Elements of Geometry: With Exercises for Students and an Introduction to Modern Geometry (Classic Reprint) - Couverture souple
Présentation de l'éditeur
Geometry, to be of sufficient merit to claim attention, must be both conservative and progressive. It should lay firm hold on the past, embody the present state of the science, and anticipate future developments. A work claiming to be wholly new might, perhaps with justice, be at once discarded as worthless; while one containing no improvements could not justify its own existence. The geometrical objects, points, lines, surfaces, solids, and angles, constitute the subject-matter of the science; the definitions are the tests by which these objects are discriminated and their classification determined; the axioms are the warrants for the steps taken in the course of demonstration; the postulates justify the assumption of magnitudes having any position, form, and extent. The logical principles which underlie the demonstrations of this volume have be.en carefully-discriminated and illustrated. The discussion of the axioms and postulates is the result of research, and intent,arid prolonged thought. That fundamental principles have been. rache,d? is. manifest from their underivability, and the simplicity of the deduction of the ordinary so-called axioms from ttreT nas corollaries. Mr. Bain has observed of the principle, If A be greater than B, and Bgreater than O, much more is A greater than C: If it can not be deductively inferred from the proper axioms, it will have to be received as a third axiom. Not only can this principle be inferred (23, 20), but also Mr. Bain sso-called proper axioms (23, 3, 6).
(Typographical errors above are due to OCR software and don't occur in the book.)
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Elements of Geometry (Classic Reprint)
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Paperback. Etat : New. Print on Demand. This book by the author explores the fundamental concepts of logic and their application in a systematic and comprehensive manner. It begins with definitions and classifications of logical terms, laying the groundwork for understanding the principles of logical reasoning. The author presents an in-depth analysis of logical facts and laws, examining their interrelationships and implications. These concepts are illustrated with practical examples, making them relatable and applicable to real-world scenarios. Moving beyond the theoretical foundations, the book delves into the intricate world of logical fallacies, exploring the patterns and types of errors in reasoning. It equips readers with the tools to identify and avoid logical pitfalls, fostering critical thinking and sound judgment. Through engaging discussions and thought-provoking exercises, the author challenges readers to examine the validity and reliability of arguments, empowering them to engage in informed and constructive discourse. In conclusion, this book provides a valuable resource for students, scholars, and anyone seeking to enhance their understanding of logic and logical reasoning. Its insights into the principles of logic and the analysis of fallacies offer invaluable tools for navigating the complexities of human pensamiento, promoting intellectual rigor and the pursuit of truth. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item. N° de réf. du vendeur 9781330097007_0
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Elements of Geometry With Exercises for Students and an Introduction to Modern Geometry Classic Reprint
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