Solution of the Pyramid Problem

With the firm conviction that the Pyramids of Egypt were built and employed, among other purposes, for one special, main, and important purpose of the greatest utility and convenience, I find it necessary before I can establish the theory I advance, to endeavor to determine the proportions and measures of one of the principal groups. I take that of Gïzeh as being the one affording most data, and as being probably one of the most important groups.

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It appears from what I have already set forth that the plan of the Pyramids under consideration is geometrically exact, a perfect set of measures.

I shall now show how these edifices were applied to a thoroughly geometrical purpose in the true meaning of the word-to measure the Earth.

I shall show how true straight lines could be extended from the Pyramids in given directions useful in right-angled trigonometry, by direct observation of the buildings, and without the aid of other instruments.

And I shall show how by the aid of a simple instrument angles could be exactly observed from any point.

This Survey theory does not stand or fall on the merits of my theory of the Gïzeh plan. Let it be proved that this group is not built on the exact system of triangulation set forth by me, it is still a fact that its plan is in a similar shape, and any such shape would enable a surveyor acquainted with the plan to lay down accurate surveys by observations of the group even should it not occupy the precise lines assumed by me.

And here I must state that although the lines of the plan as laid down herein agree nearly with the lines as laid down in Piazzi Smyth's book, in the Penny Cyclopædia, and in an essay of Proctor's in the Gentleman's Magazine, still I find that they do not agree at all satisfactorily with a map of the Pyramids in Sharp's "Egypt," said to be copied from Wilkinson's map.

We will, however, for the time, and to explain my survey theory, suppose the plan theory to be correct, as I firmly believe it is.

And then, supposing it may be proved that the respective positions of the pyramids are slightly different to those that I have allotted to them on my plan, it will only make a similar slight difference to the lines and angles which I shall here show could be laid out by their aid.

Let us in the first place comprehend clearly the shape of the land of Egypt.

A sector or fan, with a long handle-the fan or sector, the delta; and the handle of the fan, the Nile Valley, running nearly due south.

The Pyramids of Gïzeh are situate at the angle of the sector, on a rocky eminence whence they can all be seen for many miles. The summits of the two high ones can be seen from the delta, and from the Nile Valley to a very great distance; how far, I am unable to say; but I should think that while the group could be made general use of for a radius of fifteen miles, the summits of Cephren and Cheops could be made use of for a distance of thirty miles; taking into consideration the general fall of the country.

It must be admitted that if meridian observations of the star Alpha of the Dragon could be made with accuracy by peeping up a small hole in one of the pyramids, then surely might the surveyors have carried true north and south lines up the Nile Valley as far as the summit of Cheops was visible, by "plumbing in" the star and the apex of the pyramid by the aid of a string and a stone.

True east and west lines could have been made to intersect such north and south lines from the various groups of pyramids along the river banks, by whose aid also such lines would be prolonged.Next, supposing that their astronomers had been aware of the latitude of Cheops, and the annual northing and southing of the sun, straight lines could have been laid out in various sectoral directions to the north-eastward and north-westward of Cheops, across the delta, as far as the extreme apex of the pyramid was visible, by observations of the sun, rising or setting over his summit. (That the Dog-star was observed in this manner from the north-west, I have little doubt.)