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Introduction 3

tion of their armies, the building of seagoing ships, the levying and collection of taxes, and at all the thought and effort concomitant with the proper organization of a civilization that existed successfully, virtually unchanged, for centuries longer than that of any other nation in recorded history.

What we today call science and mathematics must have played an important role in the achievement of all this. I am reminded of a piece of wisdom attributed to Arnold Buffum Chace, the principal author of The Rhind Mathematical Papyrus:

I venture to suggest that if one were to ask for that single attribute of the human intellect which would most clearly indicate the degree of civilization of a race, the answer would be, the power of close reasoning, and that this power could best be determined in a general way by the mathematical skill which members of the race displayed. Judged by this standard the Egyptians of the nineteenth century before Christ had a high degree of civilization.*

If we accept this thought as one containing a solid measure of truth, then it will surely come as a great surprise to the readers of this history to find that whatever great heights the ancient Egyptians may have achieved scientifically, their mathematics was based on two very elementary concepts. The first was their complete knowledge of the twicetimes table, and the second, their ability to find two-thirds Of any number, whether integral or fractional. Upon these two very simple foundations the whole structure of Egyptian mathematics was erected, as we shall see in the following pages.

* A. B. Chace; L. Bull; H. P. Manning; and R. C. Archibald, The Rhind Mathematical Papyrus, Vol. 1, Mathematical Association of America, Merlin, Ohio, 1927, Preface.