"The principle of the invariant velocity of light states that in whatever Galilean system we might have operated, the measured velocity of light in vacuo would always be the same. ...The mathematical translation of this principle of physics yields us the following equation, which must remain invariably zero in value for all Galilean frames:dx^2 + dy^2 + dz^2 -c^2dt^2 = 0 (using differentials)[ Note: the above is derived from the velocity of light c being equal to the change in length divided by the change in time, i.e., \frac{\vartriangle l}{\vartriangle t} = c, or expressed as differentials, \frac{dl}{dt} = c, which implies \frac{dl^2}{dt^2} = c^2 and {dl^2} - c^2dt^2 = 0. But, by the Pythagorean theorem, {dl^2} = {dx^2} + {dy^2} + {dz^2} ]. From a purely mathematical standpoint problems of this type form a branch of mathematics known as the theory of invariants. ...the transformations to which it was necessary to subject these variables (in order to satisfy the condition of invariance...), were given by a wide group of transformations known as conformal transformations. Conformal transformations are those which vary the shape of the lines while leaving the values of their angles of intersections unaltered. They are of wide use in maps, e.g., in Mercator's projection or in the stereographic projection. But when, in addition, the relative velocity is taken into consideration it is seen that conformal transformations are far too general. ...when the required restrictions are imposed we find that the rules of transformation according to which the space and time co-ordinates of one Galilean observer are connected with those of another depend in a very simple way on the relative velocity v existing between the two systems. These rules of transformation are given by the Lorentz-Einstein transformations."