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Syriac translations and Syriac scholars played an important role in the transmission of the sciences, including the mathematical sciences, from the Greek to the Arabic world. Relatively little, unfortunately, remains of the translations and original mathematical works of earlier Syriac scholars, but some materials have survived, and further glimpses of what once existed may be gained from works of later authors. The paper will provide an overview of the earlier materials that have survived or are known to have existed. This will be followed by an account of some of the later materials, which will include an example illustrating how further earlier materials can be recovered from the writings of later authors, and a mention, by way of an epilogue, of an instance where a Syriac scholar was involved in a major historical and scientific event in the West, namely the reform of the calendar by Gregory XIII. (Contains 66 footnotes.)

This paper gives an account of the establishment and expansion of a Faculty of Science at the Calvinist "Free University" in the Netherlands in the 1930s. It describes the efforts of a group of orthodox Christians to come to terms with the natural sciences in the early twentieth century. The statutes of the university, which had been founded in 1880, prescribed that all research and teaching should be based on Calvinist, biblical principles. This ideal was formulated in opposition to the claim of nineteenth-century scientific naturalists that there was an inherent conflict between science and religion. However, despite their selection on the basis of their strict Calvinist beliefs, the first science professors attributed a certain independence to the domain of science. They agreed with the criticism of the conflict thesis, and tried to defuse the tensions between science and religion, although mainly at the level of philosophy and history, looking for example for harmony between science and religion in the past. Ironically, as a result of this approach, the Calvinist scientists mainly contributed to the acceptance of mainstream science in Dutch Calvinist circles, contrary to developments in other countries (notably the USA) where the conflict between science and orthodox Christianity has reasserted itself. (Contains 3 figures.)

This paper focuses on the scholastic approach to the intensity of complexions and presents some evidence as to how the meaning of complexio evolved in fourteenth-century Italian medicine: namely, how it was conceptualized, visualized, and finally quantified. In the first part, I summarize the philosophical development of complexio, pointing out how the concept differs from simple mixtures, thereby allowing for the mathematisation of compounds and their intensity. I then move on to consider the links between medicine and mathematics and present the schemes provided by Gentile Gentili da Foligno (1280/90 - 1348) as a case study, analysing their philosophical premises and implications for medical treatment more generally. In the final part, I argue that, quite aside from representing early forms of the mathematisation of qualities, schemata and diagrams also captured the medieval ideal of the cosmos, a hierarchical progression of forms ordered in ascending degrees of perfection and nobility. [ABSTRACT FROM AUTHOR]

This paper will consider the range of British participation in mathematics internationally during the nineteenth century through an analysis of British mathematical contributions to scientific journals outside of Britain. Viewing scientific papers contained in journals as significant indicators of research, we consider scientists who authored or read and responded in print to papers in a given area within a given group of journals to constitute a publication community. The extent of publication by British mathematicians in these journals can help characterize the role of foreign publication in nineteenth-century British mathematics. Moreover, the isolation of educational, societal, and personal circumstances which motivated British mathematicians to present their work to foreign journals highlights limited but concentrated groups of mathematicians committed to developing and strengthening international mathematical ties with Britain. [ABSTRACT FROM AUTHOR]

This paper offers a re-interpretation of the development of practical mathematics in Elizabethan England, placing artisanal know-how and the materials of the discipline at the heart of analysis, and bringing attention to Tudor economic policy by way of historical context. A major new source for the early instrument trade is presented: a manuscript volume of Chancery Court documents c.1565-c.1603, containing details of a patent granting a monopoly on making and selling mathematical instruments, circa 1575, to an unnamed individual, identified here as the instrument maker Humphrey Cole. Drawing on economic and legal history, the paper argues that practical mathematics needs to be understood as one 'project' among many, at a time when monopoly patents were used to advance industry, lower unemployment, secure the realm and reward invention. Drawing on the history and sociology of technology, it argues that the management and control of materials - mathematical instruments themselves, and the local socio-legal context within which they could be made - needs to be understood as prior to and separate from the rhetoric of mathematical authors, which is of interest in its own right but which may not have a direct relationship to mathematical practice.

