Editions and Translations of Grundlagen Der Geometrie
The original monograph, based on his own lectures, was organized and written by Hilbert for a memorial address given in 1899. This was quickly followed by a French translation, in which Hilbert added V.2, the Completeness Axiom. An English translation, authorized by Hilbert, was made by E.J. Townsend and copyrighted in 1902. This translation incorporated the changes made in the French translation and so is considered to be a translation of the 2nd edition. Hilbert continued to make changes in the text and several editions appeared in German. The 7th edition was the last to appear in Hilbert's lifetime. In the Preface of this edition Hilbert wrote:
- "The present Seventh Edition of my book Foundations of Geometry brings considerable improvements and additions to the previous edition, partly from my subsequent lectures on this subject and partly from improvements made in the meantime by other writers. The main text of the book has been revised accordingly."
New editions followed the 7th, but the main text was essentially not revised. The modifications in these editions occur in the appendices and in supplements. The changes in the text were large when compared to the original and a new English translation was commissioned by Open Court Publishers, who had published the Townsend translation. So, the 2nd English Edition was translated by Leo Unger from the 10th German edition in 1971. This translation incorporates several revisions and enlargements of the later German editions by Paul Bernays.
The Unger translation differs from the Townsend translation with respect to the axioms in the following ways:
- Old axiom II.4 (Pasch's Theorem) is renamed as Theorem 4 and moved.
- Old axiom II.5 (Pasch's Axiom) is renumbered as II.4.
- V.2, the Axiom of Completeness, has been replaced by:
-
- The Axiom of Line Completeness. An extension of a set of points on a line with its order and congruence relations that would preserve the relations existing among the original elements as well as the fundamental properties of line order and congruence that follows from Axioms I-III, and from V.1 is impossible.
- The old axiom V.2 is now Theorem 32.
The last two modifications are due to P. Bernays.
Read more about this topic: Hilbert's Axioms
Famous quotes containing the words editions, translations and/or der:
“The next Augustan age will dawn on the other side of the Atlantic. There will, perhaps, be a Thucydides at Boston, a Xenophon at New York, and, in time, a Virgil at Mexico, and a Newton at Peru. At last, some curious traveller from Lima will visit England and give a description of the ruins of St. Paul’s, like the editions of Balbec and Palmyra.”
—Horace Walpole (1717–1797)
“Woe to the world because of stumbling blocks! Occasions for stumbling are bound to come, but woe to the one by whom the stumbling block comes!”
—Bible: New Testament, Matthew 18:7.
Other translations use “temptations.”
“Under the lindens on the heather,
There was our double resting-place.”
—Walther Von Der Vogelweide (1170?–1230?)