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Foundations of Geometry Paperback – January 22, 1999

by David Hilbert (Author)
4.4 out of 5 stars 5 customer reviews
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Product Details

  • Paperback: 226 pages
  • Publisher: Open Court; 2 edition (January 22, 1999)
  • Language: English
  • ISBN-10: 0875481647
  • ISBN-13: 978-0875481647
  • Product Dimensions: 0.5 x 6.2 x 9 inches
  • Shipping Weight: 13.6 ounces
  • Average Customer Review: 4.4 out of 5 stars  See all reviews (5 customer reviews)
  • Amazon Best Sellers Rank: #894,077 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

66 of 69 people found the following review helpful
Wonderful work --- Miserable Translation
By Anthony Adler on April 29, 2002
Format: Paperback
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.
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38 of 38 people found the following review helpful
Available for Free
By Michael Kazlow on January 31, 2006
Format: Paperback
This historic book is available for free from Project Gutenberg [...] 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.
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1 of 4 people found the following review helpful
Enjoyable
By Viktor Blasjo on March 28, 2007
Format: Paperback
Hilbert gives his new system of axioms and studies their consistency, independence and necessity. Consider for example the theorem that the angle sum in any triangle cannot be greater than two right angles. We can prove it as follows. Consider a triangle ABC with the angles labelled so that ABC<=ACB. Let D be the midpoint of BC. Draw AD and extend it to E so that AD=DE. By SAS, ACD=BDE, so that angle CAD=angle BAE and angle DBE=angle ACB. Thus ABC has the same angle sum as ABE. ABC<=ACB means that AC=BE<=AB, so angle BAE<=angle AEB, so angle BAE<=angle BAC/2. In other words: for any angle A in any triangle we can construct a new triangle with equal angle sum that has as one of its angles A/2. By repeating this process we can make the angle A as small as we like. Thus, if the angle sum of some triangle was greater than two right angles, and we applied this procedure, we would get a new triangle where two of the angles are greater than two right angles, which is impossible. The "as small as we like" part gives away the fact that we are relying on Archimedes' axiom, which is necessary. "The investigation of this matter which [Max] Dehn has undertaken at my urging led to a complete clarification of this problem. ... If Archimedes' axiom is dropped then from the assumption of infinitely many parallels through a point it does not follow that the sum of the angles in a triangle is less than two right angles. Moreover, there exists a geometry (the non-Legendrian geometry) in which it is possible to draw through a point infinitely many parallels to a line and in which nevertheless the theorems of Riemannian (elliptic) geometry hold.Read more ›
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0 of 1 people found the following review helpful
Five Stars
By Luis A. Gonzalez on December 12, 2014
Format: Paperback Verified Purchase
got it ty
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4 of 35 people found the following review helpful
The Best Book Of Axiomization Geometry
By Hil on June 1, 2000
Format: Paperback
Unlike other books of geometry , the author of this book constructed geometry in a axiomatic method . This is the feature which differ from other books of geometry and the way I like . Let's see how the author constructed axiomization geometry . Intuition and deduction are two powerful ways to knowledge . The axioms are the intuitive principles which are needless to be proved . The theorems are the demonstrated propositions which are deduced from axioms . Although axioms are intuitive , they may have the demonstrated propositions called theorems which contradict . If they do , the system of the axiomization geometry would break down . Because it has some false propositions if you think the contradictory ones as truth , and vice versa . There are all the discussions of the problems above in chapter 2 called consistency which is very important in an axiomatic system .
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