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| diophantus arithmetica book: Diophantus And Arithmetica Dr. Arun Kumar Mishra, 2022-12-13 ‘Arithmetica’ is an eminent book of mathematics, written by a Greek mathematician Diophantus. A systematic work on Diophantus was performed by Sir Thomas L. Heath, K.C.B. Sir Thomas L. Heath had written a very impressive book entitled, “Diophantus of Alexandria: A study in the History of Greek Algebra”. The first edition of the book in English on Diophantus appeared in 1885. |
| diophantus arithmetica book: The Arithmetica of Diophantus Jean Christianidis, Jeffrey Oaks, 2022-11-01 This volume offers an English translation of all ten extant books of Diophantus of Alexandria’s Arithmetica, along with a comprehensive conceptual, historical, and mathematical commentary. Before his work became the inspiration for the emerging field of number theory in the seventeenth century, Diophantus (ca. 3rd c. CE) was known primarily as an algebraist. This volume explains how his method of solving arithmetical problems agrees both conceptually and procedurally with the premodern algebra later practiced in Arabic, Latin, and European vernaculars, and how this algebra differs radically from the modern algebra initiated by François Viète and René Descartes. It also discusses other surviving traces of ancient Greek algebra and follows the influence of the Arithmetica in medieval Islam, Byzantium, and the European Renaissance down to the 1621 publication of Claude-Gaspard Bachet’s edition. After the English translation the book provides a problem-by-problem commentary explaining the solutions in a manner compatible with Diophantus’s mode of thought. The Arithmetica of Diophantus provides an invaluable resource for historians of mathematics, science, and technology, as well as those studying ancient Greek, medieval Islamic and Byzantine, and Renaissance history. In addition, the volume is also suitable for mathematicians and mathematics educators. |
| diophantus arithmetica book: Diophantus of Alexandria Thomas L. Heath, 1910 |
| diophantus arithmetica book: The Fermat Diary Charles J. Mozzochi, 2000 This book concentrates on the final chapter of the story of perhaps the most famous mathematics problem of our time: Fermat's Last Theorem. The full story begins in 1637, with Pierre de Fermat's enigmatic marginal note in his copy of Diophantus's Arithmetica. It ends with the spectacular solution by Andrew Wiles some 350 years later. The Fermat Diary provides a record in pictures and words of the dramatic time from June 1993 to August 1995, including the period when Wiles completed the last stages of the proof and concluding with the mathematical world's celebration of Wiles' result at Boston University. This diary takes us through the process of discovery as reported by those who worked on the great puzzle: Gerhard Frey who conjectured that Shimura-Taniyama implies Fermat; Ken Ribet who followed a difficult and speculative plan of attack suggested by Jean-Pierre Serre and established the statement by Frey; and Andrew Wiles who announced a proof of enough of the Shimura-Taniyama conjecture to settle Fermat's Last Theorem, only to announce months later that there was a gap in the proof. Finally, we are brought to the historic event on September 19, 1994, when Wiles, with the collaboration of Richard Taylor, dramatically closed the gap. The book follows the much-in-demand Wiles through his travels and lectures, finishing with the Instructional Conference on Number Theory and Arithmetic Geometry at Boston University. There are many important names in the recent history of Fermat's Last Theorem. This book puts faces and personalities to those names. Mozzochi also uncovers the details of certain key pieces of the story. For instance, we learn in Frey's own words the story of his conjecture, about his informal discussion and later lecture at Oberwolfach and his letter containing the actual statement. We learn from Faltings about his crucial role in the weeks before Wiles made his final announcement. An appendix contains the Introduction of Wiles' Annals paper in which he describes the evolution of his solution and gives a broad overview of his methods. Shimura explains his position concerning the evolution of the Shimura-Taniyama conjecture. Mozzochi also conveys the atmosphere of the mathematical community--and the Princeton Mathematics Department in particular--during this important period in mathematics. This eyewitness account and wonderful collection of photographs capture the marvel and unfolding drama of this great mathematical and human story. |
| diophantus arithmetica book: An Adventurer's Guide to Number Theory Richard Friedberg, 1968 Presents an historical approach to number theory, treating the properties of numbers as abstract concepts, and encouraging the young student to use his imagination. |
