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The Foundations of Geometry Paperback – May 19, 2007

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About the Author

David Hilbert (1862 – 1943) was a German mathematician. He is recognized as one of the most influential and universal mathematicians of the 19th and early 20th centuries. Hilbert discovered and developed a broad range of fundamental ideas in many areas, including invariant theory and the axiomatization of geometry. He also formulated the theory of Hilbert spaces, one of the foundations of functional analysis. Hilbert adopted and warmly defended Georg Cantor's set theory and transfinite numbers. A famous example of his leadership in mathematics is his 1900 presentation of a collection of problems that set the course for much of the mathematical research of the 20th century. Hilbert and his students contributed significantly to establishing rigor and developed important tools used in modern mathematical physics. Hilbert is known as one of the founders of proof theory and mathematical logic, as well as for being among the first to distinguish between mathematics and meta/mathematics. INTRODUCTION. Geometry, like arithmetic, requires for its logical development only a small number of simple, fundamental principles. These fundamental principles are called the axioms of geometry. The choice of the axioms and the investigation of their relations to one another is a problem which, since the time of Euclid, has been discussed in numerous excellent memoirs to be found in the mathematical literature. This problem is tantamount to the logical analysis of our intuition of space. The following investigation is a new attempt to choose for geometry a simple and complete set of independent axioms and to deduce from these the most important geometrical theorems in such a manner as to bring out as clearly as possible the significance of the different groups of axioms and the scope of the conclusions to be derived from the individual axioms. --This text refers to an alternate Paperback edition.

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Product Details

  • Paperback: 96 pages
  • Publisher: Merchant Books (May 19, 2007)
  • Language: English
  • ISBN-10: 1603860088
  • ISBN-13: 978-1603860086
  • Product Dimensions: 7.5 x 0.2 x 9.2 inches
  • Shipping Weight: 6.4 ounces (View shipping rates and policies)
  • Average Customer Review: 3.5 out of 5 stars  See all reviews (6 customer reviews)
  • Amazon Best Sellers Rank: #3,466,945 in Books (See Top 100 in Books)

Customer Reviews

Most Helpful Customer Reviews

11 of 12 people found the following review helpful By J. Bogaarts on November 18, 2007
Format: 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.
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6 of 7 people found the following review helpful By Sam Adams on July 1, 2010
Format: Paperback Verified Purchase
The FORGOTTEN BOOKS edition of Hilbert's Foundations of Geometry isn't Hilbert's Geometry. Notice the number of pages (which I didn't when ordering it). This publication contains ONLY the diagrams in large format (with a very few absent) from the text of Hilbert's Geometry. There is no title page or author listed, but this is in fact what the content is from. It is clearly a scan from an old book, so there must be some historical context for it. Maybe someone can clarify the mystery. I give it 5 stars because these comments will probably show up among the reviews of Hilbert's full text and I don't want to skew the star rating of the book, but this particular reprint I don't find of any actual value, except that it's from Hilbert and there may be some interesting reason why it occurs as an independent publication.

Along with this reprint, I also ordered the FB Classic Reprint of Elements of Geometry and Trigonometry by Charles Davies. These two books are the first reprints I've purchased from any of the reprint publishers selling on amazon. For more on the quality of Forgotten Books reprints, see my review of Davies' book. The mysterious Hilbert-diagrams text they sell under the title of Hilbert's Foundations of Geometry is, I suspect, an anomaly. Besides, their honest page-count should raise questions about the content. Now you know what that content is.
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9 of 11 people found the following review helpful By Terrence W. Kennedy on December 6, 2010
Format: Kindle Edition Verified Purchase
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