"Minkowski demonstrated the significance of the expression for ds^2 by taking the new variable T = ict, where i stands for \sqrt{-1}. With this change, ds^2 can be written:ds^2 = dx^2 + dy^2 + dz^2 + dT^2,which is the expression of the square of a distance in a four-dimensional Euclidean space when a Cartesian co-ordinate system is taken. Since this expression is to remain unmodified in value and form in all Galilean frames, we must conclude that in a space-time representation a passage from one Galilean frame to another is given by a rotation of our four-dimensional Cartesian space-time mesh-system. Now rotation constitutes... a variation in the co-ordinates of the points of the continuum. In other words, they correspond to mathematical transformations. The transformations which accompany a rotation of a Cartesian co-ordinate system are of a particularly simple nature; they are called "orthogonal transformations." It follows that if we write out the orthogonal transformations for Minkowski's four-dimensional Euclidean space-time, we should obtain ipso facto the celebrated Lorentz-Einstein transformations which represent the passage from one Galilean system to another. ...we obtain the following result: Two Galilean systems moving with a relative velocity v are represented by two space-time Cartesian co-ordinate systems differing in orientation by the imaginary angle \theta, where \theta is connected with v by the formula tan\theta = \frac{iv}{c}."