| diophantus arithmetica book: An Introduction to Diophantine Equations Titu Andreescu, Dorin Andrica, Ion Cucurezeanu, 2010-09-02 This problem-solving book is an introduction to the study of Diophantine equations, a class of equations in which only integer solutions are allowed. The presentation features some classical Diophantine equations, including linear, Pythagorean, and some higher degree equations, as well as exponential Diophantine equations. Many of the selected exercises and problems are original or are presented with original solutions. An Introduction to Diophantine Equations: A Problem-Based Approach is intended for undergraduates, advanced high school students and teachers, mathematical contest participants — including Olympiad and Putnam competitors — as well as readers interested in essential mathematics. The work uniquely presents unconventional and non-routine examples, ideas, and techniques. |
| diophantus arithmetica book: Number Theory and Geometry: An Introduction to Arithmetic Geometry Álvaro Lozano-Robledo, 2019-03-21 Geometry and the theory of numbers are as old as some of the oldest historical records of humanity. Ever since antiquity, mathematicians have discovered many beautiful interactions between the two subjects and recorded them in such classical texts as Euclid's Elements and Diophantus's Arithmetica. Nowadays, the field of mathematics that studies the interactions between number theory and algebraic geometry is known as arithmetic geometry. This book is an introduction to number theory and arithmetic geometry, and the goal of the text is to use geometry as the motivation to prove the main theorems in the book. For example, the fundamental theorem of arithmetic is a consequence of the tools we develop in order to find all the integral points on a line in the plane. Similarly, Gauss's law of quadratic reciprocity and the theory of continued fractions naturally arise when we attempt to determine the integral points on a curve in the plane given by a quadratic polynomial equation. After an introduction to the theory of diophantine equations, the rest of the book is structured in three acts that correspond to the study of the integral and rational solutions of linear, quadratic, and cubic curves, respectively. This book describes many applications including modern applications in cryptography; it also presents some recent results in arithmetic geometry. With many exercises, this book can be used as a text for a first course in number theory or for a subsequent course on arithmetic (or diophantine) geometry at the junior-senior level. |
| diophantus arithmetica book: Elements of Algebra Leonhard Euler, 1810 |
| diophantus arithmetica book: Amazing Traces Of A Babylonian Origin In Greek Mathematics Joran Friberg, 2007-04-18 A sequel to Unexpected Links Between Egyptian and Babylonian Mathematics (World Scientific, 2005), this book is based on the author's intensive and ground breaking studies of the long history of Mesopotamian mathematics, from the late 4th to the late 1st millennium BC. It is argued in the book that several of the most famous Greek mathematicians appear to have been familiar with various aspects of Babylonian “metric algebra,” a convenient name for an elaborate combination of geometry, metrology, and quadratic equations that is known from both Babylonian and pre-Babylonian mathematical clay tablets.The book's use of “metric algebra diagrams” in the Babylonian style, where the side lengths and areas of geometric figures are explicitly indicated, instead of wholly abstract “lettered diagrams” in the Greek style, is essential for an improved understanding of many interesting propositions and constructions in Greek mathematical works. The author's comparisons with Babylonian mathematics also lead to new answers to some important open questions in the history of Greek mathematics. |
| diophantus arithmetica book: Making up Numbers: A History of Invention in Mathematics Ekkehard Kopp, 2020-10-23 Making up Numbers: A History of Invention in Mathematics offers a detailed but accessible account of a wide range of mathematical ideas. Starting with elementary concepts, it leads the reader towards aspects of current mathematical research. The book explains how conceptual hurdles in the development of numbers and number systems were overcome in the course of history, from Babylon to Classical Greece, from the Middle Ages to the Renaissance, and so to the nineteenth and twentieth centuries. The narrative moves from the Pythagorean insistence on positive multiples to the gradual acceptance of negative numbers, irrationals and complex numbers as essential tools in quantitative analysis. Within this chronological framework, chapters are organised thematically, covering a variety of topics and contexts: writing and solving equations, geometric construction, coordinates and complex numbers, perceptions of ‘infinity’ and its permissible uses in mathematics, number systems, and evolving views of the role of axioms. Through this approach, the author demonstrates that changes in our understanding of numbers have often relied on the breaking of long-held conventions to make way for new inventions at once providing greater clarity and widening mathematical horizons. Viewed from this historical perspective, mathematical abstraction emerges as neither mysterious nor immutable, but as a contingent, developing human activity. Making up Numbers will be of great interest to undergraduate and A-level students of mathematics, as well as secondary school teachers of the subject. In virtue of its detailed treatment of mathematical ideas, it will be of value to anyone seeking to learn more about the development of the subject. |
