pean geometry as it exists to-day certainly did not exist preformed in the mind of the ancient Egyptian "cord-fasteners," any more than the steam-plough existed in the mind of the first men who used digging-sticks. And, as we cannot say that the geometry which now exists in Europe, is nothing more than what was present to the mind of the early Egyptian, so we cannot say that the religion of the polytheist or monotheist is nothing more than was present to minds which had not attained to the belief in personal beings superior to man. But neither can we close our eyes to the fact that what was in the mind of the Egyptian "cord-fastener" has become modern European geometry by a process of continuity, which is none the less continuous because it has been continuously changing.
Whether the Egyptian "cord-fasteners" went on fastening their cords in the primitive way even after the time of Euclid, I do not know. If they did, then we should have an earlier and a later stage of geometry existing simultaneously in different countries, in the same way that we have in Australia an earlier stage of religion existing simultaneously with later stages elsewhere.
If we consider the process by which geometry has evolved to be analogous to the process by which religion has evolved, we shall perhaps be inclined to differ somewhat from Dr. Marett in one point. He says (E.R.E., viii., p. 247b), "In the sphere of nascent religion there must have been a stage of cult or ritual (if so it may be termed), the product of sheer unreflective habit, which preceded the growth of ideas concerning the how and why of what was being done." But, I suggest, that in the sphere of nascent geometry the stage in which the Egyptian "cord-fastener" measured out the land in Egypt after each inundation of the Nile—or, in the sphere of nascent agriculture, the stage in which a digging-stick was first used—was not "the product of sheer unreflective habit."
