Note 30 — Chapter VII · SYSTEMS OF CO-ORDINATES AND DISTANCE

If we were to represent non-Euclidean geometry as arising from the behaviour of our measuring rods, squirming when displaced as compared with Euclidean rods, we should see that Euclideanism in the infinitesimal implies that when our rods are of infinitesimal length and are displaced over infinitesimal distances, they behave in the same way as rigid Euclidean rods.