The reader will remember that I have previously advanced that the level of Cephren's base was the plan level of the Gïzeh pyramids, and that at this level the base of Cheops measures 420 R.B. cubits—same as the base of Cephren.
This hypothesis is supported by the revelations of the pentangle, in which the ratio of 34 to 21 = apothem 340 to half-base 210 R.B. cubits, is so nearly approached.
Showing how proportional lines were the order of the pyramids of Gïzeh, we will summarise the proportions of the three main pyramids as shewn by my dimensions and ratios, very nearly, viz.:—
Mycerinus. Base : Apothem :: Altitude : Half-Base.
as shown by the ratios, (Fig. 13), 40 : 32 :: 25 : 20.
Cephren. Diagonal of Base : Edge :: Edge : Altitude.
as shown by ratios, (Fig. 12), 862 : 588 :: 588 : 400.
Cheops. (Apothem + Half Base): Apoth. :: Apoth. : Half Base.
as shown by the ratios, (Fig. 9), 55 : 34 :: 34 : 21.
and—Apothem : Altitude :: Altitude : Half-B.
Similar close relations to other stars may be found in other pyramids. Thus:—Suppose NHO of figure 69 to be the NHO of a heptangle instead of a pentangle, then does NH represent apothem, and NO represent base of the pyramid Mycerinus, while the co-sine of the angle NHM (being MH minus versed sine) will be equal to the altitude of the pyramid. The angle NHM in the heptangle is, 38° 34′ 17·142″, and according to my plan of the pyramid Mycerinus, the corresponding angle is 38° 40′ 56″. (See Fig. 19.) This angular difference of 0° 6′ 39″ would only make a difference in the apothem of the pyramid of eight inches, and of ten inches in its altitude (apothem being 283 ft. 1 inch, and altitude 221 ft.).
§ 17. THE MANNER IN WHICH THE SLOPE RATIOS OF THE PYRAMIDS WERE ARRIVED AT.
The manner in which I arrived at the Slope Ratios of the Pyramids, viz., 32 to 20, 33 to 20, and 34 to 21, for Mycerinus, Cephren, and Cheops, respectively (see Figures 8, 7 and 6), was as follows:—
First, believing in the connection between the relative positions of the Pyramids on plan (see Fig. 3, 4 or 5), and their slopes, I viewed their positions thus:—
Mycerinus, situate at the angle of the 3, 4, 5 triangle ADC, is likely to be connected with that "primary" in his slopes.
Cephren, situate at the angle of the 20, 21, 29 triangle FAB, and strung, as it were, on the hypotenuse of the 3, 4, 5 triangle DAC, is likely to be connected with both primaries in his slopes.