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Contents: Introduction Sebastian MA1/4nster: a brief biography 16th-century cosmography: its sources, development and ambitions The Cosmographia: genesis of an idea, methods of realisation, versions of the text From centre to periphery: the organisation, topics and content of the Cosmographiae Universalis Understanding the world of MA1/4nster's Cosmographia: evaluating man, celebrating his works and interpreting the book of the world Conclusion Bibliography Index.

This book argues that we can only understand the transformations of nature studies in the early modern period, often called the Scientific Revolution, if we take seriously the interaction between those who know by doing (practitioners or craftsmen) and those who know by thinking (scholars or philosophers). Mathematical practitioners played an essential role in this transformation; this book examines the role of mathematics and mathematical practice on the changing ideology and methodology of science. We first set out the problematic, examining the argument from both sides: articulating Zilsel, Cormack identifies those dimensions of practical mathematics that showed up as important aspects of ‘the new science’; Schuster focuses on the new scientists as selective appropriators of ideas, values and practices originally embedded in practical mathematics. This book furthers the debate about the role of mathematical practice in the scientific revolution in four ways. First, it demonstrates the variability of practical mathematicians and of their practices. Second, it argues that in spite of this variability, participants were able to recognize the family resemblance between the different types. Third, differences and nuances in practical mathematics typically depended on the different contexts in which it was practiced. Fourth, this book shows that diverse and new historiographical approaches to the study of practical mathematics should be considered.

This chapter challenges the traditional historiography of the scientific revolution, arguing that skilled artisans and mathematical practitioners were essential for a transformation of natural knowledge, the so-called ‘scholar-craftsman’ debate. Beginning with a new articulation of Edgar Zilsel’s thesis, which argued for an essential role for mathematical practitioners (or as he would have called them, “superior artisans”) in the scientific revolution, this chapter argues that historians need to take into account social, cultural, political and economic factors, rather than the simpler Marxist explanations of Zilsel. Cormack thus presents the case for the importance of social, economic, and cultural influences on the changing face of nature studies, particularly seeing the importance of mathematical practitioners in putting forward an agenda of utility, measurement, and inductive methodology. This is an argument for the important influence of both social factors and the practitioners themselves. Using English geography in the sixteenth century, and particularly the work of Edward Wright and Thomas Harriot, she argues that geography and mathematics allowed communication between theory and practice, provided new spaces for such exchanges, and changed attitudes towards mathematization, practicality and utility.

“Mathematics for Sale” investigates the location of mathematics within London, arguing that the place and community for practical mathematics provided the foundation for the coffee house culture of the seventeenth century. This paper examines mathematical lectures and especially instrument-makers both inside and outside the City walls. In particular, Thomas Hood’s mathematical lectures started a trend of such events, followed by a proposal by Edward Wright and John Tapp to fund a lecture in navigation. Gresham College played a small part in housing mathematics instruction for the larger community, but it was in the instrument shops of instrument-makers like Elias Allen and Emery Molyneux that like-minded men gathered to discuss practical mathematics and instruments. Cormack identifies 85 different instrument-makers and mathematical practitioners with shops and rooms in London between 1550 and 1630. She thus discovers a vibrant practical mathematical community, whose members were gentry, scholars, merchants, instrument-makers, and navigators. This rich mathematical exchange laid the groundwork for the natural philosophical sociability of the seventeenth century. These early mathematically-minded men and their ideas, however, did not change natural philosophy in a direct way.

James Valentine’s “On the Origin of Phyla” is divided into three main sections: “Evidence of the Origins of Metazoan Phyla,” “The Metazoan Phyla,” and “The Evolution of the Phyla.” The second section is the zoological core of the book, a more or less conventional treatment of major animal taxa, arranged in chain-of-being fashion from sponges to cnidarians to “worms” of many kinds, and so onward to arthropods, echinoderms, chordates, and all others in between. Philosophically inclined readers will be most interested in the first and third sections of the volume, which treat phylogenetic principles and macroevolution respectively. These sections are rich in detail, but Valentine adopts something of a rear-guard position on many issues, arguing in favor of a number of concepts that most systematists have now abandoned. The publisher’s advertisement describes “On the Origin of Phyla” as “one of the classic scientific texts of the twentieth century,” and for us in the 21st century, that may be the best way to regard it. It will be of greatest value to zoologists who want a good compendium of current comparative data, and to historians and philosophers of science who have an interest in the complex development of phylogenetic “tree-thinking” in systematic biology.

The teaching and learning of geographical and mathematical knowledge in early modern England was a complex interaction among scholars, practitioners, merchants, and gentry. Each group had different values and goals associated with geographical knowledge and therefore different educational venues and different topics to be investigated. This paper argues that the alternate educational sites of the universities of Oxford and Cambridge and the more entrepreneurial site of London and the merchant halls were both important to the development of geographical knowledge and produced an important synergy of practical and esoteric interests and concerns.