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.

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