Historia Mathematica最新文献

Universal presentations and interpretations of the history of mathematics have now been challenged, identifying the need of resurrecting hitherto marginalized contributions. In such studies, cognitive factors influencing the related development trajectories play a crucial role. Different societies would have had different mathematical cognitions contributing to the development of distinct forms of mathematics. This study attempts to surface the related cognitive contents of using large numbers. The principal source used for the study—the Buddhist Commentaries—determines the period and region covered. As such, it explores the conditions prevailed in 5th century CE (approximately) in Sri Lanka.

2000 Mathematics Subject Classification (MSC 2000) code: 01A07

The earliest known appearance of the decimal point was in the interpolation column of a sine table in Christopher Clavius's Astrolabium (1593). But this is a curious place to introduce such a significant new idea, and the fact that Clavius never took advantage of it in his own later writings has remained unexplained. We trace Clavius's use of decimal fractional numeration and the decimal point back to the work of Giovanni Bianchini (1440s), whose decimal system was a distinguishing feature of his calculations in spherical astronomy and metrology. While one needed to operate with Bianchini's decimal system to work with his astronomy, Regiomontanus copied it only in part. The rest of the European astronomical community followed Regiomontanus, and Bianchini's system reappeared only with its revival by Clavius.

La première apparition connue du point décimal se trouve dans la colonne d'interpolation d'une table de sinus dans l’Astrolabium de Christopher Clavius (1593). Mais il s'agit là d'un endroit curieux pour introduire une nouvelle idée aussi importante, et le fait que Clavius n'en ait jamais tiré parti dans ses écrits ultérieurs reste inexpliqué. L'utilisation par Clavius de la numération fractionnaire décimale et du point décimal remonte aux travaux de Giovanni Bianchini (années 1440), dont le système décimal était une caractéristique distinctive de ses calculs en astronomie sphérique et en métrologie. Alors qu'il fallait utiliser le système décimal de Bianchini pour travailler avec son astronomie, Regiomontanus ne l'a copié qu'en partie. Le reste de la communauté astronomique européenne suivit Regiomontanus, et le système de Bianchini ne réapparut qu'avec Clavius.

The Saṅgīta-ratnākara (Ocean of Music) of Śārṅgadeva (c. 1225 CE) is a 13th century text on musicology in Sanskrit. The fifth chapter of the Saṅgīta-ratnākara deals with a general analysis of all possible rhythms (tālas) which can be obtained by combining a set of basic rhythmic components known as tālāṅgas. Here, Śārṅgadeva describes the construction of the saṃyoga-meru (Table of Combinations), a tool that tabulates the total number of possible tālas of a given duration which are obtained by combining elements of different subsets of tālāṅgas. In this paper, we discuss the mathematical rationale employed by Śārṅgadeva in the construction of the saṃyoga-meru.

Non-standard analysis has often been presented as the proper framework for expressing rigorously Leibniz's conception of infinitesimals. This paper intends to study this interpretation from an historical point of view and to dispel a series of misunderstandings on which it rests. In order to do so, we propose to go back to Leibniz's conception of quantity, number and magnitude, an approach which has not been developed yet in the literature.

Late 18th and early 19th century Japanese mathematicians (wasanka) found solutions of two problems concerning the incircles of the quarter-triangles and skewed sectors of cyclic quadrilaterals. There is a modern proof of the first solution, but it makes extensive use of trigonometry and is therefore unlikely to be what a wasanka would have written. As for the second solution, Aida Yasuaki (1747–1817) gave two proofs for it, the second of which has been summarized in Japanese, but not the first. All three proofs are presented here together with commentary on their mathematical and historical significance.

Newton was critical of Descartes's constructivist vision of the foundations of geometry organised around certain curve-tracing principles. In unpublished work, Newton outlined a constructivist program of his own, based on his “organic” method of curve tracing, which subsumes Descartes's emblematic turning-ruler-and-moving-curve construction method as a special case, but does not suffer from the latter's flaw of being unable to trace all conics. This Newtonian program has been little studied and is more thoughtful and technically substantive than is commonly recognised. It also clashes with, and arguably supersedes and improves upon, Newton's perhaps better known earlier statements on the subject.