The Mathematicall Praeface To The Elements Of Geometrie Of Euclid Of Megara 1570
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The Mathematicall Praeface to Elements of Geometrie of Euclid of Megara
Reproduction of the original: The Mathematicall Praeface to Elements of Geometrie of Euclid of Megara by John Dee
Motion and Genetic Definitions in the Sixteenth-Century Euclidean Tradition
A significant number of works have set forth, over the past decades, the emphasis laid by seventeenth-century mathematicians and philosophers on motion and kinematic notions in geometry. These works demonstrated the crucial role attributed in this context to genetic definitions, which state the mode of generation of geometrical objects instead of their essential properties. While the growing importance of genetic definitions in sixteenth-century commentaries on Euclid’s Elements has been underlined, the place, uses and status of motion in this geometrical tradition has however never been thoroughly and comprehensively studied. This book therefore undertakes to fill a gap in the history of early modern geometry and philosophy of mathematics by investigating the different treatments of motion and genetic definitions by seven major sixteenth-century commentators on Euclid’s Elements, from Oronce Fine (1494–1555) to Christoph Clavius (1538–1612), including Jacques Peletier (1517–1582), John Dee (1527–1608/1609) and Henry Billingsley (d. 1606), among others. By investigating the ontological and epistemological conceptions underlying the introduction and uses of kinematic notions in their interpretation of Euclidean geometry, this study displays the richness of the conceptual framework, philosophical and mathematical, inherent to the sixteenth-century Euclidean tradition and shows how it contributed to a more generalised acceptance and promotion of kinematic approaches to geometry in the early modern period.
Mathematical Practitioners and the Transformation of Natural Knowledge in Early Modern Europe
This book argues that we can only understand transformations of nature studies in the Scientific Revolution if we take seriously the interaction between practitioners (those who know by doing) and scholars (those who know by thinking). These are not in opposition, however. Theory and practice are end points on a continuum, with some participants interested only in the practical, others only in the theoretical, and most in the murky intellectual and material world in between. It is this borderland where influence, appropriation, and collaboration have the potential to lead to new methods, new subjects of enquiry, and new social structures of natural philosophy and science. The case for connection between theory and practice can be most persuasively drawn in the area of mathematics, which is the focus of this book. Practical mathematics was a growing field in early modern Europe and these essays are organised into three parts which contribute to the debate about the role of mathematical practice in the Scientific Revolution. First, they demonstrate the variability of the identity of practical mathematicians, and of the practices involved in their activities in early modern Europe. Second, readers are invited to consider what practical mathematics looked like and that although practical mathematical knowledge was transmitted and circulated in a wide variety of ways, participants were able to recognize them all as practical mathematics. Third, the authors show how differences and nuances in practical mathematics typically depended on the different contexts in which it was practiced: social, cultural, political, and economic particularities matter. Historians of science, especially those interested in the Scientific Revolution period and the history of mathematics will find this book and its ground-breaking approach of particular interest.