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. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

This milestone extensive work combines the essentials of history – biography, chronology, political and economic background – with the observations, theories, principles, laws and equations that constitute the specifics of science. The 5800-page Encyclopedia arises from the conviction that the optimal perspective on science is through the lens of history, setting aside traditional divisions of discipline and specialty, and rising above geopolitical boundaries. Reaching from 4,200 BCE to the 21st century CE, the Encyclopedia tells (as the author himself puts it) "not only who did it and when it was done but also precisely what was done." The author, Ari Ben-Menahem, surveys 100 generations of great thinkers, offering 2070 detailed biographies of scientists, engineers, explorers and inventors, who left their mark on the history of science and technology. The span of coverage is all-encompassing: mathematics, philosophy, logic, physical and environmental sciences (including physics, chemistry, astronomy, earth and space sciences and cosmology), life sciences (biology, medicine, physiology, botany, zoology and biochemistry), associated engineering disciplines, and the social sciences (among them economics, psychology, sociology, anthropology, linguistics and more). The six-volume Encyclopedia also includes 380 articles summarizing the time-line of ideas in the leading fields of science, technology, mathematics and philosophy, plus useful tables, figures and photos, and 20 ‘Science Progress Reports’ detailing scientific setbacks. Interspersed throughout are quotations, gathered from the wit and wisdom of sages, savants and scholars throughout the ages from antiquity to modern times.

The central theme of these essays is the nature and role of mathematics, its growth and spread, and its involvement with ever-wider areas of knowledge. The author attempts to determine the decisive and creative aspects of the abstractness" of mathematics which have made it the dominant intellectual force that it is. He frequently confronts the mathematics and physics of today with the mathematics and physics of the Greeks, which, however renowned, was not yet capable of this abstractness. Originally published in 1981. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These paperback editions preserve the original texts of these important books while presenting them in durable paperback editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Preface. Acknowledgements and Credits. Introduction. 1: Late Nineteenth Century Background. 1.1. Hilbert's Early Career. 1.1.1 Algebraic Invariants. 1.1.2 Algebraic Number Fields. 1.1.3 Deep Roots in Tradition. 1.2. Foundations of Geometry. 1.2.1 Riemann. 1.2.2 Projective Geometry. 1.2.3 Nineteenth-Century Axiomatics. 1.2.4 Pasch and the Italian School. 1.3. Foundations of Physics. 1.3.1 Kinetic Theory, Mechanistic Foundations. 1.3.2 Carl Neumann. 1.3.3 Heinrich Hertz. 1.3.4 Paul Volkmann. 1.3.5 Ludwig Boltzmann. 1.3.6 Aurel Voss. 1.4. Mathematics and Physics in Göttingen at the Turn of the Century. 1.4.1 Felix Klein. 1.4.2 The Physicists. 2: Axiomatization in Hilbert's Early Career. 2.1. Axiomatics, Geometry and Physics in Hilbert's Early Lectures. 2.1.1 Geometry in Königsberg. 2.1.2 Geometry in Göttingen. 2.1.3 Mechanics in Göttingen. 2.2. Grundlagen der Geometrie. 2.2.1 Independence, Simplicity, Completeness. 2.2.2 Fundamental Theorems of Projective Geometry. 2.2.3 On the Concept of Number. 2.3. The 1900 List of Problems. 2.3.1 Foundational Problems. 2.3.2 A Context for the Sixth Problem. 2.4. Early Reactions to the Grundlagen. 3: The Axiomatic Method in Action: 1900-1905. 3.1. Foundational Concerns - Empiricist Standpoint. 3.2. Hilbert and Physics in Göttingen circa 1905. 3.3. Axioms for Physical Theories: Hilbert's 1905 Lectures. 3.3.1 Mechanics. 3.3.2 Thermodynamics. 3.3.3 Probability Calculus. 3.3.4 Kinetic Theory of Gases. 3.3.5 Insurance Mathematics. 3.3.6 Electrodynamics. 3.3.7 Psychophysics. 3.3.8 A post-1909 addendum. 3.4. The Axiomatization Program by 1905 - Partial Summary. 4: Minkowski and Relativity: 1907-1909. 4.1. The Principle of Relativity. 4.2. The Basic Equations of Electromagnetic Processes in Moving Bodies. 4.2.1 Three Meanings of 'Relativity'. 4.2.2 Axioms of Electrodynamics. 4.2.3 Relativity and Mechanics. 4.2.4 Relativity and Gravitation. 4.3. Space and Time. 4.3.1 Groups of Transformations. 4.3.2 EmpiricalConsiderations. 4.3.3 Relativity and Existing Physical Theories. 4.4. Max Born, Relativity, and the Theories of the Electron. 4.4.1 Rigid Bodies. 4.5. Minkowski, Axiomatics and Relativity - Summary. 5: Mechanical to Electromagnetic Reductionism: 1910-1914. 5.1. Lectures on Mechanics and Continuum Mechanics. 5.2. Kinetic Theory. 5.3. Radiation Theory. 5.3.1 Hilbert and Kirchhoff's Law: 1912. 5.3.2 Reactions and Sequels: Early 1913. 5.3.3 Pringsheim's Criticism: 1913. 5.3.4 Hilbert's Final Version: 1914. 5.3.5 Kinetic and Radiation Theory: General Remarks. 5.4. Structure of Matter and Relativity: 1912-1914. 5.4.1 Molecular Theory of Matter - 1912-13. 5.4.2 Electron Theory: 1913. 5.4.3 Axiomatization of Physics: 1913. 5.4.4 Electromagnetic Oscillations: 1913-14. 5.5. Broadening Physical Horizons - Concluding Remarks. 6: Einstein and Mie: Two Pillars of Hilbert's Unified Theory. 6.1. Einstein's Way to General Relativity. 6.2. Mie's Electromagnetic Theory of Matter. 6.2.1 First and Second Installment: Early 1912. 6.2.2 Third Installment: November 1912. 6.3. Contemporary Debates on Gravitation. 6.4. Born's Formulation of Mie's Theory. 6.5. The Background to Hilbert's Unified Theory - Summary. 7: Foundations of Physics: 1915-1916. 7.1. Einstein in Göttingen - Summer of 1915. 7.2. Hilbert's Unified Theory - General Considerations. 7.3. Hilbert's Communication to the GWG - November 1915. 7.3.1 Axioms and Basic Assumptions. 7.3.2 The Hamiltonian Function and the Field Equations. 7.3.3 Summary and Additional Considerations. 7.4. The Hilbert-Einstein Correspondence and Einstein's Four Communications - November 1915. 7.5. Hilbert's Unified Theory: First Printed Version - March 1916. 7.6. Foundations of Physics - Summary. 8: Hilbert and GTR: 1916-1918. 8.1. Mie's Reaction. 8.2. Einstein's Reaction. 8.3. Hilbert Teaches GTR - 1916-1917. 8.4. Hilbert's Second Communication - December 1916. 8.5. Göttingen Debates on Energy