This paper provides an account of Chinese translations of Newton's Principia produced over the past century and a half within the larger context of the dissemination of Newtonian philosophy in China. Given its fundamental importance in the history of science, the Principia, originally penned in Latin, has been translated into a number of other languages. While in all these languages no more than two full translations have appeared, as many as four complete versions in Chinese have been produced since the 1850s, when first attempts were made to translate the Principia in late imperial China. They include a 1931 version in semi-classical Chinese completed during the Republican era and three rival versions in modern Chinese published in contemporary China. This rich history of translating the Principia into Chinese, which remains little known to scholars in the West, is for the first time reconstructed and presented in English. This account is based on a meticulous scrutiny of manuscripts, historical records, secondary literature and interviews with some of the contemporary translators. It demonstrates that Chinese translation of the Principia is a complex process that involves scientific traditions, linguistic peculiarities, translators' subjectivity, readers' expectations and even the role of the market.

In this paper I will probe into Herman Boerhaave's (1668-1738) appropriation of Isaac Newton's natural philosophy. It will be shown that Newton's work served multiple purposes in Boerhaave's oeuvre, for he appropriated Newton's work differently in different contexts and in different episodes in his career. Three important episodes in, and contexts of, Boerhaave's appropriation of Newton's natural philosophical ideas and methods will be considered: 1710-11, the time of his often neglected lectures on the place of physics in medicine; 1715, when he delivered his most famous rectorial address; and, finally, 1731/2, in publishing his Elementa chemiae. Along the way, I will spell out the implications of Boerhaave's case for our understanding of the reception, or use, of Newton's ideas more generally.

This paper provides a detailed account of the period of the complex history of British algebra and geometry between the publication of George Peacock's Treatise on Algebra in 1830 and William Rowan Hamilton's paper on quaternions of 1843. During these years, Duncan Farquharson Gregory and William Walton published several contributions on 'algebraical geometry' and 'geometrical algebra' in the Cambridge Mathematical Journal. These contributions enabled them not only to generalize Peacock's symbolical algebra on the basis of geometrical considerations, but also to initiate the attempts to question the status of Euclidean space as the arbiter of valid geometrical interpretations. At the same time, Gregory and Walton were bound by the limits of symbolical algebra that they themselves made explicit; their work was not and could not be the 'abstract algebra' and 'abstract geometry' of figures such as Hamilton and Cayley. The central argument of the paper is that an understanding of the contributions to 'algebraical geometry' and 'geometrical algebra' of the second generation of 'scientific' symbolical algebraists is essential for a satisfactory explanation of the radical transition from symbolical to abstract algebra that took place in British mathematics in the 1830s-1840s.

The foundations of analysis offered by Cauchy and Riemann were not immediately welcomed by the mathematical community. Before 1870 the foundations of mathematics were considered more or less a national affair. In this paper, Dutch ideas of rigour in analysis between 1840 and 1870 will be discussed. These ideas show that Dutch mathematicians were aware of developments abroad but preferred the concept of infinitesimals as a foundation of mathematics. [ABSTRACT FROM AUTHOR]

The coming of mathematicians to the United States fleeing the spread of Nazism presented a serious problem to the American mathematical community. The persistence of the Depression had endangered the promising growth of mathematics in the United States. Leading mathematicians were concerned about the career prospects of their students. They (and others) feared that placing large numbers of refugees would exacerbate already present nationalistic and anti Semitic sentiments. The paper surveys a sequence of events in which the leading mathematicians reacted to the foreign-born and to the spread of Nazism, culminating in the decisions by the American Mathematical Society to found the journal Mathematical reviews and to form a War Preparedness Committee in September 1939. The most obvious consequence of the migration was an enlarged role for applied mathematics. [ABSTRACT FROM AUTHOR]

Focuses on the establishment of a mathematical community by Eliakim Hastings Moore in the U.S. Organization of an international congress of mathematicians; Delegation of students in Europe to study the advances in mathematics; Biography of Moore.

