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Thomas Harriot's Artis Analyticae Praxis by Muriel Seltman,Robert Goulding Pdf
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 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.
Thomas Harriot: Science and Discovery in the English Renaissance by Robert Fox Pdf
This volume sheds new light on one of the most remarkable polymaths of the English Renaissance. It offers original perspectives not only on Harriot’s personal achievements in mathematics and natural philosophy but also on the wider realms of exploration, colonial ambition, and philosophical debate in which he earned the attention and respect of contemporaries in and far beyond the socially elevated circles of his two great patrons, first Walter Ralegh and then Henry Percy, the ninth Earl of Northumberland. Harriot’s sixteenth-century world was one of unprecedented expansion in both scientific understanding and the discovery of new lands and peoples. The essays gathered here bring out forcefully the effect of this expanding vision, encapsulated in Harriot’s Briefe and true report of the new found land of Virginia (1588), the first detailed description of America to be published in the English language. In addition to an essay by a recent biographer of Harriot, the volume contains reworked versions of seven Thomas Harriot Lectures, an annual lecture series inaugurated in 1990 in Oriel College, Oxford. It follows two earlier volumes of Harriot Lectures, also edited by Robert Fox, that appeared in 2000 and 2012.
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.
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.
In the early modern period, a crucial transformation occurred in the classical conception of number and magnitude. Traditionally, numbers were merely collections of discrete units that measured some multiple. Magnitude, on the other hand, was usually described as being continuous, or being divisible into parts that are infinitely divisible. This traditional idea of discrete number versus continuous magnitude was challenged in the early modern period in several ways. This detailed study explores how the development of algebraic symbolism, logarithms, and the growing practical demands for an expanded number concept all contributed to a broadening of the number concept in early modern England. An interest in solving practical problems was not, in itself, enough to cause a generalisation of the number concept. It was the combined impact of novel practical applications together with the concomitant development of such mathematical advances as algebraic notation and logarithms that produced a broadened number concept.
Encyclopedia of Renaissance Philosophy by Marco Sgarbi Pdf
Gives accurate and reliable summaries of the current state of research. It includes entries on philosophers, problems, terms, historical periods, subjects and the cultural context of Renaissance Philosophy. Furthermore, it covers Latin, Arabic, Jewish, Byzantine and vernacular philosophy, and includes entries on the cross-fertilization of these philosophical traditions. A unique feature of this encyclopedia is that it does not aim to define what Renaissance philosophy is, rather simply to cover the philosophy of the period between 1300 and 1650.
The Medical World of Margaret Cavendish by Justin Begley,Benjamin Goldberg Pdf
This book is the first transcription and extensive commentary on a fascinating but almost entirely overlooked manuscript compilation of medical recipes and letters, which is held in the University of Nottingham. Collected by the Marquess and Marchioness of Newcastle, William and Margaret Cavendish, during the 1640s and 1650s, this manuscript features letters of advice, recipes, and sundry philosophical and medical reflections by some of the most formidable and influential physicians, philosophers, and courtly scholars of the early seventeenth century. These include “Europe’s physician” Theodore de Mayerne, the adventurer and courtier Kenelm Digby, and the natural philosopher, poet, and playwright Margaret Cavendish. While the transcription and accompanying annotations will allow a diverse array of readers to appreciate the manuscript for the first time, the introduction situates the Cavendishes’ recipe collecting habits, medical preoccupations, natural philosophical views, and politics within their social, cultural, and philosophical contexts, and draws out some of the most significant implications of this important document.
How the concept of proof has enabled the creation of mathematical knowledge The Story of Proof investigates the evolution of the concept of proof—one of the most significant and defining features of mathematical thought—through critical episodes in its history. From the Pythagorean theorem to modern times, and across all major mathematical disciplines, John Stillwell demonstrates that proof is a mathematically vital concept, inspiring innovation and playing a critical role in generating knowledge. Stillwell begins with Euclid and his influence on the development of geometry and its methods of proof, followed by algebra, which began as a self-contained discipline but later came to rival geometry in its mathematical impact. In particular, the infinite processes of calculus were at first viewed as “infinitesimal algebra,” and calculus became an arena for algebraic, computational proofs rather than axiomatic proofs in the style of Euclid. Stillwell proceeds to the areas of number theory, non-Euclidean geometry, topology, and logic, and peers into the deep chasm between natural number arithmetic and the real numbers. In its depths, Cantor, Gödel, Turing, and others found that the concept of proof is ultimately part of arithmetic. This startling fact imposes fundamental limits on what theorems can be proved and what problems can be solved. Shedding light on the workings of mathematics at its most fundamental levels, The Story of Proof offers a compelling new perspective on the field’s power and progress.