| diophantus arithmetica book: Books IV to VII of Diophantus' Arithmetica Jacques Sesiano, 1982-11-17 |
| diophantus arithmetica book: Fermat's last theorem Simon Singh, John Lynch, scénariste, 1997 |
| diophantus arithmetica book: Critical Mathematics Education Paul Ernest, Bharath Sriraman, Nuala Ernest, 2016-01-01 Mathematics is traditionally seen as the most neutral of disciplines, the furthest removed from the arguments and controversy of politics and social life. However, critical mathematics challenges these assumptions and actively attacks the idea that mathematics is pure, objective, and value?neutral. It argues that history, society, and politics have shaped mathematics—not only through its applications and uses but also through molding its concepts, methods, and even mathematical truth and proof, the very means of establishing truth. Critical mathematics education also attacks the neutrality of the teaching and learning of mathematics, showing how these are value?laden activities indissolubly linked to social and political life. Instead, it argues that the values of openness, dialogicality, criticality towards received opinion, empowerment of the learner, and social/political engagement and citizenship are necessary dimensions of the teaching and learning of mathematics, if it is to contribute towards democracy and social justice. This book draws together critical theoretic contributions on mathematics and mathematics education from leading researchers in the field. Recurring themes include: The natures of mathematics and critical mathematics education, issues of epistemology and ethics; Ideology, the hegemony of mathematics, ethnomathematics, and real?life education; Capitalism, globalization, politics, social class, habitus, citizenship and equity. The book demonstrates the links between these themes and the discipline of mathematics, and its critical teaching and learning. The outcome is a groundbreaking collection unified by a shared concern with critical perspectives of mathematics and education, and of the ways they impact on practice. |
| diophantus arithmetica book: Algebraic Number Theory and Fermat's Last Theorem Ian Stewart, David Tall, 2001-12-12 First published in 1979 and written by two distinguished mathematicians with a special gift for exposition, this book is now available in a completely revised third edition. It reflects the exciting developments in number theory during the past two decades that culminated in the proof of Fermat's Last Theorem. Intended as a upper level textbook, it |
| diophantus arithmetica book: Geometric Theorems, Diophantine Equations, and Arithmetic Functions J. Sándor, 2002 |
| diophantus arithmetica book: The Analytic Art François Viète, T. Richard Witmer, 2006-01-01 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. |
| diophantus arithmetica book: The Philosopher Queens Rebecca Buxton, Lisa Whiting, 2020-09-17 'This is brilliant. A book about women in philosophy by women in philosophy – love it!' Elif Shafak Where are the women philosophers? The answer is right here. The history of philosophy has not done women justice: you’ve probably heard the names Plato, Kant, Nietzsche and Locke – but what about Hypatia, Arendt, Oluwole and Young? The Philosopher Queens is a long-awaited book about the lives and works of women in philosophy by women in philosophy. This collection brings to centre stage twenty prominent women whose ideas have had a profound – but for the most part uncredited – impact on the world. You’ll learn about Ban Zhao, the first woman historian in ancient Chinese history; Angela Davis, perhaps the most iconic symbol of the American Black Power Movement; Azizah Y. al-Hibri, known for examining the intersection of Islamic law and gender equality; and many more. For anyone who has wondered where the women philosophers are, or anyone curious about the history of ideas – it's time to meet the philosopher queens. |
