Edward T Walsh - A First Course in Geometry
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- Book:A First Course in Geometry
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- Publisher:Dover Publications
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- Year:2014
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A First Course in Geometry: summary, description and annotation
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This introductory text is designed to help undergraduate students develop a solid foundation in geometry. Early chapters progress slowly, cultivating the necessary understanding and self-confidence for the more rapid development that follows. The extensive treatment can be easily adapted to accommodate shorter courses.
Starting with the language of mathematics as expressed in the algebra of logic and sets, the text covers geometric sets of points, separation and angles, triangles, parallel lines, similarity, polygons and area, circles, space geometry, and coordinate geometry. Each chapter includes a problem set arranged in order of increasing difficulty as well as review exercises and annotated references suggesting sources for further study. In addition to three helpful Appendixes, the book concludes with answers and hints for selected problems.
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| Pq | p and q |
| ~p | The negation of p |
| pq | p or q |
| pq | If p then q (p implies q) |
| pq | p is equivalent to q |
| p iff q | p if and only if q |
| {1, 2, 3} | The set containing 1, 2, and 3 as its elements |
| {x : x < 5} | The set of all numbers less than 5 |
| xA | x is an element of set A |
| AB | The union of sets A and B |
| AB | The intersection of sets A and B |
| U | The universal set |
 | The empty set |
| AB | A is a subset of B |
| ~A | The complement of set A |
 | The line containing points P and Q |
| |x| | The absolute value of x |
| c(P) = x | The coordinate of P is x. |
| PQ | The distance from P to Q |
| a < b | a is less than b. |
| a > b | a is greater than b. |
| ab | a is less than or equal to b. |
| ab | a is greater than or equal to b. |
 | The segment with endpoints A and B |
 | The ray with endpoint a and interior poin |
 |  is congruent to  . |
The P-side of  | The half plane determined by p and |
| PAQ | The angle with sides  and  |
| mA | The measure of A |
 ABC | The interior of ABC |
 ABC | The exterior of ABC |
| AB | A is congruent to B. |
 | The lines and  are perpendicular. |
| ABC | The triangle with vertices A, B, and C |
| ABC | The interior of ABC |
| ABC | The exterior of ABC |
| ABCDEF | ABC is congruent to DEF. |
| CPCTC | Corresponding parts of congruent triangle are congruent. |
| / | End of indirect proof, a contradiction |
 | Line is parallel to line . |
| ABCDEF | ABC is similar to DEF. |
 ABCD | Parallelogram ABCD |
| a(P1P...2 | The area of polygon P1P2... Pn |
| aABC | The area of ABC |
 | An arc with endpoints A and B |
m | The degree measure of |
l | The length of |
| P-AB-Q | A dihedral angle with edge  |
Walsh DOVER PUBLICATIONS, INC. Mineola, New York Copyright Copyright 1974, 2014 by Edward T. Walsh All rights reserved. Bibliographical Note This Dover edition, first published in 2014, is an unabridged republication of the work originally published in 1974 by Rinehart Press, San Francisco. The author has provided a new Preface and a list of Errata for this edition. Walsh. Walsh.
Dover edition. pages cm Originally published: San Francisco : Rinehart Press, 1974. Includes bibliographical references and index. eISBN-13: 978-0-486-79668-0 1. Geometry. Title. Title.
QA453.W22 2014 516.2dc23 2014011022 Manufactured in the United States by Courier Corporation 78020101 2014 www.doverpublications.com To Mark and Patrick
who were present at the creation
| aABC | The area of ABC |
| An arc with endpoints A and B |
| m | The degree measure of |
| l | The length of |
| P-AB-Q | A dihedral angle with edge |
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