[1] The "Apothem is a perpendicular from the vertex of a pyramid on a side of the base."—Chambers' Practical Mathematics, p. 156.

Figures 6, 7 and 8 show the exact slope ratios of Cheops, Cephren, and Mycerinus, measured as shown on the diagrams—viz., Cheops, 21 to 34, Cephren, 20 to 33, and Mycerinus, 20 to 32—that is, half base to apothem.

Fig. 6 Cheops.

Note. The Ratios of Bases to Altitudes are very nearly as follows, viz:—
Cheops33 to 21or 330 to 210
Cephren 32 to 21 or 320 to 210
Mycerīnus32 to 20 or 336 to 210

Fig. 7 Cephren.

Fig. 8 Mycerīnus.

The ratios of base to altitude are, Cheops, 33 to 21, Cephren, 32 to 21, and Mycerinus, 32 to 20: not exactly, but near enough for all practical purposes. For the sake of comparison, it will be well to call these ratios 330 to 210, 320 to 210, and 336 to 210, respectively.

Fig. 9. Cheops. Fig. 10. Cheops.

Figures 9 and 10 are meridional and diagonal sections, showing ratios of Cheops, viz., half base to apothem, 21 to 34 exactly; half base to altitude, 5½ to 7 nearly, and 183 to 233, nearer still (being the ratio of Piazzi Smyth). The ratio of Sir F. James, half diagonal 10 to altitude 9 is also very nearly correct.

My altitude for Cheops is 484·887 British feet, and the half base 380·81 British feet.

The ratio of 7 to 5½ gives 484·66, and the ratio of 233 to 183 gives 484·85 for the altitude.