Excerpt from Linear Drawing: Showing the Application of Practical Geometry This work is intended firstly as a text-book for teachers in Schools of Art and Science, Training Colleges, National and other schools, and secondly as a manual for self-instruction for artisans and the public generally. It is impossible to over estimate the importance of a knowledge of Geometry, forming as it does the basis of all the mechanical and decorative arts; and therefore the first volume of a Technical Series has been devoted to this subject, from which, as from one common highway, branches may diverge, adapted to the various industrial arts. In order to fit the course of instruction, not only to the young, but to adults whose elementary education may be deficient, the author has deemed it best to assume, in the first instance, utter ignorance on the part of the pupils. Thus it will be seer, that in Problem I, no geometrical terms, such as "describe an arc," &c., are used, the learner being merely told to place the steel point of his compass on a given spot, whilst tracing part of a circle with the pencil leg. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Cartan and Eilenberg introduce the concept of homology in abstract algebra and algebraic topology. Their text provides a rigorous treatment of the theory and applications of homological algebra, including chain complexes, cohomology, and spectral sequences. 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.

This is the fourth volume of "The Collected Mathematical Papers of James Joseph Sylvester," documenting the prolific output of the renowned 19th-century mathematician. James Joseph Sylvester (1814-1897) made significant contributions to algebra, number theory, geometry, and invariant theory. This collection, meticulously compiled and edited, offers a comprehensive view of his work, showcasing his innovative approaches and profound insights. Edited by H. F. Baker, this volume makes Sylvester's groundbreaking research accessible to modern mathematicians, historians of science, and anyone with an interest in the development of mathematical thought. Sylvester's papers are valuable not only for their mathematical content but also for their historical context, providing a glimpse into the mathematical landscape of the 19th century. This collection is an essential resource for understanding the evolution of modern mathematics and the enduring legacy of one of its most influential figures. 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 was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. 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. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. 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.

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. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

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.

"Theory of Functionals: And of Integral and Integro-Differential Equations" is a foundational treatise in the field of mathematical analysis, representing the culmination of Vito Volterra's pioneering research into the calculus of variations and the generalization of functions. As one of the most significant figures in late 19th and early 20th-century mathematics, Volterra introduces a systematic approach to functionals-functions that depend on other functions-providing a rigorous framework for what is now known as functional analysis. The work explores the properties of integral and integro-differential equations, detailing their development and their profound implications for both pure mathematics and mathematical physics. Volterra examines the transition from finite-dimensional space to infinite-dimensional space, offering insights into the behavior of systems where the current state depends on past history. Edited and expanded from his influential lectures, this volume serves as an essential resource for understanding the historical development of modern analysis. It remains a vital reference for mathematicians and physicists interested in the evolution of linear operators and the mathematical modeling of complex physical phenomena. 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 was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you may see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. 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. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. 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.