To them, the traditional mathematical approach was a solid basis for the absolute truth represented by the Catholic faith and the authority of the Pope. On the opposite side, the religious congregation of the Jesuits used these same mathematical developments in its fight against heresy and the Reformation. This established the basis of inductive reasoning, which makes broad generalisations from specific observations, and led to a new science founded on experience. Here, the prominent figure of Galileo Galilei – together with Evangelista Torricelli, Bonaventura Cavalieri and others – was at the forefront of the new mathematical approach involving the concept of infinitesimals. The first part leads the reader to late 16th century Italy, where the flourishing and creative ideas of the Renaissance had given birth to a prolific number of mathematicians and scientists. This book is divided into two parts, each devoted to a particular geographical area and period in which this battle took place. But even more striking is that the new way of thinking built around the concept of infinitesimals crossed the borders of science and strongly influenced society, up to the point that mathematics became the main focus of the struggle between the old and new orders. The consequences for mathematics and physics were enormous, giving rise to unprecedented scientific progress that continued for the following decades and centuries. The idea of indivisible quantities and their use in geometry and arithmetic, which had already been developed by ancient Greek mathematicians, underwent its own renaissance 500 years ago, at the same time as Martin Luther launched the Reformation. The former were represented by immutable divine order and the principle of authority, the latter by social change and experimentation. Set in the late 16th and early 17th centuries, it describes how the concept of infinitesimals – a quantity that is explicitly nonzero and yet smaller than any measurable quantity – took a central role in the debate between ancient medieval ideas and the new ideas arising from the Renaissance. Lying midway between the history and the philosophy of science, this book illuminates a fascinating period in European history during which mathematics clashed with common thought and religion. Above all, the book displays the crucial mid-seventeenth-century shift from geometry to arithmetic and algebra as the primary language of mathematics.One World Infinitesimal: How a Dangerous Mathematical Theory Shaped the Modern World It shows how Wallis drew on some of the most important new ideas from the preceding twenty years, and took them forward to lay the foundations on which Newton was to build. Accompanied with annotations and an introductory essay, the translation makes Wallis's work fully available for the first time to modern readers. The book is the first English translation of John Wallis's 'Arithmetica Infinitorum' (1656), a key text on the seventeenth-century development of the calculus.

William Oughtred, Rector of the Church of Aldbury in the County of Surrey.- To the Most Respected Gentleman Doctor William Oughtred, Most Widely Famed Amongst Mathematicians, by John Wallis, Savilian Professor Of Geometry at Oxford.- Glossary.- Bibliography. Stedall.- To the Most Distinguished and Worthy Gentleman and Most Skilled Mathematician, Dr. Bibliography Includes bibliographical references (p.

The arithmetic of infinitesimals