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.
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