A stadium being 360 R.B. cubits, or six seconds—and a plethron 60 R.B. cubits, or one second, the base of the Pyramid Cephren is seven plethra, or a stadium and a plethron, equal to seven seconds, or four hundred and twenty R.B. cubits.
Mycerinus' base is acknowledged to be half the base of Cephren.
Piazzi Smyth makes the base of the Pyramid Cheops 9131·05 pyramid (or geometric) inches, which divided by 20·2006 gives 452·01 R.B. cubits. I call it 452 cubits, and accept it as the measure which exactly fits the plan.
I have not sufficient data to determine the exact base of the other and smaller pyramid which I have marked on my plan.
The bases, then, of Mycerinus, Cephren, and Cheops, are 210, 420 and 452 cubits, respectively.
But in plan the bases should be reduced to one level. I have therefore drawn my plan, or horizontal section, at the level or plane of the base of Cephren, at which level or plane the bases or horizontal sections of the pyramids are—Mycerinus, 218 cubits, Cephren, 420 cubits, and Cheops, 420 cubits. I shall show how I arrive at this by-and-by, and shall also show that the horizontal section of Cheops, corresponding to the horizontal section of Cephren at the level of Cephren's base, occurs, as it should do, at the level of one of the courses of masonry, viz.—the top of the tenth course.
§ 4. THE SLOPES, RATIOS, AND ANGLES OF THE THREE PRINCIPAL PYRAMIDS OF THE GIZEH GROUP.
Before entering on the description of the exact slopes and angles of the three principal pyramids, I must premise that I was guided to my conclusions by making full use of the combined evolutions of the two wonderful right-angled triangles, 3, 4, 5, and 20, 21, 29, which seem to run through the whole design as a sort of dominant.
From the first I was firmly convinced that in such skilful workmanship some very simple and easily applied templates must have been employed, and so it turned out. Builders do not mark a dimension on a plan which they cannot measure, nor have a hidden measure of any importance without some clear outer way of establishing it.
This made me "go straight" for the slant ratios. When the Pyramids were cased from top to bottom with polished marble, there were only two feasible measures, the bases and the apothems;[1] and for that reason I conjectured that these would be the definite plan ratios.