| diophantus arithmetica book: The Equation that Couldn't Be Solved Mario Livio, 2005-09-19 What do Bach's compositions, Rubik's Cube, the way we choose our mates, and the physics of subatomic particles have in common? All are governed by the laws of symmetry, which elegantly unify scientific and artistic principles. Yet the mathematical language of symmetry-known as group theory-did not emerge from the study of symmetry at all, but from an equation that couldn't be solved. For thousands of years mathematicians solved progressively more difficult algebraic equations, until they encountered the quintic equation, which resisted solution for three centuries. Working independently, two great prodigies ultimately proved that the quintic cannot be solved by a simple formula. These geniuses, a Norwegian named Niels Henrik Abel and a romantic Frenchman named Évariste Galois, both died tragically young. Their incredible labor, however, produced the origins of group theory. The first extensive, popular account of the mathematics of symmetry and order, The Equation That Couldn't Be Solved is told not through abstract formulas but in a beautifully written and dramatic account of the lives and work of some of the greatest and most intriguing mathematicians in history. |
| diophantus arithmetica book: 13 Lectures on Fermat's Last Theorem Paulo Ribenboim, 2012-12-06 Lecture I The Early History of Fermat's Last Theorem.- 1 The Problem.- 2 Early Attempts.- 3 Kummer's Monumental Theorem.- 4 Regular Primes.- 5 Kummer's Work on Irregular Prime Exponents.- 6 Other Relevant Results.- 7 The Golden Medal and the Wolfskehl Prize.- Lecture II Recent Results.- 1 Stating the Results.- 2 Explanations.- Lecture III B.K. = Before Kummer.- 1 The Pythagorean Equation.- 2 The Biquadratic Equation.- 3 The Cubic Equation.- 4 The Quintic Equation.- 5 Fermat's Equation of Degree Seven.- Lecture IV The Naïve Approach.- 1 The Relations of Barlow and Abel.- 2 Sophie Germain.- 3 Co. |
| diophantus arithmetica book: Invitation to the Mathematics of Fermat-Wiles Yves Hellegouarch, 2002 Each chapter includes exercises and problems. |
| diophantus arithmetica book: Greek Mathematical Thought and the Origin of Algebra Jacob Klein, 2013-04-22 Important study focuses on the revival and assimilation of ancient Greek mathematics in the 13th-16th centuries, via Arabic science, and the 16th-century development of symbolic algebra. 1968 edition. Bibliography. |
| diophantus arithmetica book: The Development of Arabic Mathematics: Between Arithmetic and Algebra R. Rashed, 2013-04-18 An understanding of developments in Arabic mathematics between the IXth and XVth century is vital to a full appreciation of the history of classical mathematics. This book draws together more than ten studies to highlight one of the major developments in Arabic mathematical thinking, provoked by the double fecondation between arithmetic and the algebra of al-Khwarizmi, which led to the foundation of diverse chapters of mathematics: polynomial algebra, combinatorial analysis, algebraic geometry, algebraic theory of numbers, diophantine analysis and numerical calculus. Thanks to epistemological analysis, and the discovery of hitherto unknown material, the author has brought these chapters into the light, proposes another periodization for classical mathematics, and questions current ideology in writing its history. Since the publication of the French version of these studies and of this book, its main results have been admitted by historians of Arabic mathematics, and integrated into their recent publications. This book is already a vital reference for anyone seeking to understand history of Arabic mathematics, and its contribution to Latin as well as to later mathematics. The English translation will be of particular value to historians and philosophers of mathematics and of science. |
| diophantus arithmetica book: Brill's Companion to the Reception of Ancient Rhetoric Sophia Papaioannou, Andreas Serafim, Michael Edwards, 2022 This volume, examining the reception of ancient rhetoric, aims to demonstrate that the past is always part of the present: in the ways in which decisions about crucial political, social and economic matters have been made historically; or in organic interaction with literature, philosophy and culture at the core of the foundation principles of Western thought and values. Analysis is meant to cover the broadest possible spectrum of considerations that focus on the totality of rhetorical species (i.e. forensic, deliberative and epideictic) as they are applied to diversified topics (including, but not limited to, language, science, religion, literature, theatre and other cultural processes (e.g. athletics), politics and leadership, pedagogy and gender studies) and cross-cultural, geographical and temporal contexts-- |
| diophantus arithmetica book: The History of Mathematics Jacqueline Stedall, 2012-02-23 Mathematics is a fundamental human activity that can be practised and understood in a multitude of ways; indeed, mathematical ideas themselves are far from being fixed, but are adapted and changed by their passage across periods and cultures. In this Very Short Introduction, Jacqueline Stedall explores the rich historical and cultural diversity of mathematical endeavour from the distant past to the present day. Arranged thematically, to exemplify the varied contexts in which people have learned, used, and handed on mathematics, she also includes illustrative case studies drawn from a range of times and places, including early imperial China, the medieval Islamic world, and nineteenth-century Britain. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable. |
