The tremendous success of indivisibles methods in geometry in the seventeenth century, responds to a vast project: installation of infinity in mathematics. The pathways by the authors are very diverse, as are the characterizations of indivisibles, but there are significant factors of unity between the various doctrines of indivisible; the permanence of the language used by all authors is the strongest sign. These efforts do not lead to the stabilization of a mathematical theory (with principles or axioms, theorems respecting these first statements, followed by applications to a set of geometric situations), one must nevertheless admire the magnitude of the results obtained by these methods and highlights the rich relationships between them and integral calculus. The present book aims to be exhaustive since it analyzes the works of all major inventors of methods of indivisibles during the seventeenth century, from Kepler to Leibniz. It takes into account the rich existing literature usually devoted to a single author. This book results from the joint work of a team of specialists able to browse through this entire important episode in the history of mathematics and to comment it. The list of authors involved in indivisibles field is probably sufficient to realize the richness of this attempt; one meets Kepler, Cavalieri, Galileo, Torricelli, Gregoire de Saint Vincent, Descartes, Roberval, Pascal, Tacquet, Lalouvere, Guldin, Barrow, Mengoli, Wallis, Leibniz, Newton.

This review of literature on perspective constructions from the Renaissance through the 18th century covers 175 authors, emphasizing Peiro della Francesca, Guidobaldo del Monte, Simon Stevin, Brook Taylor, and Johann Heinrich. It treats such topics as the various methods of constructing perspective, the development of theories underlying the constructions, and the communication between mathematicians and artisans in these developments.

This volume presents a selection of papers from the Poincaré Project of the Center for the Philosophy of Science, University of Lisbon, bringing together an international group of scholars with new assessments of Henri Poincaré's philosophy of science—both its historical impact on the foundations of science and mathematics, and its relevance to contemporary philosophical inquiry. The work of Poincaré (1854-1912) extends over many fields within mathematics and mathematical physics. But his scientific work was inseparable from his groundbreaking philosophical reflections, and the scientific ferment in which he participated was inseparable from the philosophical controversies in which he played a pre-eminent part. The subsequent history of the mathematical sciences was profoundly influenced by Poincaré’s philosophical analyses of the relations between and among mathematics, logic, and physics, and, more generally, the relations between formal structures and the world of experience. The papers in this collection illuminate Poincaré’s place within his own historical context as well as the implications of his work for ours.

Exploring several of the evolutionary branches of the mathematical notion of genus, this book traces the idea from its prehistory in problems of integration, through algebraic curves and their associated Riemann surfaces, into algebraic surfaces, and finally into higher dimensions. Its importance in analysis, algebraic geometry, number theory and topology is emphasized through many theorems. Almost every chapter is organized around excerpts from a research paper in which a new perspective was brought on the genus or on one of the objects to which this notion applies. The author was motivated by the belief that a subject may best be understood and communicated by studying its broad lines of development, feeling the way one arrives at the definitions of its fundamental notions, and appreciating the amount of effort spent in order to explore its phenomena.

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. 1891 Excerpt: ...position of the face B E G F, it is easy to see that the two wedgeshaped figures Bee'b'oc and Pgg'p'ad are exactly equal; this follows from the equality of their corresponding faces. Hence the volume of the sheared figure must be equal to the volume of the right six-face. Now let us suppose in addition that the face B' E' G' P' is again moved in its own plane into the position B" E" G" F," So that B' and E' move along B' E' and p' G' respectively. Then the slant wedge-shaped figures B'b"f"p'ao and E'e"g"p'dc will again be equal, and the volume of the six-face B" E" G" P" A D C O obtained by this second shear will be equal to the volume of the figure obtained by the first shear, and therefore to the volume of the right six-face. But by n, ns of two shears we can move the face B E G P to any position in its plane, B" E" G" P," in which its sides remain parallel to their former position. Hence the volume of a six-face will remain unchanged if, one of its faces, o c D A, remaining fixed, the opposite face, B E G P, be moved anywhere parallel to itself in its own plane. We thus find that the volume of a six-face formed by three pairs of parallel planes is equal to the product of the area of one of its faces and the perpendicular distance between that face and its parallel. For this is the volume of the right six-face into which it may be sheared; and, as we have seen, shear does not alter volume. The knowledge thus gained of the volume of a sixface bounded by three pairs of parallel faces, or of a so-called parallelepiped, enables us to find the volume of an oblique cylinder. A right cylinder is the figure generated by any area moving parallel to itself in such wise that any point p ...