Thomas Harriot's Doctrine of Triangular Numbers by Janet Beery,Jacqueline A. Stedall Pdf
Thomas Harriot (1560-1621) was a mathematician and astronomer who founded the English school of algebra. He is known not only for his work in algebra and geometry but also as a prolific writer with wide-ranging interests in ballistics, navigation, and optics. (He discovered the sine law of refraction now known as Snell's law.) By about 1614, Harriot had developed finite difference interpolation methods for navigational tables. In 1618 (or slightly later) he composed a treatise entitled `De numeris triangularibus et inde de progressionibus arithmeticis, Magisteria magna', in which he derived symbolic interpolation formulae and showed how to use them. This treatise was never published and is here reproduced for the first time. Commentary has been added to help the reader follow Harriot's beautiful but almost completely nonverbal presentation. The introductory essay preceding the treatise gives an overview of the contents of the `Magisteria' and describes its influence on Harriot's contemporaries and successors over the next sixty years. Harriot's method was not superseded until Newton, apparently independently, made a similar discovery in the 1660s. The ideas in the `Magisteria' were spread primarily through personal communication and unpublished manuscripts, and so, quite apart from their intrinsic mathematical interest, their survival in England during the seventeenth century provides an important case study in the dissemination of mathematics through informal networks of friends and acquaintances.
A celebration of the seemingly simple idea that allowed us to imagine the world in new dimensions—sparking both controversy and discovery. The stars of this book, vectors and tensors, are unlikely celebrities. If you ever took a physics course, the word “vector” might remind you of the mathematics needed to determine forces on an amusement park ride, a turbine, or a projectile. You might also remember that a vector is a quantity that has magnitude and (this is the key) direction. In fact, vectors are examples of tensors, which can represent even more data. It sounds simple enough—and yet, as award-winning science writer Robyn Arianrhod shows in this riveting story, the idea of a single symbol expressing more than one thing at once was millennia in the making. And without that idea, we wouldn’t have such a deep understanding of our world. Vector and tensor calculus offers an elegant language for expressing the way things behave in space and time, and Arianrhod shows how this enabled physicists and mathematicians to think in a brand-new way. These include James Clerk Maxwell when he ushered in the wireless electromagnetic age; Einstein when he predicted the curving of space-time and the existence of gravitational waves; Paul Dirac, when he created quantum field theory; and Emmy Noether, when she connected mathematical symmetry and the conservation of energy. For it turned out that it’s not just physical quantities and dimensions that vectors and tensors can represent, but other dimensions and other kinds of information, too. This is why physicists and mathematicians can speak of four-dimensional space-time and other higher-dimensional “spaces,” and why you’re likely relying on vectors or tensors whenever you use digital applications such as search engines, GPS, or your mobile phone. In exploring the evolution of vectors and tensors—and introducing the fascinating people who gave them to us—Arianrhod takes readers on an extraordinary, five-thousand-year journey through the human imagination. She shows the genius required to reimagine the world—and how a clever mathematical construct can dramatically change discovery’s direction.
The Emergence Of Number by John Newsome Crossley Pdf
This book presents detailed studies of the development of three kinds of number. In the first part the development of the natural numbers from Stone-Age times right up to the present day is examined not only from the point of view of pure history but also taking into account archaeological, anthropological and linguistic evidence. The dramatic change caused by the introduction of logical theories of number in the 19th century is also treated and this part ends with a non-technical account of the very latest developments in the area of Gödel's theorem. The second part is concerned with the development of complex numbers and tries to answer the question as to why complex numbers were not introduced before the 16th century and then, by looking at the original materials, shows how they were introduced as a pragmatic device which was only subsequently shown to be theoretically justifiable. The third part concerns the real numbers and examines the distinction that the Greeks made between number and magnitude. It then traces the gradual development of a theory of real numbers up to the precise formulations in the nineteeth century. The importance of the Greek distinction between the number line and the geometric line is brought into sharp focus.This is an new edition of the book which first appeared privately published in 1980 and is now out of print. Substantial revisions have been made throughout the text, incorporating new material which has recently come to light and correcting a few relatively minor errors. The third part on real numbers has been very extensively revised and indeed the last chapter has been almost completely rewritten. Many revisions are the results of comments from earlier readers of the book.
William Oughtred: A Great Seventeenth-Century Teacher of Mathematics by Florian Cajori Pdf
"William Oughtred: A Great Seventeenth-Century Teacher of Mathematics" by Florian Cajori is an extensive and insightful biography that brings to life the remarkable mathematician William Oughtred. Within its pages, Cajori skillfully navigates the life and achievements of Oughtred, offering readers a profound understanding of his contributions to the world of mathematics. This biography not only serves as a tribute to Oughtred's legacy but also as a window into the intellectual landscape of the seventeenth century. Cajori's meticulous research and narrative expertise provide a captivating journey through the life and times of this influential mathematician, shedding light on his enduring impact on mathematical thought and education. For those intrigued by the history of mathematics and the individuals who shaped it, this book is an indispensable resource.