Robert Hooke's development of the theory of matter-as-vibration provides coherence to a career in natural philosophy which is commonly perceived as scattered and haphazard. It also highlights aspects of his work for which he is rarely credited: besides the creative speculative imagination and practical-instrumental ingenuity for which he is known, it displays lucid and consistent theoretical thought and mathematical skills. Most generally and importantly, however, Hooke's 'Principles ... of Congruity and Incongruity of bodies' represent a uniquely powerful approach to the most pressing challenge of the New Science: legitimizing the application of mathematics to the study of nature. This challenge required reshaping the mathematical practices and procedures; an epistemological framework supporting these practices; and a metaphysics which could make sense of this epistemology. Hooke's 'Uniform Geometrical or Mechanical Method' was a bold attempt to answer the three challenges together, by interweaving mathematics through physics into metaphysics and epistemology. Mathematics, in his rendition, was neither an abstract and ideal structure (as it was for Kepler), nor a wholly-flexible, artificial human tool (as it was for Newton). It drew its power from being contingent on the particularities of the material world. [ABSTRACT FROM AUTHOR]

Thomas Urquhart (1611–1660), celebrated for his English translation of Rabelais' Gargantua et Pantagruel, has earned some notoriety for his eccentric, putatively incomprehensible early book on trigonometry The Trissotetras (1645). The Trissotetras was too impractical to succeed in its own day as a textbook, since it lacked both trigonometric tables and sample calculations. But its current bad reputation is based on literary authors' amplifications of the verdict prefaced to its 19th century reprinting by one mathematician, William Wallace, who lacked the background to appreciate the book's historical context. Considering that context (including seventeenth century 'copious' prose, and medieval logic and 'art of memory'), the bad reputation is undeserved: the book is mathematically clear, clever (e.g. in superimposing 16 problems into one diagram), and complete. The Trissotetras may thus be viewed as simply one more of Urquhart's polymathic projects and involvements – which included education, rise of the middle class, religious and class conflicts, development of science and mathematics, search for patronage, universal language construction, and development of English prose – which serve to make him a lively and instructive intellectual Everyman for his time. [ABSTRACT FROM AUTHOR]

In 1670, the Bolognese mathematician Pietro Mengoli published his Speculationi di musica, a highly original work attempting to found the mathematical study of music on the anatomy of the ear. His anatomy was idiosyncratic and his mathematics extraordinarily complex, and he proposed a unique double mechanism of hearing. He analysed in detail the supposed behaviour of the subtle part of the air inside the ear, and the patterns of strokes made on the eardrum by simultaneous sounds. Most strikingly, he divided the musical octave into a continuous set of regions which he colour-coded to show their effects on a listener. His work did not find its way into the mainstream of seventeenth-century mathematical studies of music, but when examined in its context it has the potential to shed light on that discipline, as well as being of considerable interest in its own right. Here, I focus on the anatomical and mathematical basis of Mengoli's work. [ABSTRACT FROM AUTHOR]

Surprisingly little attention has been given hitherto to the definition of the laboratory. A space has to be specially adapted to deserve that title. It would be easy to assume that the two leading experimental sciences, physics and chemistry. have historically depended in a similar way on access to a laboratory. But while chemistry, through its alchernical ancestry with batteries of stills. had many fully fledged laboratories by the seventeenth century, physics was discovering the value of mathematics. Even experimental physics was content to make use of almost any indoor space, if not outdoors, ignoring the possible value of a laboratory. The development of the physics laboratory had to wait until the nineteenth century. [ABSTRACT FROM AUTHOR]

Focuses on the concept of repercussions in the field of mathematics. Use of differential and integral calculus; Demonstration of enigma; Rectification of curves on the spheres.

Presents the Leibniz's excerpts from the book 'Principia Mathematica,' by Isaac Newton with topics on mathematical equations for the journal 'Annals of Science.' Concept of vanishing quantities and last ratios by Newton; Edition of the manuscripts; Explanation on the causes of planetary motion.

Studies the mathematics of uniform circular motion and the problem of elliptical planetary motion. Dynamics on the linear motion to solve the complicated problems; Investigation on the coils of celestial circularity; Role of mathematics in the book 'Principia,' by Isaac Newton.

Presents an introduction and annotated translation of 'De quantitatibus,' a mathematical manuscript by Johannes Kepler. Interpretation of the Aristotelian passages relevant to mathematics by the book; Position taken by Kepler following the Aristotelian humanism of Schegk; Exhibition of original views on mathematics by Kepler.