From the time of al-Khwārizmī in the ninth century to the beginning of the sixteenth century algebraists did not allow irrational numbers to serve as coefficients. To multiply $\sqrt {18} $ by x, for instance, the result was expressed as the rhetorical equivalent of $\sqrt {18{x^2}} $ . The reason for this practice has to do with the premodern concept of a monomial. The coefficient, or “number,” of a term was thought of as how many of that term are present, and not as the scalar multiple that we work with today. Then, in sixteenth-century Europe, a few algebraists began to allow for irrational coefficients in their notation. Christoff Rudolff (1525) was the first to admit them in special cases, and subsequently they appear more liberally in Cardano (1539), Scheubel (1550), Bombelli (1572), and others, though most algebraists continued to ban them. We survey this development by examining the texts that show irrational coefficients and those that argue against them. We show that the debate took place entirely in the conceptual context of premodern, “cossic” algebra, and persisted in the sixteenth century independent of the development of the new algebra of Viète, Decartes, and Fermat. This was a formal innovation violating prevailing concepts that we propose could only be introduced because of the growing autonomy of notation from rhetorical text.

The Astronomical Book of Enoch describes the passage of the moon through the gates of heaven, which stand at the edges of the earth. In doing so, the book describes the position of the rising and setting of the moon on the horizon. Otto Neugebauer, the historian of ancient science, suggested using the detailed tables found in later Ethiopic texts in order to reconstruct the path of the moon through the gates. This paper offers a new examination of earlier versions of the Astronomical Book, using a mathematical analysis of the figures and astronomical theories presented throughout the Aramaic Astronomical Book; the results fit both the data preserved in the scrolls and the mathematical approach and religious ideology of the scroll's authors better than the details found in the late Ethiopic texts. Among other new insights, this alternate theory also teaches about the process of the composition of the Astronomical Book in the first centuries of its composition.

The paper focuses on the work of Lorenz Oken (1779–1851) in an attempt to make sense of the role played by Romantic Naturphilosophie in the development of natural history in Germany at the turn of the nineteenth century. It first focuses on the role played by Schelling and his Würzburg circle in the development of Oken's early views on natural history, then reconstructs Oken's mature programme for a reform of animal classification.

The rich tradition of Siberian science and higher education is little known outside Russian academic circles. Using institutional history, this article focuses on the founding and pre-war period of the Siberian Physical Technical Institute, the establishment of its research focus and its first difficult steps to become a leading centre of R & D in Siberia. Based on archival materials, the article describes how local and national physicists justified the institute's creation by demonstrating ties with industry and building on the presence of a cohort of locally trained physicists, whose numbers were augmented by Leningrad specialists. The strength of local cadres enabled the institute to navigate civil war and cultural revolution successfully. Physicists were able to take advantage of ongoing industrialization campaigns to gain support to create the institute, although local disputes and economic problems slowed its further development. The article describes the circulation of scientific, political and philosophical knowledge between Moscow, Leningrad and the provinces, and the impact of Bolshevik rule and Stalinism on the Siberian physics enterprise.

Having been found ‘vehemently suspected of heresy’ by the Holy Office in 1633, at the time of his death (1642) Galileo's remains were laid to rest in the tiny vestry of a lateral chapel of the Santa Croce Basilica, Florence. Throughout his life, Vincenzo Viviani, Galileo's last disciple, struggled to have his master's name rehabilitated and his banned works reprinted, as well as a proper funeral monument erected. He did not live to see all this come true, but his efforts triggered a mechanism that eventually led to the fulfilment of his wishes. A key element of his project was the transformation of the facade of his palace into a private (but publicly rendered) tribute to Galileo, with two long inscriptions celebrating Galileo's achievements and calling Florence's attention to the need to pay a proper tribute to him. Shortly afterwards, he revised the text and circulated it in print. This article presents the first critical edition and annotated translation of Viviani's original manuscript, long thought to be lost, and describes its role in Viviani's lifelong struggle for Galileo's intellectual legacy, as well as its impact on future historiography.

In the midsummer of 1872 a lighthouse apparatus was installed in the Clock Tower of the House of Commons. The installation served the practical function of communicating at a distance when the House was sitting, but also provided a highly visible symbolic indication of the importance of lighthouse technology to national concerns. Further, the installation served as an experimental space in which rival technological designs, with corresponding visions for the lighthouse system, could compete in public. This article considers nineteenth-century lighthouse technology as a case study in the power and political significance of display. Manufacturers of lighthouse lenses, such as the firm of Chance Brothers, sought to manage interpretations of the lights through the framing of exhibitions and demonstrations; so too did scientific authorities, including Michael Faraday and John Tyndall, both of whom served in the role of scientific adviser to Trinity House, the body responsible for lighthouse management. Particularly notable in this process was the significance of urban, metropolitan display environments in shaping the development of the marine lighthouse system around the nation's periphery.