The Evolution of Scientific Thought from Newton to Einstein

The Evolution of Scientific Thought from Newton to Einstein includes a chapter headed An Alternative View of the Non-Euclidean Geometries. The chapter says that if displacements of bodies which in ordinary life we consider rigid and undeformable are defined as congruent, we obtain Euclidean geometry.

The text says waves of light leaving the centre of a sphere simultaneously are found to return to the centre in coincidence after a reflection against the highly polished inner surface of the sphere, whence we conclude that their speed is the same in all directions. The text says the universal validity of the principle of action was accepted when Maxwell had proved that his equations of electromagnetics could be thrown into a form compatible with it, and when he had succeeded in amalgamating electricity, magnetism and optics into one science. The text says that a Lobatchewskian space, though of infinite extent, would appear to be finite, since stars at infinity would have a non-vanishing parallax.