§ 6A. THE CASING STONES OF THE PYRAMIDS.
Figures 23, 24, and 25, represent ordinary casing stones of the three pyramids, and Figures 26, 27, and 28, represent angle or quoin casing stones of the same.
The casing stone of Cheops, found by Colonel Vyse, is represented in Bonwick's "Pyramid Facts and Fancies," page 16, as measuring four feet three inches at the top, eight feet three inches at the bottom, four feet eleven inches at the back, and six feet three inches at the front. Taking four feet eleven inches as Radius, and six feet three inches as Secant, then the Tangent is three feet ten inches and three tenths.
Thus, in inches (√(75²-59²)) = 46·30 inches; therefore the inclination of the stone must have been—slant height 75 inches to 46·30 inches horizontal. Now, 46·30 is to 75, as 21 is to 34. Therefore, Col. Vyse's casing stone agrees exactly with my ratio for the Pyramid Cheops, viz., 21 to 34. (See Figure 29.)
Fig. 29. Col. Vyse's Casing Stone.
75 : 46·3 :: 34 : 21
This stone must have been out of plumb at the back an inch and seven tenths; perhaps to give room for grouting the back joint of the marble casing stone to the limestone body of the work: or, because, as it is not a necessity in good masonry that the back of a stone should be exactly plumb, so long as the error is on the right side, the builders might not have been particular in that respect.
Fig. 59. (Temple of Cheops, standing at angle of wall.)
Figure 59 represents such a template as the masons would have used in building Cheops, both for dressing and setting the stones. (The courses are drawn out of proportion to the template.) The other pyramids must have been built by the aid of similar templates.
Such large blocks of stone as were used in the casing of these pyramids could not have been completely dressed before setting; the back and ends, and the top and bottom beds were probably dressed off truly, and the face roughly scabbled off; but the true slope angle could not have been dressed off until the stone had been truly set and bedded, otherwise there would have been great danger to the sharp arises.
I shall now record the peculiarities of the 3, 4, 5 or Pythagorean triangle, and the right-angled triangle 20, 21, 29.