Priority, Parallel Discovery, and Pre-eminence Napier, Bürgi and the Early History of the Logarithm Relation

Clark, Kathleen M.; Montelle, Clemency

Revue d'histoire des mathématiques, Tome 18 (2012) no. 2, pp. 223-270.

Il n’y a jamais eu de doute sur l’importance du logarithme ; une relation mathématique dont l’utilité a persisté de différentes manières jusqu’à nos jours. Quelques années à peine après leur introduction, les logarithmes sont devenus indispensables aux mathématiciens, ainsi qu’aux astronomes, navigateurs et géographes. Cependant, la question de leur origine est délicate. Au moins deux savants, le noble écossais John Napier et l’artisan suisse Jost Bürgi, ont produit simultanément et indépendamment des propositions qui englobent la relation logarithmique, et à quelques années de distance ont produit des tables pour son utilisation. Partant de cette découverte parallèle, nous avons lu, analysé et interprété les textes de Napier et Bürgi pour mieux comprendre et contextualiser ces deux approches bien différentes. En guise de résultat, nous comparons les principales caractéristiques des efforts de Napier et Bürgi et la construction de leurs tables de logarithmes réciproques. À travers ces détails, nous nous posons la question de la priorité et de la pré-éminence dans la discussion du développement historique des logarithmes, ainsi que des questions critiques sur le phénomène d’intuitions parallèles et ce qu’elles peuvent dévoiler sur l’environnement mathématique de leur époque.

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.

Keywords: Logarithms, Napier, Bürgi, Renaissance, priority.
Mots clés : Logarithmes, Napier, Bürgi, Renaissance, priorité.

[Baron 1974] Baron (Margaret E.) – Napier, John, in Dictionary of Scientific Biography, New York: Scribners, 1974.

[Berggren 2003] Berggren (John Lennart) – Episodes in the Mathematics of Medieval Islam, New York: Springer, 2003. | MR | Zbl

[Boyer & Merzbach 1991] Boyer (Carl B.) & Merzbach (Uta C.) – A History of Mathematics, New York: John Wiley and Sons, 1991. | MR | Zbl

[Boyer & Merzbach 2011] Boyer (Carl B.) & Merzbach (Uta C.) – A History of Mathematics, Hoboken, NJ: John Wiley and Sons, 2011. | Zbl

[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. | DOI

[Bruins 1980] Bruins (Evert M.) – On the History of Logarithms: Bürgi, Napier, Briggs, De Decker, Vlacq, Huygens, Janus, 67 (1980), p. 241–261. | MR | Zbl

[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.

[Calinger 1999] Calinger (Ronald) – A Contextual History of Mathematics, Upper Saddle River, NJ: Prentice Hall, 1999. | MR | Zbl

[Calinger 1995] Calinger (Ronald) – Classics in Mathematics, Englewood Cliffs, NJ: Prentice Hall, 1995. | MR

[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.

[Cantor 1900] Cantor (Moritz) – Vorlesungen über Geschichte der Mathematik: Zweiter Band von 1200–1668, Leipzig: Teubner, 1900. | JFM

[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. | Zbl

[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.

[González-Velasco 2011] González-Velasco (Enrique A.) – Journey through Mathematics Creative Episodes in Its History, New York: Springer, 2011. | MR | Zbl

[Grattan-Guinness 1997] Grattan-Guinness (Ivor) – The Rainbow of Mathematics A History of the Mathematical Sciences, New York: W. W. Norton and Company, 1997. | MR | Zbl

[Gridgeman 1973] Gridgeman (Norman T.) – John Napier and the history of logarithms, Scripta Mathematica, 29 (1973), p. 49–65. | MR | Zbl

[Gronau 1996] Gronau (Detlef) – The logarithm—From calculation to functional equations, Notices of the South African Mathematical Society, 28 (1996), p. 60–66.

[Heath 1953] Heath (Thomas L.) – The Works of Archimedes, New York: Dover, 1953. | MR | Zbl

[Huxley 1970] Huxley (G.) – Briggs, Henry, in Dictionary of Scientific Biography Scribners, 1970, p. 461–463.

[Jeep 2001] Jeep (John M.) – Medieval Germany: An Encyclopedia, New York: Garland Publishing, 2001.

[Katz 1998] Katz (Victor J.) – The History of Mathematics, Reading, MA: Addison-Wesley, 1998. | Zbl

[Kepler 1627] Kepler (Johannes) – Tabulae Rudolphinae, quibus astronomicae scientiae, temporum longinquitate collapsae restauratio continetur, J. Saurius, 1627.

[Lutstorf 2005] Lutstorf (Heinz T.) – Die Logarithmentafeln Jost Bürgis: Bemerkungen zur Stellenwert und Basisfrage: mit Kommentar zu Bürgis “Gründlichem Unterricht”, Zürich: ETH-Bibliothek, 2005.

[Lutstorf & Walter 1992] Lutstorf (Heinz T.) & Walter (Max) – Jost Bürgi’s “Progress Tabulen” (Logarithmen), Zürich: ETH-Bibliothek, 1992.

[Napier 1614] Napier (John) – Mirifici Logarithmorum Canonis Descriptio, Edinburgh: Andreæ Hart, 1614.

[Naux 1966/1971] Naux (Charles) – Histoire des logarithmes de Neper à Euler, vol. 1 et 2, Paris: Albert Blanchard, 1966/1971. | MR | Zbl

[Nový 1970] Nový (Luboš) – Bürgi, Joost, in Dictionary of Scientific Biography, vol.2, New York: Scribners, 1970, p. 602–603.

[Pesic 2010] Pesic (Peter) – Hearing the Irrational Music and the Development of the Modern Concept of Number, Isis, 101 (2010), p. 501–530. | MR | Zbl

[Shell-Gellasch 2008] Shell-Gellasch (Amy) – Napier’s $e$, 2008; http://mathdl.maa.org/mathDL/46/?pa=content&sa=viewDocument&nodeId=3209. | DOI

[Smith 1958] Smith (David E.) – History of Mathematics, New York: Dover, 1958. | Zbl

[Stedall 2008] Stedall (Jacqueline) – Mathematics Emerging: A Sourcebook 1540-1900, Oxford: Oxford Univ. Press, 2008. | MR | Zbl

[Stevin 1585] Stevin (Simon) – De Thiende, Leyden: Christoffel Plantijin, 1585. | MR

[Stifel 1544] Stifel (Michael) – Arithmetica Integra, Nüremburg: Johan Petreus, 1544.

[Suzuki 2009] Suzuki (Jeff) – Mathematics in Historical Context, Washington DC: The Mathematical Association of America, 2009. | MR | Zbl

[Thoren 1988] Thoren (Victor E.) – Prosthaphaeresis revisited, Historia Mathematica, 15(32–39) (1988). | MR | Zbl

[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. | MR | Zbl

[Wright 1616] Wright (Edward) – A Description of the Admirable Table of Logarithms. Translated from Napier, J., from Latin to English, London: Nicholas Oaks, 1616.