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 speed c; in an geometry there exists an absolute length R etc.. It didn't surprised me that there appeared analogies between the two fields also in the evolutionary history of these fields. In both cases we were struggling for the values of certain parameters, to which an infinite value was attributed in the older theories, and to which a finite value was attributed in recent theories. In the evolutionary history of non-euclidean geometry some apparent contractions were posed, and some thought to find contradictions in relativity theory as well.

All of this led me to transform Einstein's formulas and to interpret them in a non-euclidean way. In the mean time 's paper was published, in which it was shown that for the composition of velocities in relativity theory the formulas of spherical trigonometry with imaginary sides do apply. Now, hyperbolic geometry is the imaginary counter-image of the spherical geometry, as it was already known to and. Then I was sure that an interesting field of application offers itself for the hyperbolic geometry. My first relevant papers in the Physikalische Zeitschrift were soon followed by two additional papers. In those papers, I gave the non-euclidean interpretation of finished formulas in relativity theory. Afterwards I took the reverse way. I based my thoughts on the assumption that the phenomena take place in an space and arrived by some simple geometrical conclusions at the formulas of relativity theory. The result of my investigation can be expressed as follows, that by using non-euclidean geometry the formulas for relativity theory were not only essentially simplified, but they also admit of a geometric interpretation that is completely analogous to the interpretation of classical theory in euclidean geometry. And this analogy sometimes goes thus far, that literal expression of the theorems of classical theory can remain unchanged, one only has to replace the euclidean figures by the corresponding figure of an space by the parameter $$c=3\cdot 10^{10}$$.

1. Definition and graphical illustration of velocities.

The speed of light plays in physics the role of an