This is the first English translation of Thomas Harriot’s seminal Artis Analyticae Praxis, first published in Latin in 1631. It has recently become clear that Harriot's editor substantially rearranged the work, and omitted sections beyond his comprehension. Commentary included with this translation relates to corresponding pages in the manuscript papers, enabling exploration of Harriot's novel and advanced mathematics. This publication provides the basis for a reassessment of the development of algebra.

This volume assembles ten studies of the life and work of Thomas Harriot (1560-1621). These are based on lectures that have been given annually at Oriel College, Oxford since 1990, by such authorities as Hugh Trevor Roper, David Quinn and John D. North. An astronomer and mathematician whose activities embraced not only science but also philosophical debate and an engagement in the early exploration of America, Harriot occupied a prominent place in intellectual and public life. He was well read in the contemporary literature of science, and his writings on algebra, his correspondence, and his early observations with the telescope, undertaken at the same time as Galileo’s, brought him to the attention of leading men of science both in Britain and abroad. Recent scholarship has enhanced historians’ appreciation of Harriot’s achievements and of the scientific context and social milieu in which he worked, a milieu distinguished by his friendship with Walter Ralegh and the Ninth Earl of Northumberland (the ’Wizard Earl’ whose association with the Gunpowder Plot led to many years of imprisonment in the Tower). The contributions to Thomas Harriot. An Elizabethan man of science shed new light on all the main aspects of Harriot’s life and stand as an important contribution to the re-evaluation of one of the most gifted and intriguing figures in early modern British science.

Symbols, Impossible Numbers, and Geometric Entanglements is the first history of the development and reception of algebra in early modern England and Scotland. Not primarily a technical history, this book analyzes the struggles of a dozen British thinkers to come to terms with early modern algebra, its symbolical style, and negative and imaginary numbers. Professor Pycior uncovers these thinkers as a "test-group" for the symbolic reasoning that would radically change not only mathematics but also logic, philosophy, and language studies. The book also shows how pedagogical and religious concerns shaped the British debate over the relative merits of algebra and geometry. The first book to position algebra firmly in the Scientific Revolution and pursue Newton the algebraist, it highlights Newton's role in completing the evolution of algebra from an esoteric subject into a major focus of British mathematics. Other thinkers covered include Oughtred, Harriot, Wallis, Hobbes, Barrow, Berkeley, and MacLaurin.

This historic work consists of several treatises that developed the first consistent, coherent, and systematic conception of algebraic equations. Originally published in 1591, it pioneered the notion of using symbols of one kind (vowels) for unknowns and of another kind (consonants) for known quantities, thus streamlining the solution of equations. Francois Viète (1540-1603), a lawyer at the court of King Henry II in Tours and Paris, wrote several treatises that are known collectively as The Analytic Art. His novel approach to the study of algebra developed the earliest articulated theory of equations, allowing not only flexibility and generality in solving linear and quadratic equations, but also something completely new—a clear analysis of the relationship between the forms of the solutions and the values of the coefficients of the original equation. Viète regarded his contribution as developing a "systematic way of thinking" leading to general solutions, rather than just a "bag of tricks" to solve specific problems. These essays demonstrate his method of applying his own ideas to existing usage in ways that led to clear formulation and solution of equations.

As Robyn Arianrhod shows in this new biography, the most complete to date, Thomas Harriot was a pioneer in both the figurative and literal sense. Navigational adviser and loyal friend to Sir Walter Ralegh, Harriot--whose life was almost exactly contemporaneous to Shakespeare's--took part in the first expedition to colonize Virginia in 1585. Not only was he responsible for getting Ralegh's ships safely to harbor in the New World, he was also the first European to acquire a working knowledge of an indigenous language from what is today the US, and to record in detail the local people's way of life. In addition to his groundbreaking navigational, linguistic, and ethnological work, Harriot was the first to use a telescope to map the moon's surface, and, independently of Galileo, recorded the behavior of sunspots and discovered the law of free fall. He preceded Newton in his discovery of the properties of the prism and the nature of the rainbow, to name just two more of his unsung "firsts." Indeed many have argued that Harriot was the best mathematician of his age, and one of the finest experimental scientists of all time. Yet he has remained an elusive figure. He had no close family to pass down records, and few of his letters survive. Most importantly, he never published his scientific discoveries, and not long after his death in 1621 had all but been forgotten. In recent decades, many scholars have been intent on restoring Harriot to his rightful place in scientific history, but Arianrhod's biography is the first to pull him fully into the limelight. She has done it the only way it can be done: through his science. Using Harriot's re-discovered manuscripts, Arianrhod illuminates the full extent of his scientific and cultural achievements, expertly guiding us through what makes them original and important, and the story behind them. Harriot's papers provide unique insight into the scientific process itself. Though his thinking depended on a more natural, intuitive approach than those who followed him, and who achieved the lasting fame that escaped him, Harriot helped lay the foundations of what in Newton's time would become modern physics. Thomas Harriot: A Life in Science puts a human face to scientific inquiry in the Elizabethan and Jacobean worlds, and at long last gives proper due to the life and times of one of history's most remarkable minds.

