Volume 2 of 3-volume set containing complete English text of all 13 books of the Elements plus critical analysis of each definition, postulate and proposition. Vol. 2 includes Books 3-9: Circles, relationships, rectilineal figures.
The definitive edition of one of the very greatest classics of all time--the full Euclid, encompassing almost 2500 years of mathematical and historical study. This unabridged republication of the original enlarged edition contains the complete English text of all 13 books of the ELEMENTS, plus analyses of each definition, postulate, and proposition.
Excerpt from The Thirteen Books of Euclid's Elements, Vol. 2 1. Equal circles are those the diameters of which are equal, or the radii of which are equal. 2. A straight line is said to touch a circle which, meeting the circle and being produced, does not cut the circle. 3. Circles are said to touch one another which, meeting one another, do not cut one another. 4. In a circle straight lines are said to be equally distant from the centre when the perpendiculars drawn to them from the centre are equal. 5. And that straight line is said to be at a greater distance on which the greater perpendicular falls. 6. A segment of a circle is the figure contained by a straight line and a circumference of a circle. 7. An angle of a segment is that contained by a straight line and a circumference of a circle. 8. An angle in a segment is the angle which, when a point is taken on the circumference of the segment and straight lines are joined from it to the extremities of the straight line which is the base of the segment, is contained by the straight lines so joined. 9. And, when the straight lines containing the angle cut off a circumference, the angle is said to stand upon that circumference. 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.
This graduate-level text and reference in probability, with numerous applications to several fields of science, presents nonmeasure-theoretic introduction to theory of Markov processes. The work also covers mathematical models based on the theory, employed in various applied fields. Prerequisites are a knowledge of elementary probability theory, mathematical statistics, and analysis. Appendixes. Bibliographies. 1960 edition.
Classic text explores intermediate steps between basics of calculus and ultimate stage of mathematics — abstraction and generalization. Covers fundamental concepts, real number system, point sets, functions of a real variable, Fourier series, more. Over 500 exercises.
Topology continues to be a topic of prime importance in contemporary mathematics, but until the publication of this book there were few if any introductions to topology for undergraduates. This book remedied that need by offering a carefully thought-out, graduated approach to point set topology at the undergraduate level. To make the book as accessible as possible, the author approaches topology from a geometric and axiomatic standpoint; geometric, because most students come to the subject with a good deal of geometry behind them, enabling them to use their geometric intuition; axiomatic, because it parallels the student's experience with modern algebra, and keeps the book in harmony with current trends in mathematics. After a discussion of such preliminary topics as the algebra of sets, Euler-Venn diagrams and infinite sets, the author takes up basic definitions and theorems regarding topological spaces (Chapter 1). The second chapter deals with continuous functions (mappings) and homeomorphisms, followed by two chapters on special types of topological spaces (varieties of compactness and varieties of connectedness). Chapter 5 covers metric spaces. Since basic point set topology serves as a foundation not only for functional analysis but also for more advanced work in point set topology and algebraic topology, the author has included topics aimed at students with interests other than analysis. Moreover, Dr. Baum has supplied quite detailed proofs in the beginning to help students approaching this type of axiomatic mathematics for the first time. Similarly, in the first part of the book problems are elementary, but they become progressively more difficult toward the end of the book. References have been supplied to suggest further reading to the interested student.
French philosopher Gilles Deleuze wrote two 'logic' books: Francis Bacon: The Logic of Sensation and The Logic of Sense. However, in neither of these books nor in any other works does Deleuze articulate in a formal way the features of the logic he employs. He certainly does not use classical logic. And the best options for the non-classical logic that he may be implementing are: fuzzy, intuitionist, and many-valued. These are applicable to his concepts of heterogeneous composition and becoming, affirmative synthetic disjunction, and powers of the false. In The Logic of Gilles Deleuze: Basic Principles, Corry Shores examines the applicability of three non-classical logics to Deleuze's philosophy, by building from the philosophical and logical writings of Graham Priest, the world's leading proponent of dialetheism. Through so doing, Shores argues that Deleuze's logic is best understood as a dialetheic, paraconsistent, many-valued logic.