Throughout his early life, Isaac Todhunter (1820-84) excelled as a student of mathematics, gaining a scholarship at the University of London and numerous awards during his time at St John's College, Cambridge. Taking up fellowship of the college in 1849, he became widely known for both his educational texts and his historical accounts of various branches of mathematics. The present work, first published in 1865, describes the rise of probability theory as a recognised subject, beginning with a discussion of the famous 'problem of points', as considered by the likes of the Chevalier de Mere, Blaise Pascal and Pierre de Fermat during the latter half of the seventeenth century. Subsequently, the application of advanced methods that had been developed in classical areas of mathematics led to rapid progress in probability theory. Todhunter traces this growth, closing with a thorough account of Pierre-Simon Laplace's far-reaching work in the area.

This modern translation of Sophus Lie's and Friedrich Engel's “Theorie der Transformationsgruppen I� will allow readers to discover the striking conceptual clarity and remarkably systematic organizational thought of the original German text. Volume I presents a comprehensive introduction to the theory and is mainly directed towards the generalization of ideas drawn from the study of examples. The major part of the present volume offers an extremely clear translation of the lucid original. The first four chapters provide not only a translation, but also a contemporary approach, which will help present day readers to familiarize themselves with the concepts at the heart of the subject. The editor's main objective was to encourage a renewed interest in the detailed classification of Lie algebras in dimensions 1, 2 and 3, and to offer access to Sophus Lie's monumental Galois theory of continuous transformation groups, established at the end of the 19th Century. Lie groups are widespread in mathematics, playing a role in representation theory, algebraic geometry, Galois theory, the theory of partial differential equations and also in physics, for example in general relativity. This volume is of interest to researchers in Lie theory and exterior differential systems and also to historians of mathematics. The prerequisites are a basic knowledge of differential calculus, ordinary differential equations and differential geometry.

The Theory of the Top was originally presented by Felix Klein as an 1895 lecture at Goettingen University that was broadened in scope and clarified as a result of collaboration with Arnold Sommerfeld. The Theory of the Top: Volume IV. Technical Applications of the Theory of the Top is the fourth and final installment in a series of self-contained English translations that provide insights into kinetic theory and kinematics.

In this fascinating book, the author traces the careers, ideas, discoveries, and inventions of two renowned scientists, Athanasius Kircher and Galileo Galilei, one a Jesuit, the other a sincere man of faith whose relations with the Jesuits deteriorated badly. The Author documents Kircher's often intuitive work in many areas, including translating the hieroglyphs, developing sundials, and inventing the magic lantern, and explains how Kircher was a forerunner of Darwin in suggesting that animal species evolve. Galileo's work on scales, telescopes, and sun spots is mapped and discussed, and care is taken to place his discoveries within their cultural environment. While Galileo is without doubt the "winner" in the comparison with Kircher, the latter achieved extraordinary insights by unconventional means. For all Galileo's fine work, the author believes that scientists do need to regain the power of dreaming, vindicating Kirchner's view.

This book collects the papers of the conference held in Berlin, Germany, 27-29 August 2012, on 'Space, Geometry and the Imagination from Antiquity to the Modern Age'. The conference was a joint effort by the Max Planck Institute for the History of Science (Berlin) and the Centro die Ricerca Matematica Ennio De Giorgi (Pisa).