| diophantus arithmetica book: Fermat's Last Theorem Amir D. Azcel, Amir D. Aczel, 2007-10-12 Simple, elegant, and utterly impossible to prove, Fermat's last theorem captured the imaginations of mathematicians for more than three centuries. For some, it became a wonderful passion. For others it was an obsession that led to deceit, intrigue, or insanity. In a volume filled with the clues, red herrings, and suspense of a mystery novel, Amir D. Aczel reveals the previously untold story of the people, the history, and the cultures that lie behind this scientific triumph. From formulas devised from the farmers of ancient Babylonia to the dramatic proof of Fermat's theorem in 1993, this extraordinary work takes us along on an exhilarating intellectual treasure hunt. Revealing the hidden mathematical order of the natural world in everything from stars to sunflowers, Fermat's Last Theorem brilliantly combines philosophy and hard science with investigative journalism. The result: a real-life detective story of the intellect, at once intriguing, thought-provoking, and impossible to put down. |
| diophantus arithmetica book: The History of Mathematics: An Introduction David Burton, 2010-02-09 The History of Mathematics: An Introduction, Seventh Edition, is written for the one- or two-semester math history course taken by juniors or seniors, and covers the history behind the topics typically covered in an undergraduate math curriculum or in elementary schools or high schools. Elegantly written in David Burton’s imitable prose, this classic text provides rich historical context to the mathematics that undergrad math and math education majors encounter every day. Burton illuminates the people, stories, and social context behind mathematics’ greatest historical advances while maintaining appropriate focus on the mathematical concepts themselves. Its wealth of information, mathematical and historical accuracy, and renowned presentation make The History of Mathematics: An Introduction, Seventh Edition a valuable resource that teachers and students will want as part of a permanent library. |
| diophantus arithmetica book: The Math Book Clifford A. Pickover, 2009 This book covers 250 milestones in mathematical history, beginning millions of years ago with ancient ant odometers and moving through time to our modern-day quest for new dimensions. |
| diophantus arithmetica book: Recreations in Mathematics and Natural Philosophy, Recomposed by M. Montucla and Tr. by C. Hutton Jacques Ozanam, 2022-10-27 This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. |
| diophantus arithmetica book: Recipients, Commonly Called the Data Euclid, 1987-05 |
| diophantus arithmetica book: Tales of Impossibility David S. Richeson, 2021-11-02 A comprehensive look at four of the most famous problems in mathematics Tales of Impossibility recounts the intriguing story of the renowned problems of antiquity, four of the most famous and studied questions in the history of mathematics. First posed by the ancient Greeks, these compass and straightedge problems—squaring the circle, trisecting an angle, doubling the cube, and inscribing regular polygons in a circle—have served as ever-present muses for mathematicians for more than two millennia. David Richeson follows the trail of these problems to show that ultimately their proofs—which demonstrated the impossibility of solving them using only a compass and straightedge—depended on and resulted in the growth of mathematics. Richeson investigates how celebrated luminaries, including Euclid, Archimedes, Viète, Descartes, Newton, and Gauss, labored to understand these problems and how many major mathematical discoveries were related to their explorations. Although the problems were based in geometry, their resolutions were not, and had to wait until the nineteenth century, when mathematicians had developed the theory of real and complex numbers, analytic geometry, algebra, and calculus. Pierre Wantzel, a little-known mathematician, and Ferdinand von Lindemann, through his work on pi, finally determined the problems were impossible to solve. Along the way, Richeson provides entertaining anecdotes connected to the problems, such as how the Indiana state legislature passed a bill setting an incorrect value for pi and how Leonardo da Vinci made elegant contributions in his own study of these problems. Taking readers from the classical period to the present, Tales of Impossibility chronicles how four unsolvable problems have captivated mathematical thinking for centuries. |
