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HILBERT, DAVID.

Neue Begründung der Bolyai-Lobatschefskyschen Geometrie..

Leipzig, B.G. Teubner, 1903. Orig. printed wrappers, no backstrip. In: "Mathematische Annalen begründet durch Alfred Clebsch und Carl Neumann.", 57. Bd., 2 Heft. Pp. 137-264. The whole issue offered (Heft 2). Hilbert's paper:pp. 137-150 a. 7 textfigs.

First edition and first printing of Hilbert's importent proof of the possibility of the non-euclidean parallel-construction, in which he showes that only with the aid of ruler and compass it is possible to draw with the samer instruments, the common perpendicular to two lines which are not parallel and do not meet each other (the non-intersecting lines), the common parallel to the two lines which bound an angle; and the line which is perpendicular to one of the bounding lines of an acute angle and parallel to the other, and how these constructions can be carried out. (Bonola: Non-Euclidean Geometry). The paper was reprinted in the second edition of his "Grundlagen der Geometrie" as Appendix III. (Sommerville: 1903 p. 196).

Order-nr.: 41352