The Finnish mathematician and astronomer Anders Johan Lexell (1740-1784) was a long-time close collaborator as well as the academic successor of Leonhard Euler at the Imperial Academy of Sciences in Saint Petersburg. Lexell was initially invited by Euler from his native town of Abo (Turku) in Finland to Saint Petersburg to assist in the mathematical processing of the astronomical data of the forthcoming transit of Venus of 1769. A few years later he became an ordinary member of the Academy. This is the first-ever full-length biography devoted to Lexell and his prolific scientific output. His rich correspondence especially from his grand tour to Germany, France and England reveals him as a lucid observer of the intellectual landscape of enlightened Europe. In the skies, a comet, a minor planet and a crater on the Moon named after Lexell also perpetuate his memory.

This book is a history of complex function theory from its origins to 1914, when the essential features of the modern theory were in place. It is the first history of mathematics devoted to complex function theory, and it draws on a wide range of published and unpublished sources. In addition to an extensive and detailed coverage of the three founders of the subject - Cauchy, Riemann, and Weierstrass - it looks at the contributions of authors from d'Alembert to Hilbert, and Laplace to Weyl. Particular chapters examine the rise and importance of elliptic function theory, differential equations in the complex domain, geometric function theory, and the early years of complex function theory in several variables. Unique emphasis has been devoted to the creation of a textbook tradition in complex analysis by considering some seventy textbooks in nine different languages. The book is not a mere sequence of disembodied results and theories, but offers a comprehensive picture of the broad cultural and social context in which the main actors lived and worked by paying attention to the rise of mathematical schools and of contrasting national traditions. The book is unrivaled for its breadth and depth, both in the core theory and its implications for other fields of mathematics. It documents the motivations for the early ideas and their gradual refinement into a rigorous theory.

This book honors the career of historian of mathematics J.L. Berggren, his scholarship, and service to the broader community. The first part, of value to scholars, graduate students, and interested readers, is a survey of scholarship in the mathematical sciences in ancient Greece and medieval Islam. It consists of six articles (three by Berggren himself) covering research from the middle of the 20th century to the present. The remainder of the book contains studies by eminent scholars of the ancient and medieval mathematical sciences. They serve both as examples of the breadth of current approaches and topics, and as tributes to Berggren's interests by his friends and colleagues.

Vladimir Maz'ya (born 1937) is an outstanding mathematician who systematically made fundamental contributions to a wide array of areas in mathematical analysis and in the theory of partial differential equations. In this fascinating book he describes the first thirty years of his life. He starts with the story of his family, speaks about his childhood, high school and university years, describe his formative years as a mathematician. Behind the author's personal recollections, with his own joys, sorrows and hopes, one sees a vivid picture of the time. He speaks warmly about his friends, both outside and inside mathematics. The author describes the awakening of his passion for mathematics and his early achievements. He mentions a number of mathematicians who influenced his professional life. The book is written in a readable and inviting way sometimes with a touch of humor. It can be of interest for a very broad readership.

Sofia Kovalevskaya was a brilliant and determined young Russian woman of the 19th century who wanted to become a mathematician and who succeeded, in often difficult circumstances, in becoming arguably the first woman to have a professional university career in the way we understand it today. This memoir, written by a mathematician who specialises in symplectic geometry and integrable systems, is a personal exploration of the life, the writings and the mathematical achievements of a remarkable woman. It emphasises the originality of Kovalevskaya's work and assesses her legacy and reputation as a mathematician and scientist. Her ideas are explained in a way that is accessible to a general audience, with diagrams, marginal notes and commentary to help explain the mathematical concepts and provide context. This fascinating book, which also examines Kovalevskaya's love of literature, will be of interest to historians looking for a treatment of the mathematics, and those doing feminist or gender studies.

