A large discourse concerning algebra: John Wallis's 1685 <i>Treatise of algebra</i>

A treatise of algebra historical and practical (London 1685) by John Wallis (1616-1703) was the first full length history of algebra. In four hundred pages Wallis explored the development of algebra from its appearances in Classical, Islamic and medieval cultures to the modern forms that had evolved by the end of the seventeenth century. Wallis dwelt especially on the work of his countrymen and contemporaries, Oughtred, Harriot, Pell, Brouncker and Newton, and on his own contribution to the emergence of algebra as the common language of mathematics. This thesis explores why and how A treatise of algebra was written, and the sources Wallis used. It begins by analysing Wallis's account of mathematical learning in medieval England, never previously investigated. In his researches on the origins and spread of the numeral system Wallis was at his best as a historian, and initiated many modern historiographical techniques. His summary of algebra in Renaissance Europe was less detailed, but for Wallis this part of the story set the scene for the English flowering that was to be his main theme. The influence of Oughtred's Clavis on Wallis and his contemporaries, and Wallis's efforts to promote the book, are explored in detail. Wallis's controversial account of Harriot's algebra is also examined and it is argued that it was better founded than has sometimes been supposed and that Wallis had direct access to Harriot's algebra through Pell. Many other chapters of A treatise of algebra contain mathematics that can be linked or traced to Pell, a hitherto unsuspected secret of the book. The later chapters of the thesis, like the final part of A treatise of algebra, explore Wallis's Arithmetica infinitorum and the work which arose from it up to Newton's foundation of modern analysis, and include a discussion of Brouncker's treatment of the number challenges set by Fermat. The thesis ends with a summary of contemporary and later reactions to A treatise of algebra and an assessment of Wallis's view of algebra and its history

Bronx Community College Catalog 1962-1964

Course catalog for Bronx Community College for 1962-64. Also includes Supplement to Catalog No. 2 1962-1964, dated September 1, 1963

Edmund Burke and the Scottish enlightenment

This study examines Edmund Burke's reliance upon the philosophical assumptions of the Scottish "Common Sense" school of critical realism. Scottish realism was articulated in the writings of Thomas Reid, Dugald Stewart and James Beattie, and constituted a significant part of the generally-accepted intellectual phenomenon of the Scottish Enlightenment, which reached its zenith in the last half of the eighteenth century. By identifying the various forms which Burke's Scottish connections took, this study seeks to narrow the gap between Burke studies and recent historiography of the Scottish Enlightenment. The Scottish Enlightenment is now seen as second only to the French Enlightenment as a formative influence upon the course of thought in eighteenth-century Europe. Older writings have established the "critical" nature of the Scottish Common Sense school and of the Scottish Enlightenment in general. A number of commentators have noted the philosophical similarity between the critical cast of the thought of the Scottish school and that of the contemporary critical idealism of Immanuel Kant. This study suggests that the historical and philosophical connection between Burke and the Scottish Enlightenment, as well as the philosophical similarity between Scottish and Kantian critical realism and idealism, together indicate a philosophical kinship between critical realism, critical idealism, and some of the assumptions in Burke s thought

Fundamental Theorem of Algebra: A Survey of History and Proofs

Higher Educatio