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From this consideration we see that it will be advantageous if,

in the description of position, it should be possible by means of

numerical measures to make ourselves independent of the existence

of marked positions (possessing names) on the rigid body of

reference. In the physics of measurement this is attained by the

application of the Cartesian system of co-ordinates.

This consists of three plane surfaces perpendicular to each other

and rigidly attached to a rigid body. Referred to a system of

co-ordinates, the scene of any event will be determined (for the

main part) by the specification of the lengths of the three

perpendiculars or co-ordinates (x, y, z) which can be dropped

from the scene of the event to those three plane surfaces. The

lengths of these three perpendiculars can be determined by a

series of manipulations with rigid measuring-rods performed

according to the rules and methods laid down by Euclidean

geometry.