For textual studies relating to the ancient mathematical corpus the efforts by the Danish philologist, 1. L. Heiberg (1854-1928), are especially significant. Beginning with his doctoral dissertation, Quaestiones Archimedeae (Copen hagen, 1879), Heiberg produced an astonishing series of editions and critical studies that remain the foundation of scholarship on Greek mathematical 4 science. For comprehensiveness and accuracy, his editions are exemplary. In his textual studies, as also in the prolegomena to his editions, he carefully described the extant evidence, organized the manuscripts into stemmata, and drew out the implications for the state of the text. 5 With regard to his Archimedean work, Heiberg sometimes betrayed signs of the philologist's occupational disease - the tendency to rewrite a text deemed on subjective grounds to be unworthy. 6 But he did so less often than his prominent 7 contemporaries, and not as to detract appreciably from the value of his editions. In examining textual questions bearing on the Archimedean corpus, he attempted to exploit as much as possible evidence from the ancient commentators, and in some instances from the medieval translations. It is here that opportunities abound for new work, extending, and in some instances superseding, Heiberg's findings. For at his time the availability of the medieval materials was limited. In recent years Marshall Clagett has completed a mammoth critical edition of the medieval Latin tradition of Archimedes,8 while the bibliographical instruments for the Arabic tradition are in good order thanks to the work of Fuat Sezgin.

This volume deals with a variety of moments in the history of mechanics when conflicts arose within one textual tradition, between different traditions, or between textual traditions and the wider world of practice. Its purpose is to show how the accommodations sometimes made in the course of these conflicts ultimately contributed to the emergence of modern mechanics.

From water, air, and fire to tennessine and oganesson, celebrated science writer Philip Ball leads us through the full sweep of the field of chemistry in this exquisitely illustrated history of the elements. The Elements is a stunning visual journey through the discovery of the chemical building blocks of our universe. By piecing together the history of the periodic table, Ball explores not only how we have come to understand what everything is made of, but also how chemistry developed into a modern science. Ball groups the elements into chronological eras of discovery, covering seven millennia from the first known to the last named. As he moves from prehistory and classical antiquity to the age of atomic bombs and particle accelerators, Ball highlights images and stories from around the world and sheds needed light on those who struggled for their ideas to gain inclusion. By also featuring some elements that aren’t true elements but were long thought to be—from the foundational prote hyle and heavenly aetherof the ancient Greeks to more recent false elements like phlogiston and caloric—The Elements boldly tells the full history of the central science of chemistry.

This book documents the history of pi from the dawn of mathematical time to the present. One of the beauties of the literature on pi is that it allows for the inclusion of very modern, yet accessible, mathematics. The articles on pi collected herein fall into various classes. First and foremost there is a selection from the mathematical and computational literature of four millennia. There is also a variety of historical studies on the cultural significance of the number. Additionally, there is a selection of pieces that are anecdotal, fanciful, or simply amusing. For this new edition, the authors have updated the original material while adding new material of historical and cultural interest. There is a substantial exposition of the recent history of the computation of digits of pi, a discussion of the normality of the distribution of the digits, and new translations of works by Viete and Huygen.

Calculating Ethics in the Fourteenth Century addresses a moment in the history of ethics, when discoveries in natural philosophy blurred the boundary between the possible and the impossible, and made the impossible a preferred territory in discussions on practical reason. The volume studies the onset and expansion of a new movement in constructing ethics, as the methods, arguments, and cases adopted from logic and natural philosophy came to be extensively applied at Oxford and swiftly disseminated among other Oxonians eventually making their way outside Oxford. It shows how the Oxford Calculators triggered a unique and durable transformation in ethics. Contributors are Pascale Bermon, Valeria Buffon, Michael W. Dunne, Marek Gensler, Simon Kemp, Edit A. Lukács, Monika Michałowska, and Andrea Nannini.

The book presents a history of classical mechanics by focusing on issues of equilibrium. The historical point of view adopted here restricts attention to cases where the effectiveness of forces is assessed on the basis of the virtual motion of their points of application. For completeness, hints of the alternative approach are also referred, the Archimedean for ancient mechanics and the Newtonian for modern mechanics. The laws resulting from consideration of virtual motions are named laws of virtual work. The modern formulations of the principle of virtual work are only a particular form of them. The book begins with the first documented formulations of laws of virtual work in the IV century BC in Greece and proceeds to the end of the XIX century AD in Europe. A significant space is devoted to Arabic and Latin mechanics of Middle Ages. With the Renaissance it began to appear slightly different wordings of the laws, which were often proposed as unique principles of statics. The process reached its apex with Bernoulli and Lagrange in the XVIII century. The book ends with some chapters dealing with the discussions that took place in the French school on the role of the Lagrangian version of the law of virtual work and its applications to continuum mechanics.

Early Music History is devoted to the study of music from the early Middle Ages to the end of the seventeenth century. It demands the highest standards of scholarship from its contributors, all of whom are leading academics in their fields. It gives preference to studies pursuing interdisciplinary approaches and to those developing novel methodological ideas. The scope is exceptionally broad and includes manuscript studies, textual criticism, iconography, studies of the relationship between words and music and the relationship between music and society. Articles in volume one include: A lost guide to Tinctoris's teachings recovered; two English motets on Simon de Montfort; the Mary Magdalene scene in the Visitatio sepulchri ceremonies; and European politics and the distribution of music in the early fifteenth century.