Historia Mathematica最新文献

Homology was among the concepts introduced in Jean Victor Poncelet's 1822 Traité des Propriétés Projectives des Figures. Homology is a projective transformation which has an axis, a line of fixed points. The Traité develops a straightedge construction of points under homology, essentially that found in work on perspective drawing and by Phillipe de la Hire, 1673. However, Poncelet's very distinct path to homology was through similitude, where the radical axis of a pair of circles became the axis of homology. We end with Poncelet's application of homology involving the focus of a conic section.

Leibniz's manuscripts on perspective geometry remained unpublished and unknown until very recently. Among them, Scientia perspectiva stands out as the most complex and the most original. In this paper, we offer a thorough analysis of this manuscript, showing how Leibniz moves from perspective concepts fairly common at that time to a completely new idea of the practice that could have affected its entire history. This new science represents not only Leibniz's unique contribution to the development of perspective but also casts a new light on his own notion of space and geometry and their philosophical grounding.

In 1682, Leibniz published an essay containing his solution to the classic problem of squaring the circle: the alternating converging series that now bears his name. Yet his attempts to disseminate his quadrature results began seven years earlier and included four distinct approaches: the conventional (journal article), the grand (treatise), the impostrous (pseudepigraphia), and the extravagant (medals). This paper examines Leibniz's various attempts to disseminate his series formula. By examining oft-ignored writings, as well as unpublished manuscripts, this paper answers the question of how one of the greatest mathematicians sought to introduce his first great geometrical discovery to the world.

It remains unknown how the approximation of $\sqrt{2}$ scribed on Babylonian tablet YBC 7289 was calculated. In this article I show how it can be straightforwardly computed using a well-known regular number as the input for the Babylonian method of estimating square roots. My objective is to demonstrate that Babylonian mathematics was sufficiently evolved for the approximation to be easily derived and thus propose an approach that may have been used to calculate it.

The present article describes for the first time the book of Vaclav Josef Pelikan titled Arithmeticus Perfectus Qui tria numerare nescit. Seu Arithmetica dualis, In qua Numerando non proceditur, nisi ad duo, & tamen omnes quaestiones Arithmeticae negotio facili enodari possunt, published in Prague in 1712. The book is written in Latin on 86 pages and consists of a dedication, a message to the reader and four chapters. Operations in the binary system, including the extraction of square and cube roots, methods of converting numbers from the decimal system to the binary system and vice versa, etc., are given. In general, we may say that the book by Vaclav Josef Pelikan is the first fully fledged and methodologically sound textbook of arithmetic using the binary number system as well as containing original methods of solution.

There is a prevalent claim in the literature examining the history of numbers and the development of number words that some African group (“Bushmen” or “Pygmies”) counts in a particular way, where their numerals are of the form 1, 2, 3, 2+2, 2+2+1, etc. Numerous forms of this claim are traced back to their original sources through an extensive search of the available literature. The author argues that the different forms can be traced back to two early sources, which have been misquoted and bastardized along the way.

The Mainardi-Codazzi equations (MCE) and the fundamental theorem of surface theory (FT) are regarded as crucial achievements in the development of surface theory. The paper offers an analysis of three papers by Bour, Codazzi and Bonnet, submitted on the occasion of the Grand Prix des Mathématiques (1859), in which the MCE and the FT were systematically employed to deal with applicability problems. Our analysis provides a new insight into the historical process leading to a recognition of the relevance of the MCE and the FT and helps explaining why previous contributions on the subject could go unnoticed for years.

In the preamble of the 1818 sangaku tablet of Sugino'o Shrine, the proposers acknowledged the help of an unnamed teacher/master in understanding and solving certain mathematical problems. Endō Tadashi argued that this unnamed teacher could be Saitō Naonaka (1773-1844). In this paper, we examine the famous travel diary of Yamaguchi Kanzan (?-1850) especially on his second trip to the Northeast. We compare the content of Yamaguchi's diary with the three problems of Sugino'o's tablet. Together with the timing of Yamaguchi's travel, we conclude that Yamaguchi Kanzan was likely the unnamed master mentioned in the preface of the Sugino'o Shrine sangaku.