Dynasty documents and is the basis of Sethe's discussion. Compare Gunn (1922). A reference may be added to M. A. Murray, "Egyptian finger counting rhymes," Folk Lore, vol. 36, 1925, pp. 186-187; she gives a free English translation of the finger numbering spell. The first sentence of her article is as follows: "It has often been suggested that many children's games and rhymes may be derived from, or in imitation of religious ritual." Only disciples of Petrie will agree with Miss Murray's suggested date for the above mentioned finger numbering spell.
1919
Karpinski, L. C., "Origines et développement de 1’a1gèbre," Scientia, vol. 26, 1919, pp. 89-101.
A translation by M. E. Philippi of the English original, published in School Science and Mathematics, vol. 23, 1923, pp. 54-65; Egyptian mathematics is referred to on pp. 54-57 (89-93 of the translation).
1921
Heath, T. L.,A History of Greek Mathematics, Oxford, 1921. Vol. I, pp. 122——I28 ("Egyptian geometry, i.e., mensuration"), 130, 131; vol. 2, pp. 440-441 ("'Han'-calculations").
See also Baillet (1892). Attributes to Borchardt, instead of to the Revillouts (1881), the now generally accepted cotangent interpretation of seked. Quotation (p. 128): "But. lastly, the se-qet in No. 56 is 1⁄18/25 and, if se-qet is taken in the sense of cot HFE [defined in the previous discussion], this gives for the angle HFE the value of 54° 14′16″, which is precisely, to the seconds, the slope of the lower half of the southern stone pyramid of Dakshūr [sic]; in Nos. 57-9 the se—qet, 3⁄4, is the cotangent of an angle of 53° 7′48″, which again is exactly the slope of the second pyramid of Gizeh as measured by Flinders Petrie; and the se-qet in No. 60, which is 1⁄4, is the cotangent of an angle of 75°57′50″, corresponding exactly to the slope of the Mastaba-tombs of the Ancient Empire and of the sides of the Mēdūm pyramid."[1]
This paragraph is based, apparently, on Borchardt (1893, p. 16) and Griffith (1894, p. 238); a similar series of statements occurs in the Nature review listed under Ahmes (1898). From what we have indicated under Petrie (1883), it is clear that the paragraph is replete with error and false suggestion. The angles 53°7′48″ and 75°57′50″ are, as we have seen, "theoretical angles"—quite different from even the mean of the observed angles; but apart from this we have noted that the angle 75°57′50″ is more than 24° in error for the Medum pyramid! It is palpably absurd to employ in this connection such terms as: "precisely, to the seconds," "exactly the slope," and "exactly to the slope."
But again, the angle 54°14′16″ is not given by either Petrie (1883) or Borchardt (1893); perhaps it is a misprint for 54°14′46″, a value apparently
- ↑ "Flinders Petrie, Pyramids and Temples of Gizeh, p. 162."
