Abstract
THIS work will be found really valuable by all students of geometry, especially by those who know little or nothing of the non-Euclidean theories. First of all we have a discussion of the elementary axioms; in this the plane is deduced from what may be called a triangular frame, in the manner of Peano and Schur, Then comes the discrimination of the three cases;, according as the sum of the angles of a plane triangle is equal to, greater than, or less than two right angles; and this is followed by the fundamental trigonometric formulæ for a triangle, deduced very neatly from Saccheri's isosceles birectan-gular quadrilateral. It is also proved at this stage that the non-Euclidean plane can be developed upon a surface of constant curvature in Euclidean space.
The Elements of Non-Euclidean Geometry.
By Dr. J. L. Coolidge. Pp. 292. (Oxford: Clarendon Press, 1909.) Price 15S. net.
Article PDF
Rights and permissions
About this article
Cite this article
M., G. The Elements of Non-Euclidean Geometry . Nature 82, 185 (1909). https://doi.org/10.1038/082185a0
Issue Date:
DOI: https://doi.org/10.1038/082185a0