Archive for History of Exact Sciences最新文献

In 1927, Paul Dirac first explicitly introduced the idea that electrodynamical processes can be evaluated by decomposing them into virtual (modern terminology), energy non-conserving subprocesses. This mode of reasoning structured a lot of the perturbative evaluations of quantum electrodynamics during the 1930s. Although the physical picture connected to Feynman diagrams is no longer based on energy non-conserving transitions but on off-shell particles, emission and absorption subprocesses still remain their fundamental constituents. This article will access the introduction and the initial reception of this picture of subsequent transitions (PST) by conceiving of concepts, models, and their representations as tools for the practitioners. I will argue for a multi-factorial explanation of Dirac’s initial, verbally explicit introduction: the mathematical representation he had developed was highly suggestive and already partly conceptualized; Dirac was philosophical flexible enough to talk about transitions when no actual transitions, according to the general interpretation of quantum mechanics of the time, occurred; and, importantly, Dirac eventually used the verbal exposition in the same paper in which he introduced it. The direct impact of PST on the conception of quantum electrodynamical processes will be exemplified by its reflection in diagrammatical representations. The study of the diverging ontological commitments towards PST immediately after its introduction opens up the prehistory of a philosophical debate that stretches out into the present: the dispute about the representational and ontological status of the physical picture connected to the evaluation of the perturbative series of QED and QFT.

Aristarchus’s De magnitudinis et distantiis solis et lunae was translated into Latin and printed by Federico Commandino in 1572. All subsequent editions of Aristarchus’ treatise, published by John Wallis (1688), Fortia d’ Urban (1823) and Thomas Heath (1913), followed Commandino’s work. In this article, through a philological approach to the geometric diagrams, I tracked down one of the Greek sources used by Commandino for preparing his Latin version. Commandino pays particular attention to drawing figures. This article sheds light on the interaction between mathematical skills and the drawing of geometric diagrams implemented in his Latin edition of Aristarchus’ book.

The paper brings into light and discusses a concentric solar model briefly described in Chapter 5 of Section III of ‘Abd al-Raḥmān al-Khāzinī’s On experimental astronomy, a treatise embedded in the prolegomenon of his comprehensive Mu‘tabar zīj, completed about 1121 c.e. In it, the Sun is assumed to rotate on the circumference of a circle concentric with the Earth and coplanar with the ecliptic, but the motion of the vector joining the Earth and Sun is monitored by a small eccentric hypocycle. The ratio between the distance of the hypocycle’s center from the Earth and the hypocycle’s radius is equal to the solar eccentricity in the eccentric model. The model is to account for the constancy of the apparent diameter of the solar disk as held by Ptolemy. The source of the model is unknown. Since the mechanism employed in it clearly resembles the pin-and-slot device, whose use in mechanical astronomical instruments has a long history from the Antikythera Mechanism to the medieval solar, lunar, and planetary equatoria and dials, we argue that the solar model can be positioned within this long-standing tradition and considered the result of the correct understanding of some Byzantine prototype and thus a typical example of the transmission of astronomical ideas via media of the material culture.

We consider the Geometria Practica of Christopher Clavius, S.J., a surprisingly eclectic and comprehensive practical geometry text, whose first edition appeared in 1604. Our focus is on four particular sections from Books IV and VI where Clavius has either used his sources in an interesting way or where he has been uncharacteristically reticent about them. These include the treatments of Heron’s Formula, Archimedes’ Measurement of the Circle, four methods for constructing two mean proportionals between two lines, and finally an algorithm for computing nth roots of numbers.

The manuscript UCLA 170/624 (ff. 75–76) contains Galileo’s proof of the center of gravity of the frustum of a cone, which was ultimately published as Theoremata circa centrum gravitatis solidorum in Discorsi e dimostrazioni matematiche intorno a due nuove scienze (Leiden 1638). The UCLA copy opens the possibility of giving a fuller account of Theoremata dating and development, and it can shed light on the origins of this research by the young Galileo. A comparison of the UCLA manuscript with the other extant copies is carried out to propose a new dating for the composition of the Theoremata. This dating will then be reconsidered in light of the mathematical content. The paper ends with a complete description of the content of the UCLA manuscript and the edition of Galileo’s text there contained.

This paper addresses an article by Felix Klein of 1886, in which he generalized his theory of polynomial equations of degree 5—comprehensively discussed in his Lectures on the Icosahedron two years earlier—to equations of degree 6 and 7. To do so, Klein used results previously established in line geometry. I review Klein’s 1886 article, its diverse mathematical background, and its place within the broader history of mathematics. I argue that the program advanced by this article, although historically overlooked due to its eventual failure, offers a valuable insight into a time of crucial evolution of the subject.

Gauss’ 1809 discussion of least squares, which can be viewed as the beginning of mathematical statistics, is reviewed. The general consensus seems to be that Gauss’ arguments are at fault, but we show that his reasoning is in fact correct, given his self-imposed restrictions, and persuasive without these restrictions.