| diophantus arithmetica book: Sleepers Lorenzo Carcaterra, 2010-09-29 #1 NEW YORK TIMES BESTSELLER • The extraordinary true story of four men who take the law into their own hands. This is the story of four young boys. Four lifelong friends. Intelligent, fun-loving, wise beyond their years, they are inseparable. Their potential is unlimited, but they are content to live within the closed world of New York City’s Hell’s Kitchen. And to play as many pranks as they can on the denizens of the street. They never get caught. And they know they never will. Until one disastrous summer afternoon. On that day, what begins as a harmless scheme goes horrible wrong. And the four find themselves facing a year’s imprisonment in the Wilkinson Home for Boys. The oldest of them is fifteen, the youngest twelve. What happens to them over the course of that year—brutal beatings, unimaginable humiliation—will change their lives forever. Years later, one has become a lawyer. One a reporter. And two have grown up to be murderers, professional hit men. For all of them, the pain and fear of Wilkinson still rages within. Only one thing can erase it. Revenge. To exact it, they will twist the legal system. Commandeer the courtroom for their agenda. Use the wiles they observed on the streets, the violence they learned at Wilkinson. If they get caught this time, they only have one thing left to lose: their lives. Praise for Sleepers “Undeniably powerful, an enormously affecting and intensely human story . . . Sleepers is a thriller, to be sure, but it is equally a wistful hymn to another age.”—The Washington Post Book World “A powerful book, hard to forget . . . Carcaterra is an excellent writer, changing pace here and there but never letting the reader go. . . . Sensitive, humorous, and harrowing, featuring dialogue with perfect pitch.”—The Denver Post “A gut-wrenching piece of work . . . [Lorenzo] Carcaterra’s graphic narrative grips like gunfire in a dark alley.”—The Atlanta Journal-Constitution “A terrifying account of brutality and retribution, searing in its emotional truth, peopled with murderers, sadists, and thugs, but biblical in its passion and scope.”—People |
| diophantus arithmetica book: Makers of Mathematics Stuart Hollingdale, 2006-01-01 Each chapter of this portrait of the evolution of mathematics examines the work of an individual — Archimedes, Descartes, Fermat, Pascal, Newton, Einstein, and others — to explore the mathematics of his era. Rather than a series of biographical profiles, readers encounter an accessible chronology of pioneering developments in mathematics. 1989 edition. |
| diophantus arithmetica book: Elementary Number Theory in Nine Chapters James J. Tattersall, 1999-10-14 This book is intended to serve as a one-semester introductory course in number theory. Throughout the book a historical perspective has been adopted and emphasis is given to some of the subject's applied aspects; in particular the field of cryptography is highlighted. At the heart of the book are the major number theoretic accomplishments of Euclid, Fermat, Gauss, Legendre, and Euler, and to fully illustrate the properties of numbers and concepts developed in the text, a wealth of exercises have been included. It is assumed that the reader will have 'pencil in hand' and ready access to a calculator or computer. For students new to number theory, whatever their background, this is a stimulating and entertaining introduction to the subject. |
| diophantus arithmetica book: Books IV to VII of Diophantus’ Arithmetica Jacques Sesiano, 2012-12-06 This edition of Books IV to VII of Diophantus' Arithmetica, which are extant only in a recently discovered Arabic translation, is the outgrowth of a doctoral dissertation submitted to the Brown University Department of the History of Mathematics in May 1975. Early in 1973, my thesis adviser, Gerald Toomer, learned of the existence of this manuscript in A. Gulchln-i Macanl's just-published catalogue of the mathematical manuscripts in the Mashhad Shrine Library, and secured a photographic copy of it. In Sep tember 1973, he proposed that the study of it be the subject of my dissertation. Since limitations of time compelled us to decide on priorities, the first objective was to establish a critical text and to translate it. For this reason, the Arabic text and the English translation appear here virtually as they did in my thesis. Major changes, however, are found in the mathematical com mentary and, even more so, in the Arabic index. The discussion of Greek and Arabic interpolations is entirely new, as is the reconstruction of the history of the Arithmetica from Diophantine to Arabic times. It is with the deepest gratitude that I acknowledge my great debt to Gerald Toomer for his constant encouragement and invaluable assistance. |
