The Solution of the Pyramid Problem; or, Pyramid Discoveries / With a New Theory as to their Ancient Use

by Robert Ballard

§ 13. THE SIZE AND SHAPE OF THE PYRAMIDS INDICATED BY THE PLAN.

I pursued my investigations into the slopes and altitudes of the pyramids without reference to the plan, after once deciding their exact bases.

Now it will be interesting to note some of the ways in which the plan hints at the shape and size of these pyramids, and corroborates my work.

The dimensions of Cheops are indicated on the plan by the lines EA to YA, measuring 840 and 288 R.B. cubits respectively, being the half periphery of its horizontal section at the level of Cephren's base, and its own altitude from its own base. (See Fig. 5.)

The line EA, in fact, represents in R.B. cubits the half periphery of the bases of either Cheops or Cephren measured at the level which I have set forth as the plan level, viz., base of Cephren.

The ratio of Cephren's base to Cephren's altitude is indicated on the plan by the ratios of the lines BC to EB, or FO to OR, viz., 32 to 21. (See Fig. 4.)

The altitude of Mycerinus above Cephren's base appears on plan in the line EF, measuring 136 R.B. cubits.

The line EO on plan measures 888 cubits, which would be the length of a line stretched from the apex of Cheops to the point E, at the level of Cheops' base.

This merits consideration:—the lines EA and AY are connected on plan at the centre of Cheops, and the lines EO and EA are connected on plan at the point E.

Now the lines EO, EA and AY are sides of a "primary triangle," whose ratio is 37, 35, 12, and whose measure in cubits is 888, 840, and 288; and if we suppose the line EA to be stretched horizontally beneath the pyramids at the level of the base of Cheops from E to A on plan, and the line AY to be a plumb line hanging from the apex of Cheops to the level of his base, then will the line EO just stretch from the point E to the apex of Cheops, and the three lines will connect the two main pyramids by a vertical triangle of which EA, AY and EO form the base, perpendicular, and hypotenuse. Or, to explain it in another manner: let the line EA be a cord stretching horizontally from A at the centre of the base of Cheops to the point E, both ends being at the same level; let the line AY be a rod, lift it on the end A till it stands erect, then is the end Y the apex of Cheops. Now, the line EO would just stretch from the top of the rod AY to the point E first described.

It is a singular coincidence, and one that may be interesting to students of the interior of the Pyramids, that the side EP, of the small 3, 4, 5 triangle, EP, PF, FE, in the centre of the plan, measures 81·60 R.B. cubits, which is very nearly eight times the "true breadth" of the King's chamber in Cheops, according to Piazzi Smyth; for 81·60/8 = 10·20 R.B. cubits, or 206·046 pyramid inches (one R.B. cubit being 20·2006 pyramid inches). The sides of this little triangle measure 81·60, 108·80, and 136, R.B. cubits respectively, as can be easily proved from the plan ratio table.