John Pell worked in the Netherlands from 1643 until 1652. He therefore deserves a place in a survey of mathematics c. 1650 in the Netherlands. During his stay he was mainly concerned with refuting a quadrature of the circle that was published in 1644 in Amsterdam by the Danish astronomer and mathematician Longomontanus. We therefore make Pell's refutation the main theme of this paper, but other aspects of Pell's work and some biographical information will be discussed within this framework. This (...) paper includes a discussion of the refuted quadrature, and the first publication of a copy of the original one-leaf refutation, which was thought to be lost. In addition, we survey Pell's correspondence about the affair and in that connection discuss some unknown letters from Mersenne. (shrink)

Hobbes' philosophy of geometry was eccentric to contemporary movements and worsted in specific controversy. But he laid down stipulations defining geometry and its method which might provide a significant and workable alternative "meta-geometry". Some of these are isolated and reinterpreted here, especially those concerned with describing magnitudes, motions and quantities, and with his use of proportions. Rather than refutation of commentaries and historical rehash, the effort here is to isolate definitive texts and to offer a reinterpretation of their arguments in (...) succinct form showing their coherence and their interdependence with his other philosophic principles. (shrink)

The seventeenth century saw dramatic advances in mathematical theory and practice. With the recovery of many of the classical Greek mathematical texts, new techniques were introduced, and within 100 years, the rules of analytic geometry, geometry of indivisibles, arithmatic of infinites, and calculus were developed. Although many technical studies have been devoted to these innovations, Mancosu provides the first comprehensive account of the relationship between mathematical advances of the seventeenth century and the philosophy of mathematics of the period. Starting with (...) the Renaissance debates on the certainty of mathematics, Mancosu leads the reader through the foundational issues raised by the emergence of these new mathematical techniques, including the influence of the Aristotelian conception of science in Cavalieri and Guldin, the foundational relevance of Descartes' Geometrie, the relation between geometrical and epistemological theories of the infinite, and the Leibnizian calculus and the opposition to infinitesimalist procedures. In the process Mancosu draws a sophisticated picture of the subtle dependencies between technical development and philosophical reflection in seventeenth century mathematics. (shrink)

This article examines Hobbes’s conception of mathematical method, situating his methodological writings in the context of disputed mathematical issues of the seventeenth century. After a brief exposition of the Hobbesian philosophy of mathematics, it investigates Hobbes’s attempts to resolve three important mathematical controversies of the seventeenth century: the debates over the status of analytic geometry, disputes over the nature of ratios, and the problem of the “angle of contact” between a curve and tangent. In the course of these investigations, Hobbes’s (...) account of mathematics and its method is contrasted with the those of Descartes, Isaac Barrow, John Wallis, and Christopher Clavius. (shrink)

Hobbes ' geometrical disputes are significant since they highlight several important strands in his thought - issues concerning the right to make definitions, his anti-clericalism, the maker's knowledge argument and his objections to algebra. These are examined, and the foundational position, according to Hobbes, of geomentry in relation to philosophy, science and technology, explained and discussed.

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Thomas Hobbes is one of the most important figures in the history of European thought. Although interest in his life and work has grown enomrously in recent years, this is the first complete edition of his correspondence. The texts of the letters are richly supplemented with explanatory notes and full biographical and bibliographical information. This landmark publication sheds new light in abundance on the intellectual life of a major thinker.

A cornerstone of modern western philosophy, addressing the role of man in government, society and religion In 1651, Hobbes published his work about the relationship between the government and the individual. More than four centuries old, this brilliant yet ruthless book analyzes not only the bases of government but also physical nature and the roles of man. Comparable to Plato's Republic in depth and insight, Leviathan includes two society-changing phenomena that Plato didn't dare to dream of -- the rise of (...) great nation-states with their claims to absolute sovereignty, and modern science, with its unprecedented analytic power. To Hobbes, the leviathan -- a mythical sea creature described in the Old Testament -- represented his central thesis: that the state must be strong in order to control and protect its citizens. Even today, Hobbes's thesis in Leviathan is debated among scholars and philosophy aficionados around the globe. One of the earliest attempts at a genuinely scientific understanding of politics and society in their modern form, this book also remains one of the most stimulating. In his timeless work, Hobbes outlines his ideas about the passions and the conduct of man, and how his theories are realized in every individual. Addressing free will and religion, Hobbes constructs an intelligent argument for the basis of religion within government and how to organize a peaceful and successful Christian commonwealth. Like Plato's Republic, this book contains ideas on psychology, ethics, law, language, and religion that continue to challenge modern thinkers and exercise a profound influence on Western thought. A classic treatise of philosophy, Leviathan is critical reading for anyone who wishes to examine the human mind through the prisms of government and society. (shrink)