Foundations of Geometry (Paperback)

by David Hilbert (Author) "DEFINITION. Consider three distinct sets of objects..." (more)
Key Phrases: triangle congruence axiom, base angle theorem, segment arithmetic, Pascal's Theorem, Archimedean Axiom, Axiom Group (more...)

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Product Description
This volume is produced from digital images created through the University of Michigan University Library's preservation reformatting program. The Library seeks to preserve the intellectual content of items in a manner that facilitates and promotes a variety of uses. The digital reformatting process results in an electronic version of the text that can both be accessed online and used to create new print copies. This book and thousands of others can be found in the digital collections of the University of Michigan Library. The University Library also understands and values the utility of print, and makes reprints available through its Scholarly Publishing Office. --This text refers to an out of print or unavailable edition of this title.

Product Details

• Paperback: 226 pages
• Publisher: Open Court; 2 edition (January 22, 1999)
• Language: English
• ISBN-10: 0875481647
• ISBN-13: 978-0875481647
• Product Dimensions: 9 x 6 x 0.6 inches
• Shipping Weight: 12.8 ounces
• Average Customer Review: 4.5 out of 5 stars See all reviews (6 customer reviews)
• Amazon.com Sales Rank: #1,213,326 in Books (See Bestsellers in Books)

Customer Reviews

Most Helpful Customer Reviews

49 of 51 people found the following review helpful:

3.0 out of 5 stars Wonderful work --- Miserable Translation, April 29, 2002

By	Anthony Adler (Chicago, IL United States) - See all my reviews (REAL NAME)

David Hilbert's "Grundlagen der Geometrie" is a work of great significance for anyone interested in mathematical foundationalism, the history of geometry, and intellectual history and philosophy in general. Sadly, however, the translation of this edition is extremely poor --- not simply akward, or rough, but careless to the point of making the text unreadable. If I did not have access to the German original, I would have long ago given up on making sense of the translation. In Theorem 7, for example, it speaks of "points which are not on the plane alpha." The German is extremely ambiguous, but mathematically it only makes sense if you interpret the sentence as referring to the "line a." On page 31, the translator commits the unpardonable error of mistaking "nun" (now) for "nur" (only). At the end of theorem 34, and entire equation was left out, and the meaning of the sentence completely bungled. Most extraordinary is Theorem 35, where what should be translated as "It follows from Theorem 22 that the sum of two angles of a triangle is less than two right angles" becomes "the sum of the angles of a triangle is less than two right triangles." In the very next sentence, "mithin" is interpreted as "hence," implying a direct logical entailment where there is none. It should have been rendered simply as "of course." Finally, in the next paragraph, it reads "where epsilon denotes any angles." The German has "irgendeinen Winkel" --- unambiguously singular.

Given the tremendous importance of Hilbert's Foundations, it is quite sad that there is not a quality translation available.

19 of 19 people found the following review helpful:

4.0 out of 5 stars Available for Free, January 31, 2006

By	Michael Kazlow - See all my reviews (REAL NAME)

This historic book is available for free from Project Gutenberg http://www.gutenberg.org. Search for Geometry. This book is one of a few books available. This is the complete Open Court text. It is available both as a pdf file and a TeX file.

4 of 4 people found the following review helpful:

5.0 out of 5 stars Incomplete, November 18, 2007

By	J. Bogaarts (Netherlands) - See all my reviews (REAL NAME)

This review is from: The Foundations Of Geometry (Paperback)

This is the first book ever to present the axiomatic foundations of euclidean geometry. The first edition appeared in the nineties of the nineteenth century.

Most of the book can be read and appreciated by someone who is mature in elementary euclidean geometry (in fact the material was originally conceived to be used in a summer school for mathematics teachers in Germany). If you expect to find a treatment that will fill up all the gaps in the elementary books you will be disappointed, it does not. If you are looking for a text that does fill all the gaps try to get a copy Forders' book The foundations of Euclidean geometry,.

This edition is not based on the last German edition that is available and does not contain the appendices by Hilbert and the supplements by Paul Bernays, so as a text on the foundations of euclidean geometry it is not useless but it is surely crippled.

I do not dare to give a book with Hilberts name on it less than five stars.