Dr. Arnott on the Proportion* of tlie Pyramids of Egypt 217 



Other modern observers, such as Niebuhr, Greaves, Davidson, and 

 Trench, do not by any means agree with each other, and, as M. Savary 

 says, " to determine the precise dimensions is still a problem." But we 

 may arrive at a somewhat satisfactory conclusion by taking the average 

 of their measurements reduced to a supposed base of 750 English feet. 

 Thus:— 



Height 



Niebuhr, 750 465 



Greaves, 750 514 



Davidson, 750 464 



Trench, 750 500 



Head, 750 484 



Approximation in Ency. Brit., art. Egypt, 750 477 



Sum, 4500 2914 



Average, 750 485 



At the summit of the greater pyramid is at present a platform of about 

 32 feet square. Supposing the height in the above average to be that of 

 the platform, it will be requisite to add about 21 feet to get the height, 

 if the pyramid were carried up to a sharp point ;* this gives the extreme 

 height, if the pyramid were complete, of about 506 to the base of 750, 

 numbers not very remote from the proportion already derived from Bel- 

 zoni's measurements, by which the base and height are as 3 to 2, or as 

 6 to 4. 



These, then, I conceive may be assumed as the true proportions, or 

 rather perhaps, the proportions originally contemplated; and consequently, 

 the right angled triangle formed by the half base, the perpendicular 

 height, and the slanting height, exhibits the remarkable numbers 3, 4, 5, 

 the lowest integers that indicate a right angled triangle, and which made 

 these numbers be looked on with great veneration centuries before Euclid 

 became acquainted with the properties of right angled triangles, and 

 which, with many other portions of his geometrical knowledge, he derived 

 from the Egyptian sages. 



I have said that Herodotus states that the base and height of the 

 pyramid are equal. He may have arrived at this conclusion in two 

 ways ; either by supposing that the phenomenon of the pyramid casting 

 no shadow at noon, was limited to the precise period between the two 

 equinoxes ; in which case, as the latitude was 30°, a vertical section would 

 exhibit an equilateral triangle, the height he gave being thus the slanting 

 height ; or he may have given the length of the ridge formed by two con- 

 tiguous faces of the pyramid, and it is to this, as I conceive, ho refers, 

 although in reality this ridge is a few feot shorter than the base, or in 

 tho proportion of 31 to 32 nearly. And if we suppose that, in Strabo's 



* Somo of the above do not require this correction, but in others it may not suffice : 

 it may be allowed to the average. 



