Historia Mathematica最新文献

Lorenzo Mascheroni's 1797 work La geometria del compasso, which develops a geometry based solely on compass constructions, is considered by the author as stepping back behind the “demarcation line” of Euclidean geometry. In this work Mascheroni emphasizes the practical aspects of this geometry over a theoretical approach. A century later, in 1899, David Hilbert and his student Michael Feldblum proposed a totally different approach – algebraic and axiomatic – concerning geometric constructions based on various instruments. Taking into account that, at the end of the 18th century, straightedge geometry was also developed, one may ask what happened to the image of instrument-based geometry during the 19th century? By focusing on Mascheroni's book and its reception, this article aims to examine the various views and conceptions of mathematicians with respect to this geometry.

Much research has been devoted to two problems, Yi yuancai fang (From a circular timber [find] a square) and Yi fangcai yuan (From a square timber [find] a circle), both of which appear in the Suanshu shu, an early Han dynasty mathematical work written on bamboo slips, excavated from tomb 247 at Zhangjiashan in Hubei Province, China. In this article, the geometric relations between circles and squares and the methods for determining their mutual relations in these two problems are interpreted in a different way, and an alternative approach is offered for reconciling these two problems.

In 1804 the chair of Elementary Mathematics at Prague University became vacant and a selection procedure, which consisted of a written and an oral examination, was announced. Only Bernard Bolzano and Ladislav Jandera took part in it. Jandera was appointed to the chair, whereas Bolzano became Professor of “Religious Doctrine.” In this paper we examine the context of this Concursprüfung, the performance of both candidates and the outcome, based on a number of related papers preserved at the Czech National Archives. In addition to this, we publish for the first time, albeit only in the online version of this paper, the transcription and English translation of Bolzano's written examination.

This paper is a historical account of the chords theorem, for conic sections from Apollonius to Boscovich. We comment the most significant proofs and applications, focusing on Newton's solution of the Pappus four lines problem. Newton's geometrical achievements drew L'Hospital's attention to the chords theorem as a fundamental one, and led him to search for a simple and direct proof, that he finally obtained by the method of projection. Stirling gave a very elegant algebraic proof; then Boscovich succeeded in finding an almost immediate geometrical proof, and showed how to develop the elements of conic sections starting from this theorem.

After providing a summarised biographical and scientific profile of F.G. Tricomi, we describe the structure and contents of his archive and miscellany, which jointly represent a documentary heritage of great historical importance, as well as one of the major patrimonies of the Department of Mathematics ‘G. Peano’ at the University of Turin.

In many languages in Micronesia, clever ways of extending their counting systems to numbers far beyond imagination were developed in precolonial times. Here, we provide an exhaustive overview of these systems, highlight their characteristics, and account for some of their most intriguing features. Based on a critical assessment of the available data and the in-depth analysis of both paradigmatic cases and peculiarities, we draw inferences about some more general patterns that suggest a rather long tradition of specific ways of counting both in Micronesia and the area beyond.