​The book records the essential discoveries of mathematical and computational scientists in chronological order, following the birth of ideas on the basis of prior ideas ad infinitum. The authors document the winding path of mathematical scholarship throughout history, and most importantly, the thought process of each individual that resulted in the mastery of their subject. The book implicitly addresses the nature and character of every scientist as one tries to understand their visible actions in both adverse and congenial environments. The authors hope that this will enable the reader to understand their mode of thinking, and perhaps even to emulate their virtues in life.

This second volume of papers on Thomas Harriot edited by Professor Robert Fox is based on the annual Harriot lectures delivered at Oriel College, Oxford between 2000 and 2009. It complements the previous volume, published as Thomas Harriot: An Elizabethan Man of Science in 2000. The focus in several of the papers is on Harriot's outstanding achievements as a mathematician; others consider why he has never received the recognition accorded to his great contemporary, Galileo; others again examine his association with his entrepreneurial patron Walter Ralegh and his contributions to the intensely practical world of exploration and seamanship, as exemplified in his voyage to the coast of present-day North Carolina in 1585. The volume adds significantly to our understanding of a true Renaissance man who wrote accomplished Latin, earned the respect of Europe's leading mathematicians and astronomers, and moved easily in circles close to the English court and whose 'Brief and true report of the new found land of Virginia' (1588) was the first detailed description of America to be published in the English language.

This is a collection of surveys on important mathematical ideas, their origin, their evolution and their impact in current research. The authors are mathematicians who are leading experts in their fields. The book is addressed to all mathematicians, from undergraduate students to senior researchers, regardless of the specialty.

Described even today as "unsurpassed," this history of mathematical notation stretching back to the Babylonians and Egyptians is one of the most comprehensive written. In two impressive volumes-first published in 1928-9-distinguished mathematician Florian Cajori shows the origin, evolution, and dissemination of each symbol and the competition it faced in its rise to popularity or fall into obscurity. Illustrated with more than a hundred diagrams and figures, this "mirror of past and present conditions in mathematics" will give students and historians a whole new appreciation for "1 + 1 = 2." Swiss-American author, educator, and mathematician FLORIAN CAJORI (1859-1930) was one of the world's most distinguished mathematical historians. Appointed to a specially created chair in the history of mathematics at the University of California, Berkeley, he also wrote An Introduction to the Theory of Equations, A History of Elementary Mathematics, and The Chequered Career of Ferdinand Rudolph Hassler.

Described even today as "unsurpassed," this history of mathematical notation stretching back to the Babylonians and Egyptians is one of the most comprehensive written. In two impressive volumes, first published in 1928-9 and reproduced here under one cover, distinguished mathematician Florian Cajori shows the origin, evolution, and dissemination of each symbol and the competition it faced in its rise to popularity or fall into obscurity. Illustrated with more than a hundred diagrams and figures, this "mirror of past and present conditions in mathematics" will give students and historians a whole new appreciation for "1 + 1 = 2." Swiss-American author, educator, and mathematician FLORIAN CAJORI (1859-1930) was one of the world's most distinguished mathematical historians. Appointed to a specially created chair in the history of mathematics at the University of California, Berkeley, he also wrote An Introduction to the Theory of Equations, A History of Mathematical Notations, and The Chequered Career of Ferdinand Rudolph Hassler.