Sinopsis
Explore the foundations of geometry beyond distance and shapes. This volume presents a fresh approach to geometric ideas, prioritizing relations and continuity over traditional notions of distance and congruence. It pairs geometric reasoning with algebraic symbolism to fix ideas and verify results, while introducing the possibility of imagining higher dimensions and imaginary elements as essential tools.
This edition aims to be self-contained, gradually building a coherent view of abstract geometry and its real‑world implications. It foregrounds a synthetic path while acknowledging the role of symbolic methods, and it explains why some ideas may appear unfamiliar at first but become clear through careful reasoning.
- Replaces distance with a theory of related ranges and continuity, yet preserves rigorous proofs
- Integrates algebraic symbolism to support geometric thinking and verification
- Introduces the notion of imaginary elements as a legitimate part of the framework
- Emphasizes the study of higher dimensions and their impact on curves and surfaces
Ideal for readers of rigorous introductory geometry who want a logically complete, concept‑driven path that blends synthetic and symbolic approaches.
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Reseña del editor
Excerpt from Principles of Geometry, Vol. 1
Erratum. In Ex. 9, p. 175, instead of by taking three positions of P upon p, read in general, by taking three positions of P upon the real line p through the intersection of the two given lines, so chosen that the corresponding points U, V, W are in line.
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.
Reseña del editor
Excerpt from Principles of Geometry, Vol. 1
The volumes of which this is the first have the purpose of introducing the reader to those parts of geometry which appear most important in developments taking place to-day. The present volume is devoted to the indispensable logical preliminaries. It assumes only those relations of position, for points, lines and planes, which, furnished with a pencil, a ruler, some rods and some string, a student may learn by drawing diagrams and making models. It seeks to set these relations in an ordered framework of deduction, gradually rendered comprehensive and precise enough to include all the subsequent theory; to this end it puts aside, at first, most of those intricate details which make up the burden of what is generally called elementary geometry. That such a plan can be carried through, thanks to the work of many generations of thinkers, is well enough known; and experience has shewn that many students, especially of the class who look forward to becoming Engineers or Physicists, to whom the geometry of the ill 1 1 usual textbooks is tiresome, find such a course stimulating and easy, when the matter is properly presented to them. The mathematician who has followed such a course will find that he has no cause to think he has learnt the wrong things. The preliminary theorems in this method of approaching the subject are indeed of Greek origin; only, these are here made to lead to general principles, giving a command of detail unknown to the Greeks. Subsequent volumes will deal, on the basis of the results obtained in this volume, with conics (and circles), with quadric surfaces and cubic curves in space, and with cubic surfaces and certain quartic surfaces. These volumes are ready to print; it is hoped that they may appear in no long time.
Speaking in more detail of the present volume, it rejects the consideration of distance, and of congruence, as fundamental ideas; these are, in effect, replaced by a theory of related ranges; the geometry usually described with the help of the notion of distance appears later, in a more general, but not more difficult, form. By what means it is possible, so to dispense with this notion, should be of interest to others than the student of geometry. An account is given, however, of the consequences of accepting as fundamental the continuity of the real points of the line.
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.
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Principles of Geometry, Vol. 1 (Classic Reprint)
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Paperback. Condición: New. Print on Demand. This book offers a stimulating journey into the realm of geometry, focusing on concepts relevant to contemporary advancements in the field. It delves into the fundamental principles of geometry, building a framework that encompasses a range of topics, from points, lines, and planes to more complex curves and surfaces. Distancing itself from conventional approaches that rely on metrical geometry, this book explores an alternative perspective where the notion of distance is not treated as a foundational element. Instead, it introduces the concept of related ranges and delves into the intriguing implications of accepting the continuity of real points on a line as a fundamental principle. The author seamlessly integrates algebraic symbolism as a tool for clarifying geometric ideas and facilitating verification, while emphasizing the importance of geometric reasoning as a self-contained entity. The exploration extends beyond three-dimensional space, venturing into the realm of higher dimensions and the concept of imaginary elements. This approach unveils the elegance and power of geometric principles in tackling complex problems related to curves and surfaces. By challenging traditional perspectives and embracing innovative concepts, this book offers profound insights into the nature of geometry and its potential for solving intricate mathematical problems. 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. Nº de ref. del artículo: 9781330400951_0
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