The Arithmetic Of Infinitesimals
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| Author | : John Wallis |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 234 |
| Release | : 2004-08-06 |
| Genre | : Mathematics |
| ISBN | : 9780387207094 |
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. Accompanied with annotations and an introductory essay, the translation makes Wallis's work fully available for the first time to modern readers. 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. Above all, the book displays the crucial mid-seventeenth-century shift from geometry to arithmetic and algebra as the primary language of mathematics.
| Author | : John Wallis |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 226 |
| Release | : 2013-06-29 |
| Genre | : Mathematics |
| ISBN | : 1475743122 |
John Wallis (1616-1703) was the most influential English mathematician prior to Newton. He published his most famous work, Arithmetica Infinitorum, in Latin in 1656. This book studied the quadrature of curves and systematised the analysis of Descartes and Cavelieri. Upon publication, this text immediately became the standard book on the subject and was frequently referred to by subsequent writers. This will be the first English translation of this text ever to be published.
| Author | : Amir Alexander |
| Publisher | : Simon and Schuster |
| Total Pages | : 317 |
| Release | : 2014-07-03 |
| Genre | : Science |
| ISBN | : 1780745338 |
On August 10, 1632, five leading Jesuits convened in a sombre Roman palazzo to pass judgment on a simple idea: that a continuous line is composed of distinct and limitlessly tiny parts. The doctrine would become the foundation of calculus, but on that fateful day the judges ruled that it was forbidden. With the stroke of a pen they set off a war for the soul of the modern world. Amir Alexander takes us from the bloody religious strife of the sixteenth century to the battlefields of the English civil war and the fierce confrontations between leading thinkers like Galileo and Hobbes. The legitimacy of popes and kings, as well as our modern beliefs in human liberty and progressive science, hung in the balance; the answer hinged on the infinitesimal. Pulsing with drama and excitement, Infinitesimal will forever change the way you look at a simple line.
| Author | : Margaret E. Baron |
| Publisher | : Elsevier |
| Total Pages | : 313 |
| Release | : 2014-05-09 |
| Genre | : Mathematics |
| ISBN | : 1483280926 |
The Origins of Infinitesimal Calculus focuses on the evolution, development, and applications of infinitesimal calculus. The publication first ponders on Greek mathematics, transition to Western Europe, and some center of gravity determinations in the later 16th century. Discussions focus on the growth of kinematics in the West, latitude of forms, influence of Aristotle, axiomatization of Greek mathematics, theory of proportion and means, method of exhaustion, discovery method of Archimedes, and curves, normals, tangents, and curvature. The manuscript then examines infinitesimals and indivisibles in the early 17th century and further advances in France and Italy. Topics include the link between differential and integral processes, concept of tangent, first investigations of the cycloid, and arithmetization of integration methods. The book reviews the infinitesimal methods in England and Low Countries and rectification of arcs. The publication is a vital source of information for historians, mathematicians, and researchers interested in infinitesimal calculus.
| Author | : Dan Sloughter |
| Publisher | : Orange Grove Texts Plus |
| Total Pages | : 0 |
| Release | : 2009-09-24 |
| Genre | : |
| ISBN | : 9781616100896 |
| Author | : John Wallis |
| Publisher | : Springer |
| Total Pages | : 192 |
| Release | : 2013-04-03 |
| Genre | : Mathematics |
| ISBN | : 9781475743135 |
John Wallis (1616-1703) was the most influential English mathematician prior to Newton. He published his most famous work, Arithmetica Infinitorum, in Latin in 1656. This book studied the quadrature of curves and systematised the analysis of Descartes and Cavelieri. Upon publication, this text immediately became the standard book on the subject and was frequently referred to by subsequent writers. This will be the first English translation of this text ever to be published.
| Author | : Abraham Robinson |
| Publisher | : Princeton University Press |
| Total Pages | : 315 |
| Release | : 2016-08-11 |
| Genre | : Mathematics |
| ISBN | : 1400884225 |
Considered by many to be Abraham Robinson's magnum opus, this book offers an explanation of the development and applications of non-standard analysis by the mathematician who founded the subject. Non-standard analysis grew out of Robinson's attempt to resolve the contradictions posed by infinitesimals within calculus. He introduced this new subject in a seminar at Princeton in 1960, and it remains as controversial today as it was then. This paperback reprint of the 1974 revised edition is indispensable reading for anyone interested in non-standard analysis. It treats in rich detail many areas of application, including topology, functions of a real variable, functions of a complex variable, and normed linear spaces, together with problems of boundary layer flow of viscous fluids and rederivations of Saint-Venant's hypothesis concerning the distribution of stresses in an elastic body.
| Author | : Ian Stewart |
| Publisher | : Oxford University Press |
| Total Pages | : 161 |
| Release | : 2017 |
| Genre | : Mathematics |
| ISBN | : 0198755236 |
Ian Stewart considers the concept of infinity and the profound role it plays in mathematics, logic, physics, cosmology, and philosophy. He shows that working with infinity is not just an abstract, intellectual exercise, and analyses its important practical everyday applications.
| Author | : Vieri Benci |
| Publisher | : World Scientific |
| Total Pages | : 346 |
| Release | : 2019-02-19 |
| Genre | : Mathematics |
| ISBN | : 9813276606 |
'This text shows that the study of the almost-forgotten, non-Archimedean mathematics deserves to be utilized more intently in a variety of fields within the larger domain of applied mathematics.'CHOICEThis book contains an original introduction to the use of infinitesimal and infinite numbers, namely, the Alpha-Theory, which can be considered as an alternative approach to nonstandard analysis.The basic principles are presented in an elementary way by using the ordinary language of mathematics; this is to be contrasted with other presentations of nonstandard analysis where technical notions from logic are required since the beginning. Some applications are included and aimed at showing the power of the theory.The book also provides a comprehensive exposition of the Theory of Numerosity, a new way of counting (countable) infinite sets that maintains the ancient Euclid's Principle: 'The whole is larger than its parts'. The book is organized into five parts: Alpha-Calculus, Alpha-Theory, Applications, Foundations, and Numerosity Theory.
| Author | : Jacqueline A. Stedall |
| Publisher | : Mathematics |
| Total Pages | : 314 |
| Release | : 2002 |
| Genre | : Mathematics |
| ISBN | : 9780198524953 |
A Discourse Concerning Algebra, provides a new and readable account of the rise of algebra in England from the Medieval period to the later years of the 17th Century.Stedall's book follows the reception and dissemination of important algebraic ideas and methods from continental Europe and the consequent revolution in the state of English mathematics in the 17th century.
