[2014]. The problem [of Euclid’s Parallel Axiom] is now at a par with the squaring of the circle and the trisection of an angle by means of ruler and compass. So far as the mathematical public is concerned, the famous problem of the parallel is settled for all time.—Young, John Wesley.
Fundamental Concepts of Algebra and Geometry (New York, 1911), p. 32.
[2015]. If the Euclidean assumptions are true, the constitution of those parts of space which are at an infinite distance from us, “geometry upon the plane at infinity,” is just as well known as the geometry of any portion of this room. In this infinite and thoroughly well-known space the Universe is situated during at least some portion of an infinite and thoroughly well-known time. So that here we have real knowledge of something at least that concerns the Cosmos; something that is true throughout the Immensities and the Eternities. That something Lobatchewsky and his successors have taken away. The geometer of to-day knows nothing about the nature of the actually existing space at an infinite distance; he knows nothing about the properties of this present space in a past or future eternity. He knows, indeed, that the laws assumed by Euclid are true with an accuracy that no direct experiment can approach, not only in this place where we are, but in places at a distance from us that no astronomer has conceived; but he knows this as of Here and Now; beyond this range is a There and Then of which he knows nothing at present, but may ultimately come to know more.—Clifford, W. K.
Lectures and Essays (New York, 1901), Vol. 1, pp. 358-359.
[2016]. The truth is that other systems of geometry are possible, yet after all, these other systems are not spaces but other methods of space measurements. There is one space only, though we may conceive of many different manifolds, which are contrivances or ideal constructions invented for the purpose of determining space.—Carus, Paul.
Science, Vol. 18 (1903), p. 106.
[2017]. As I have formerly stated that from the philosophic side Non-Euclidean Geometry has as yet not frequently met with full understanding, so I must now emphasize that it is universally recognized in the science of mathematics; indeed, for many purposes, as for instance in the modern theory of functions, it is used as an extremely convenient means for the visual representation of highly complicated arithmetical relations.—Klein, F.
Elementarmathematik vom höheren Standpunkte aus (Leipzig, 1909), Bd. 2, p. 377.
[2018]. Everything in physical science, from the law of gravitation to the building of bridges, from the spectroscope to the art of navigation, would be profoundly modified by any considerable inaccuracy in the hypothesis that our actual space is Euclidean. The observed truth of physical science, therefore, constitutes overwhelming empirical evidence that this hypothesis is very approximately correct, even if not rigidly true.—Russell, Bertrand.
Foundations of Geometry (Cambridge, 1897), p. 6.