This book presents a historical and scientific analysis as historical epistemology of the science of weights and mechanics in the sixteenth century, particularly as developed by Tartaglia in his Quesiti et inventioni diverse, Book VII and Book VIII (1546; 1554). In the early 16th century mechanics was concerned mainly with what is now called statics and was referred to as the Scientia de ponderibus, generally pursued by two very different approaches. The first was usually referred to as Aristotelian, where the equilibrium of bodies was set as a balance of opposite tendencies to motion. The second, usually referred to as Archimedean, identified statics with centrobarica, the theory of centres of gravity based on symmetry considerations. In between the two traditions the Italian scholar Niccolo Fontana, better known as Tartaglia (1500?-1557), wrote the treatise Quesiti et inventioni diverse (1546). This volume consists of three main parts. In the first, a historical excursus regarding Tartaglia's lifetime, his scientific production and the Scientia de ponderibus in the Arabic-Islamic culture, and from the Middle Ages to the Renaissance, is presented. Secondly, all the propositions of Books VII and VIII, by relating them with the Problemata mechanica by the Aristotelian school and Iordani opvsculvm de ponderositate by Jordanus de Nemore are examined within the history and historical epistemology of science. The last part is relative to the original texts and critical transcriptions into Italian and Latin and an English translation. This work gathers and re-evaluates the current thinking on this subject. It brings together contributions from two distinguished experts in the history and historical epistemology of science, within the fields of physics, mathematics and engineering. It also gives much-needed insight into the subject from historical and scientific points of view. The volume composition makes for absorbing reading for historians, epistemologists, philosophers and scientists.

This book traces the history of the concept of work from its earliest stages and shows that its further formalization leads to equilibrium principle and to the principle of virtual works, and so pointing the way ahead for future research and applications. The idea that something remains constant in a machine operation is very old and has been expressed by many mathematicians and philosophers such as, for instance, Aristotle. Thus, a concept of energy developed. Another important idea in machine operation is Archimedes' lever principle. In modern times the concept of work is analyzed in the context of applied mechanics mainly in Lazare Carnot mechanics and the mechanics of the new generation of polytechnical engineers like Navier, Coriolis and Poncelet. In this context the word "work" is finally adopted. These engineers are also responsible for the incorporation of the concept of work into the discipline of economics when they endeavoured to combine the study of the work of machines and men together.

This book presents new insights into Leibniz's research on planetary theory and his system of pre-established harmony. Although some aspects of this theory have been explored in the literature, others are less well known. In particular, the book offers new contributions on the connection between the planetary theory and the theory of gravitation. It also provides an in-depth discussion of Kepler's influence on Leibniz's planetary theory and more generally, on Leibniz's concept of pre-established harmony. Three initial chapters presenting the mathematical and physical details of Leibniz's works provide a frame of reference. The book then goes on to discuss research on Leibniz's conception of gravity and the connection between Leibniz and Kepler.

The book aims to provide an overview of the state of the art on the mechanics of arches and masonry structures. It is addressed to an international audience, arising from the international context in which the Associazione Edoardo Benvenuto has carried out its activities in recent years, under the honorary presidency of Jacques Heyman. The book belongs to the collection Between Mechanics and Architecture, born in 1995 from the collaboration of several renowned scholars, including Edoardo Benvenuto (P. Radelet-de Grave, E. Benvenuto (eds.), Entre Mecanique et Architecture / Between Mechanics and Architecture, Birkhauser, Basel 1995).

The discovery of a gradual acceleration in the moon's mean motion by Edmond Halley in the last decade of the seventeenth century led to a revival of interest in reports of astronomical observations from antiquity. These observations provided the only means to study the moon's 'secular acceleration', as this newly-discovered acceleration became known. This book contains the first detailed study of the use of ancient and medieval astronomical observations in order to investigate the moon's secular acceleration from its discovery by Halley to the establishment of the magnitude of the acceleration by Richard Dunthorne, Tobias Mayer and Jerome Lalande in the 1740s and 1750s. Making extensive use of previously unstudied manuscripts, this work shows how different astronomers used the same small body of preserved ancient observations in different ways in their work on the secular acceleration. In addition, this work looks at the wider context of the study of the moon's secular acceleration, including its use in debates of biblical chronology, whether the heavens were made up of aether, and the use of astronomy in determining geographical longitude. It also discusses wider issues of the perceptions and knowledge of ancient and medieval astronomy in the early-modern period. This book will be of interest to historians of astronomy, astronomers and historians of the ancient world.

