Archive for History of Exact Sciences最新文献

The article provides a reconstruction of Eudoxus' approach to simultaneous risings and settings in his two works dedicated to the issue: the Phaenomena and the Enoptron. This reconstruction is based on the analysis of Eudoxus’ fragments transmitted by Hipparchus. These fragments are difficult and problematic, but a close analysis and a comparison with the corresponding passages in Aratus suggests a possible solution.

It is well known that over the eighteenth century the calculus moved away from its geometric origins; Euler, and later Lagrange, aspired to transform it into a “purely analytical” discipline. In the 1780 s, the Portuguese mathematician José Anastácio da Cunha developed an original version of the calculus whose interpretation in view of that process presents challenges. Cunha was a strong admirer of Newton (who famously favoured geometry over algebra) and criticized Euler’s faith in analysis. However, the fundamental propositions of his calculus follow the analytical trend. This appears to have been possible due to a nominalistic conception of variable that allowed him to deal with expressions as names, rather than abstract quantities. Still, Cunha tried to keep the definition of fluxion directly applicable to geometrical magnitudes. According to a friend of Cunha’s, his calculus had an algebraic (analytical) branch and a geometrical branch, and it was because of this that his definition of fluxion appeared too complex to some contemporaries.

This article surveys measurements of celestial (chiefly solar) altitudes documented from twelfth- and thirteenth-century Latin Europe. It consists of four main parts providing (i) an overview of the instruments available for altitude measurements and described in contemporary sources, viz. astrolabes, quadrants, shadow sticks, and the torquetum; (ii) a survey of the role played by altitude measurements in the determination of geographic latitude, which takes into account more than 70 preserved estimates; (iii) case studies of four sets of measured solar altitudes in twelfth-century Latin sources; (iv) an in-depth discussion of the evidence relating to altitude measurements performed in Paris in the period 1281–1290. The findings from the last part indicate that by the end of the thirteenth century Parisian astronomer had developed rigorous standards of observational practice in which altitudes were typically measured to a precision of minutes of arc and with a level of accuracy higher than ± 0;5°, and sometimes exceeding ± 0;1°.

This Editorial reports an exchange in form of a comment and reply on the article “History and Nature of the Jeffreys–Lindley Paradox” (Arch Hist Exact Sci 77:25, 2023) by Eric-Jan Wagenmakers and Alexander Ly.

Federico Commandino’s Latin editions of the mathematical works written by the ancient Greeks constituted an essential reference for the scientific research undertaken by the moderns. In his Latin editions, Commandino cleverly combined his philological and mathematical skills. Philology and mathematics, moreover, nurtured each other. In this article, I analyze the Greek and Latin manuscripts and the printed edition of Apollonius’ Conics to highlight in a specific case study the role of the editions of the classics in the renaissance of modern mathematics.

The eighth-century Latin manuscript Milan, Veneranda Biblioteca Ambrosiana, L 99 Sup. contains fifteen palimpsest leaves previously used for three Greek scientific texts: a text of unknown authorship on mathematical mechanics and catoptrics, known as the Fragmentum Mathematicum Bobiense (three leaves), Ptolemy's Analemma (six leaves), and an astronomical text that has hitherto remained unidentified and almost entirely unread (six leaves). We report here on the current state of our research on this last text, based on multispectral images. The text, incompletely preserved, is a treatise on the construction and uses of a nine-ringed armillary instrument, identifiable as the “meteoroscope” invented by Ptolemy and known to us from passages in Ptolemy's Geography and in writings of Pappus and Proclus. We further argue that the author of our text was Ptolemy himself.

Much of the mathematics with which Felix Klein and Sophus Lie are now associated (Klein’s Erlangen Program and Lie’s theory of transformation groups) is rooted in ideas they developed in their early work: the consideration of geometric objects or properties preserved by systems of transformations. As early as 1870, Lie studied particular examples of what he later called contact transformations, which preserve tangency and which came to play a crucial role in his systematic study of transformation groups and differential equations. This note examines Klein’s efforts in the 1870s to interpret contact transformations in terms of connexes and traces that interpretation (which included a false assumption) over the decades that follow. The analysis passes from Klein’s letters to Lie through Lindemann’s edition of Clebsch’s lectures on geometry in 1876, Lie’s criticism of it in his treatise on transformation groups in 1893, and the careful development of that interpretation by Dohmen, a student of Engel, in his 1905 dissertation. The now-obscure notion of connexes and its relation to Lie’s line elements and surface elements are discussed here in some detail.

This essay traces the history of early molecular dynamics simulations, specifically exploring the development of SHAKE, a constraint-based technique devised in 1976 by Jean-Paul Ryckaert, Giovanni Ciccotti and the late Herman Berendsen at CECAM (Centre Européen de Calcul Atomique et Moléculaire). The work of the three scientists proved to be instrumental in giving impetus to the MD simulation of complex polymer systems and it currently underpins the work of thousands of researchers worldwide who are engaged in computational physics, chemistry and biology. Despite its impact and its role in bringing different scientific fields together, accurate historical studies on the birth of SHAKE are virtually absent. By collecting and elaborating on the accounts of Ryckaert and Ciccotti, this essay aims to fill this gap, while also commenting on the conceptual and computational difficulties faced by its developers.

The idea of a canonical transformation emerged in 1837 in the course of Carl Jacobi's researches in analytical dynamics. To understand Jacobi's moment of discovery it is necessary to examine some background, especially the work of Joseph Lagrange and Siméon Poisson on the variation of arbitrary constants as well as some of the dynamical discoveries of William Rowan Hamilton. Significant figures following Jacobi in the middle of the century were Adolphe Desboves and William Donkin, while the delayed posthumous publication in 1866 of Jacobi's full dynamical corpus was a critical event. François Tisserand's doctoral dissertation of 1868 was devoted primarily to lunar and planetary theory but placed Hamilton–Jacobi mathematical methods at the forefront of the investigation. Henri Poincaré's writings on celestial mechanics in the period 1890–1910 succeeded in making canonical transformations a fundamental part of the dynamical theory. Poincaré offered a mathematical vision of the subject that differed from Jacobi's and would become influential in subsequent research. Two prominent researchers around 1900 were Carl Charlier and Edmund Whittaker, and their books included chapters devoted explicitly to transformation theory. In the first three decades of the twentieth century Hamilton–Jacobi theory in general and canonical transformations in particular would be embraced by a range of researchers in astronomy, physics and mathematics.

Modern color science finds its birth in the middle of the nineteenth century. Among the chief architects of the new color theory, the name of the polymath Hermann von Helmholtz stands out. A keen experimenter and profound expert of the latest developments of the fields of physiological optics, psychophysics, and geometry, he exploited his transdisciplinary knowledge to define the first non-Euclidean line element in color space, i.e., a three-dimensional mathematical model used to describe color differences in terms of color distances. Considered as the first step toward a metrically significant model of color space, his work inaugurated researches on higher color metrics, which describes how distance in the color space translates into perceptual difference. This paper focuses on the development of Helmholtz’s mathematical derivation of the line element. Starting from the first experimental evidence which opened the door to his reflections about the geometry of color space, it will be highlighted the pivotal role played by the studies conducted by his assistants in Berlin, which provided precious material for the elaboration of the final model proposed by Helmholtz in three papers published between 1891 and 1892. Although fallen into oblivion for about three decades, Helmholtz’s masterful work was rediscovered by Schrödinger and, since the 1920s, it has provided the basis for all subsequent studies on the geometry of color spaces up to the present time.