صفحة 137 من 212

We can sum this up as follows: Gauss invented a method for the

mathematical treatment of continua in general, in which

"size-relations" ("distances" between neighbouring points) are

defined. To every point of a continuum are assigned as many

numbers (Gaussian coordinates) as the continuum has dimensions.

This is done in such a way, that only one meaning can be attached

to the assignment, and that numbers (Gaussian coordinates) which

differ by an indefinitely small amount are assigned to adjacent

points. The Gaussian coordinate system is a logical

generalisation of the Cartesian co-ordinate system. It is also

applicable to non-Euclidean continua, but only when, with respect

to the defined "size" or "distance," small parts of the continuum

under consideration behave more nearly like a Euclidean system,

the smaller the part of the continuum under our notice.

XXVI.

THE SPACE-TIME CONTINUUM OF THE SPECIAL THEORY OF RELATIVITY

CONSIDERED AS A EUCLIDEAN CONTINUUM