A companion publication to the international exhibition "Transcending Tradition: Jewish Mathematicians in German-Speaking Academic Culture", the catalogue explores the working lives and activities of Jewish mathematicians in German-speaking countries during the period between the legal and political emancipation of the Jews in the 19th century and their persecution in Nazi Germany. It highlights the important role Jewish mathematicians played in all areas of mathematical culture during the Wilhelmine Empire and the Weimar Republic, and recalls their emigration, flight or death after 1933.

From the end of antiquity to the middle of the nineteenth century it was generally believed that Aristotle had said all that there was to say concerning the rules of logic and inference. One of the ablest British mathematicians of his age, Augustus De Morgan (1806-71) played an important role in overturning that assumption with the publication of this book in 1847. He attempts to do several things with what we now see as varying degrees of success. The first is to treat logic as a branch of mathematics, more specifically as algebra. Here his contributions include his laws of complementation and the notion of a universe set. De Morgan also tries to tie together formal and probabilistic inference. Although he is never less than acute, the major advances in probability and statistics at the beginning of the twentieth century make this part of the book rather less prophetic.

In the preface to this work, mathematician Augustus De Morgan (1806 71) claims that 'The most worthless book of a bygone day is a record worthy of preservation.' His purpose in writing this catalogue, published in 1847, was to provide an accurate record of the early history of publishing on arithmetic, but describing only those books which he had examined himself. He surveyed the library of the Royal Society, works in the British Museum, the wares of specialist booksellers, and the private collections of himself and his friends to compile a chronological list of books from 1491 to 1846 (the final book being a work of his own), giving bibliographical details, a description of the contents, and sometimes comments on the mathematics on display. De Morgan's Formal Logic and a Memoir of Augustus De Morgan by his widow are also reissued in the Cambridge Library Collection."

Walter Gautschi has written extensively on topics ranging from special functions, quadrature and orthogonal polynomials to difference and differential equations, software implementations, and the history of mathematics. He is world renowned for his pioneering work in numerical analysis and constructive orthogonal polynomials, including a definitive textbook in the former, and a monograph in the latter area. This three-volume set, Walter Gautschi: Selected Works with Commentaries, is a compilation of Gautschi's most influential papers and includes commentaries by leading experts. The work begins with a detailed biographical section and ends with a section commemorating Walter's prematurely deceased twin brother. This title will appeal to graduate students and researchers in numerical analysis, as well as to historians of science. Selected Works with Commentaries, Vol. 1 Numerical Conditioning Special Functions Interpolation and Approximation Selected Works with Commentaries, Vol. 2 Orthogonal Polynomials on the Real Line Orthogonal Polynomials on the Semicircle Chebyshev Quadrature Kronrod and Other Quadratures Gauss-type Quadrature Selected Works with Commentaries, Vol. 3 Linear Difference Equations Ordinary Differential Equations Software History and Biography Miscellanea Works of Werner Gautschi

This engaging text describes the development of singular perturbations, including its history, accumulating literature, and its current status. While the approach of the text is sophisticated, the literature is accessible to a broad audience. A particularly valuable bonus are the historical remarks. These remarks are found throughout the manuscript. They demonstrate the growth of mathematical thinking on this topic by engineers and mathematicians. The book focuses on detailing how the various methods are to be applied. These are illustrated by a number and variety of examples. Readers are expected to have a working knowledge of elementary ordinary differential equations, including some familiarity with power series techniques, and of some advanced calculus. Dr. O'Malley has written a number of books on singular perturbations. This book has developed from many of his works in the field of perturbation theory.