| diophantus arithmetica book: Diophantus of Alexandria -A Study in the History of Greek Algebra Sir Thomas L. Heath, 2008-11 This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1902 Excerpt: ...earth. r' = radius of moon, or other body. P = moon's horizontal parallax = earth's angular semidiameter as seen from the moon. f = moon's angular semidiameter. Now = P (in circular measure), r'-r = r (in circular measure);.'. r: r':: P: P', or (radius of earth): (radios of moon):: (moon's parallax): (moon's semidiameter). Examples. 1. Taking the moon's horizontal parallax as 57', and its angular diameter as 32', find its radius in miles, assuming the earth's radius to be 4000 miles. Here moon's semidiameter = 16';.-. 4000::: 57': 16';.-. r = 400 16 = 1123 miles. 2. The sun's horizontal parallax being 88, and his angular diameter 32V find his diameter in miles. ' Am. 872,727 miles. 3. The synodic period of Venus being 584 days, find the angle gained in each minute of time on the earth round the sun as centre. Am. l-54 per minute. 4. Find the angular velocity with which Venus crosses the sun's disc, assuming the distances of Venus and the earth from the sun are as 7 to 10, as given by Bode's Law. Since (fig. 50) S V: VA:: 7: 3. But Srhas a relative angular velocity round the sun of l-54 per minute (see Example 3); therefore, the relative angular velocity of A V round A is greater than this in the ratio of 7: 3, which gives an approximate result of 3-6 per minute, the true rate being about 4 per minute. Annual ParaUax. 95. We have already seen that no displacement of the observer due to a change of position on the earth's surface could apparently affect the direction of a fixed star. However, as the earth in its annual motion describes an orbit of about 92 million miles radius round the sun, the different positions in space from which an observer views the fixed stars from time to time throughout the year must be separated ... |
| diophantus arithmetica book: Exponential Diophantine Equations T. N. Shorey, R. Tijdeman, 1986-11-27 This is a integrated presentation of the theory of exponential diophantine equations. The authors present, in a clear and unified fashion, applications to exponential diophantine equations and linear recurrence sequences of the Gelfond-Baker theory of linear forms in logarithms of algebraic numbers. Topics covered include the Thue equations, the generalised hyperelliptic equation, and the Fermat and Catalan equations. The necessary preliminaries are given in the first three chapters. Each chapter ends with a section giving details of related results. |
| diophantus arithmetica book: A History of Greek Mathematics Sir Thomas Little Heath, Thomas Little Heath, 1981-01-01 Volume 1 of an authoritative two-volume set that covers the essentials of mathematics and includes every landmark innovation and every important figure. This volume features Euclid, Apollonius, others. |
| diophantus arithmetica book: Books IV to VII of Diophantus' Arithmetica in the Arabic Translation Attributed to Qusṭā Ibn Lūqā Jacques Sesiano, 1982-01-01 |
| diophantus arithmetica book: The Saga of Mathematics Marty Lewinter, William Widulski, 2001 For undergraduate-level courses in the History of Mathematics, or Liberal Arts Mathematics. Perfect for the non-math major, this inexpensive paperback text uses lively language to put mathematics in an interesting, historical context and points out the many links to art, philosophy, music, computers, navigation, science, and technology. The arithmetic, algebra, and geometry are presented in a way that makes them relevant to daily life as well as larger issues. |
| diophantus arithmetica book: Revolutions and Continuity in Greek Mathematics Michalis Sialaros, 2018-04-23 This volume brings together a number of leading scholars working in the field of ancient Greek mathematics to present their latest research. In their respective area of specialization, all contributors offer stimulating approaches to questions of historical and historiographical ‘revolutions’ and ‘continuity’. Taken together, they provide a powerful lens for evaluating the applicability of Thomas Kuhn’s ideas on ‘scientific revolutions’ to the discipline of ancient Greek mathematics. Besides the latest historiographical studies on ‘geometrical algebra’ and ‘premodern algebra’, the reader will find here some papers which offer new insights into the controversial relationship between Greek and pre-Hellenic mathematical practices. Some other contributions place emphasis on the other edge of the historical spectrum, by exploring historical lines of ‘continuity’ between ancient Greek, Byzantine and post-Hellenic mathematics. The terminology employed by Greek mathematicians, along with various non-textual and material elements, is another topic which some of the essays in the volume explore. Finally, the last three articles focus on a traditionally rich source on ancient Greek mathematics; namely the works of Plato and Aristotle. |
Diophantus' Lifespan - Mathematics Stack Exchange
Today I saw Diophantus' Epitaph. For those of you who don't know it and don't feel like googling: 'Here lies Diophantus,' the wonder behold. Through art algebraic, the stone tells how old: 'God...
reference request - Is there an English translation of Diophantus's ...
