, 29 (1973), p. 49–65. Zbl0259.01005MR335228
  17. [Gronau 1996] Gronau ( Detlef) – The logarithm—From calculation to functional equations, Notices of the South African Mathematical Society, 28 (1996), p. 60–66. 
  18. [Heath 1953] Heath ( Thomas L.) – The Works of Archimedes, New York: Dover, 1953. Zbl0051.24205MR2000800
  19. [Huxley 1970] Huxley ( G.) – Briggs, Henry, in Dictionary of Scientific Biography Scribners, 1970, p. 461–463. 
  20. [Jeep 2001] Jeep ( John M.) – Medieval Germany: An Encyclopedia, New York: Garland Publishing, 2001. 
  21. [Katz 1998] Katz ( Victor J.) – The History of Mathematics, Reading, MA: Addison-Wesley, 1998. Zbl1066.01500
  22. [Kepler 1627] Kepler ( Johannes) – Tabulae Rudolphinae, quibus astronomicae scientiae, temporum longinquitate collapsae restauratio continetur, J. Saurius, 1627. 
  23. [Lutstorf 2005] Lutstorf ( Heinz T.) – Die Logarithmentafeln Jost Bürgis: Bemerkungen zur Stellenwert und Basisfrage: mit Kommentar zu Bürgis “Gründlichem Unterricht”, Zürich: ETH-Bibliothek, 2005. 
  24. [Lutstorf & Walter 1992] Lutstorf ( Heinz T.) & Walter ( Max) – Jost Bürgi’s “Progress Tabulen” (Logarithmen), Zürich: ETH-Bibliothek, 1992. 
  25. [Napier 1614] Napier ( John) – Mirifici Logarithmorum Canonis Descriptio, Edinburgh: Andreæ Hart, 1614. 
  26. [Naux 1966/1971] Naux ( Charles) – Histoire des logarithmes de Neper à Euler, vol. 1 et 2, Paris: Albert Blanchard, 1966/1971. 
  27. [Nový 1970] Nový ( Luboš) – Bürgi, Joost, in Dictionary of Scientific Biography, vol.2, New York: Scribners, 1970, p. 602–603. 
  28. [Pesic 2010] Pesic ( Peter) – Hearing the Irrational Music and the Development of the Modern Concept of Number, Isis, 101 (2010), p. 501–530. Zbl1230.01008MR2743036
  29. [Shell-Gellasch 2008] Shell-Gellasch ( Amy) – Napier’s e , 2008; http://mathdl.maa.org/mathDL/46/?pa=content&sa=viewDocument&nodeId=3209. 
  30. [Smith 1958] Smith ( David E.) – History of Mathematics, New York: Dover, 1958. Zbl0081.00411
  31. [Stedall 2008] Stedall ( Jacqueline) – Mathematics Emerging: A Sourcebook 1540-1900, Oxford: Oxford Univ. Press, 2008. Zbl1219.01003MR2473212
  32. [Stevin 1585] Stevin ( Simon) – De Thiende, Leyden: Christoffel Plantijin, 1585. 
  33. [Stifel 1544] Stifel ( Michael) – Arithmetica Integra, Nüremburg: Johan Petreus, 1544. 
  34. [Suzuki 2009] Suzuki ( Jeff) – Mathematics in Historical Context, Washington DC: The Mathematical Association of America, 2009. Zbl1173.01002MR2541249
  35. [Thoren 1988] Thoren ( Victor E.) – Prosthaphaeresis revisited, Historia Mathematica, 15(32–39) (1988). Zbl0641.01002MR931677
  36. [Whiteside 1961] Whiteside ( Derek T.) – Patterns of mathematical thought in the later 17th century, Archive for History of Exact Sciences, 1 (1961), p. 179–338. Zbl0099.24401MR130146
  37. [Wright 1616] Wright ( Edward) – A Description of the Admirable Table of Logarithms. Translated from Napier, J., from Latin to English, London: Nicholas Oaks, 1616. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.