Foundations of Geometry - HILBERT, D.

Foundations of Geometry


Yayınevi: Open Court Publishing

Yayın tarihi: 04/1977

ISBN: 9780875481647

İngilizce | 226 Sayfa | 14,99x22,61x1,78 cm.

Tür: Matematik-İstatistik

  • Temin Süresi 28 - 42 iş günü


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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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