Aug 24, 2011 · Is Heath's book really a translation? It seems more like a book ABOUT Diophantus's "Arithmetica", not the translation of the actual book. There's just an "abstract" …
How to solve the problem that determines the age of Diophantus?
Let D D be the number of years Diophantus lived, and S S the number of years his son lived. First we make an obvious relation, that his son lived for half his own lifetime.
Are problems in "Arithmetica" of Diophantus all solved now?
Jan 31, 2019 · It's well-known that Diophantus had written ”Diophantus“ which contains many problems about solving arithmetic equations. I wonder whether all of them has been solved …
Fermat's Notes on Diophantus - Mathematics Stack Exchange
Aug 17, 2016 · I am looking for a free online copy of Diophantus' Arithmetica as well as Fermat's Notes on it. After some google searching, I couldn't find any. Thanks for your help! Edit: …
How to find solutions of linear Diophantine ax + by = c?
The diophantine equation ax + by = c has solutions if and only if gcd(a, b) c. If so, it has infinitely many solutions, and any one solution can be used to generate all the other ones. To see this, …
abstract algebra - Diophantus math - Mathematics Stack Exchange
Diophantus math Ask Question Asked 11 years, 7 months ago Modified 11 years, 7 months ago
Nonlinear system Diophantus. - Mathematics Stack Exchange
Aug 18, 2015 · In the extant books of Diophantus, are considered in the system of equations. Of interest is the non-linear system of Diophantine equations. Some simple systems from his book …
Question on proving Primitive Pythagorean triples using …
Jan 25, 2020 · Question on proving Primitive Pythagorean triples using Diophantus method? [duplicate] Ask Question Asked 5 years, 4 months ago Modified 5 years, 4 months ago
abstract algebra - Diophantus mathematics - Mathematics Stack …
Find a number whose subtraction from two given numbers (say, $9$ and $21$) allows both differences to be squares. Call the required number $9 - x^2$ so that the condition holds …
Diophantus' Lifespan - Mathematics Stack Exchange
Today I saw Diophantus' Epitaph. For those of you who don't know it and don't feel like googling: 'Here lies Diophantus,' the wonder behold. Through art algebraic, the stone tells how old: 'God...
reference request - Is there an English translation of Diophantus's ...
Aug 24, 2011 · Is Heath's book really a translation? It seems more like a book ABOUT Diophantus's "Arithmetica", not the translation of the actual book. There's just an "abstract" …
How to solve the problem that determines the age of Diophantus?
Let D D be the number of years Diophantus lived, and S S the number of years his son lived. First we make an obvious relation, that his son lived for half his own lifetime.
Are problems in "Arithmetica" of Diophantus all solved now?
Jan 31, 2019 · It's well-known that Diophantus had written ”Diophantus“ which contains many problems about solving arithmetic equations. I wonder whether all of them has been solved …
Fermat's Notes on Diophantus - Mathematics Stack Exchange
Aug 17, 2016 · I am looking for a free online copy of Diophantus' Arithmetica as well as Fermat's Notes on it. After some google searching, I couldn't find any. Thanks for your help! Edit: …
How to find solutions of linear Diophantine ax + by = c?
The diophantine equation ax + by = c has solutions if and only if gcd(a, b) c. If so, it has infinitely many solutions, and any one solution can be used to generate all the other ones. To see this, …
abstract algebra - Diophantus math - Mathematics Stack Exchange
Diophantus math Ask Question Asked 11 years, 7 months ago Modified 11 years, 7 months ago
Nonlinear system Diophantus. - Mathematics Stack Exchange
Aug 18, 2015 · In the extant books of Diophantus, are considered in the system of equations. Of interest is the non-linear system of Diophantine equations. Some simple systems from his …
Question on proving Primitive Pythagorean triples using …
Jan 25, 2020 · Question on proving Primitive Pythagorean triples using Diophantus method? [duplicate] Ask Question Asked 5 years, 4 months ago Modified 5 years, 4 months ago
abstract algebra - Diophantus mathematics - Mathematics Stack …
Find a number whose subtraction from two given numbers (say, $9$ and $21$) allows both differences to be squares. Call the required number $9 - x^2$ so that the condition holds …
