(no error given), theoretical angle 54° 9′ 4″, 13: 18 (difference, 5').[1] Petrie well remarked that these values "cannot be considered as very satisfactory." He found later that the first of these two measurements was entirely wrong; that the observed angle was "within a few minutes of 51° 52'," "just that of the Great pyramid of Gizeh" (W. M. F. Petrie, et al., Medum, London, 1892, p. 6). After ten observations in the second case he found the mean to be 55° 1′, the variations of observations being + 22′ to — 23′ (W. M. F. Petrie, A Season in Egypt, 1887, London, 1888, p. 30).
If we interpret the seked of the Rhind mathematical papyrus, not as Eisenlohr (1877), Petrie (1883), and Cantor (1885) do, but as the Revillouts (1881), followed by Borchardt (1893), and Petrie (later),[2] we find the following ratios for the sekeds in the six examples on pyramidal shapes in the Rhind papyrus: no. 56, in Eisenlohr (1877), 18 : 25, corresponding to an angle of 54° 14′ 4″; nos. 57, 58, 59, 59a. 3 :4, corresponding to 53° 7′ 48″; and no. 60, 1 :4 corresponding to 75° 57′ 50″.
Compare Heath (1921), where the reason for giving the details indicated above will be apparent.
Vaschenko-Zakharechenko, M. E., Istoriya matematiki. Istoricheskii ocherk razvitiya geometrii [History of Mathematics. Historical sketch of the development of geometry], Kiev, vol. 1, 1883, 11 + 684 pp.
The chapter on Egyptian mathematics is on pages 327—350. The work is of minor importance; compare the review by Bobynin in Bibliotheca Mathematica, series 2, vol. 1, 1887, pp. 114-116.
1884
Gow, J., A Short History of Greek Mathematics, Cambridge, 1884, pp. 16-21, 126-129, 142, 285, 286.
Refers to Eisenlohr (1877) and Cantor (1880).
Lspsisus, K. R., "Über die 6 palmige grosse Elle von 7 kleinen Palmen Länge in dem ‘Mathematischen Handbuche’ von Eisenlohr," Zeit-schrift für Äigyptische Sprache . . . , vol. 22, 1884, pp. 6-11.
Especially discusses the pyramid problems, nos. 56-59a; compare Lepsius (1866). See Heath (1921).
Tannery, P.,"Questions Héroniennes," Bulletin des Sciences Mathematiques, Paris, series 2, vol. 8, 1884, pp. 329-344 and 359-376.
- ↑ Borchardt (1893), p. 16, pointed out that 54° 14′ 46″ corresponds to 18 : 25 (difference, 0″).
- ↑ In the new, revised, and much abridged edition of his Pyramids . . ., London, [1885], p. 68, Petrie states: "The design of the various slopes that are met with, appears to be always a simple relation of the vertical and horizontal distance, agreeing with the method of stating the slopes in the mathematical papyrus of Aahmes."
