of the Heptagon. 131 



9. My own studies have not been such as to entitle me to express 

 an opinion whether the architectural and geometrical drawings 

 of Rober in connexion with the plan of the temple at Edfu, and 

 his comparisons of the numbers deduced from the details of his 

 construction with French measurements previously made, are 

 sufficient to bear out his conclusion, that the process had been 

 anciently used : but I wish that some qualified person would 

 take up the inquiry, which appears to me one of great interest, 

 especially as I see no antecedent improbability in the supposi- 

 tion that the construction in question may have been invented 

 in a very distant age. The geometry which it employs is in 

 no degree more difficult than that of the Fourth Book of Euclid*; 

 and although I have no conjecture to offer as to what may have 

 suggested the particular process employed, yet it seems to me 

 quite as likely to have been discovered thousands of years ago, 

 perhaps after centuries of tentation, as to have been first found 

 in our own time, which does not generally attach so much im- 

 portance to the heptagon as a former age may have done, and 

 which perhaps enjoys no special facilities in the search after such 

 a construction, although it supplies means of proving, as above, 

 that the proposed solution of the problem is not mathematically 

 perfect. 



10. If Roberts professional skill as an architect, combined 

 with the circumstance stated of his having previously invented 

 the construction for himself, did really lead him to a correct 

 interpretation f of the plan of the temple at Edfu, which he 

 believed to embody a tradition much older than itself, we are 

 thus admitted to a very curious glimpse, or even a partial view, 

 of the nature and extent, but at the same time the imperfection, 

 of that knowledge of geometry which was possessed, but kept 

 secret, by the ancient priests of Egypt. I say the imperfection, 

 on the supposition that the above described construction of the 

 heptagon, if known to them at all, was thought by them to be 

 equal in rigour, as the elder Rober appears to have thought it to 

 be, to that construction of the pentagon which Euclid may have 

 learned from them, rejecting perhaps, at the same time, the 



* The segment p' of the side p of the pentagon, and the fourth propor- 

 r'r" 

 tional — — to the three radii, which enter into the equations (A), and of which 



the latter is the greater segment of the third diameter, 2r", if this last be 

 cut in extreme and mean ratio, may at first appear to depend on the Sixth 

 Book of Euclid, but will be found to be easily constructive without going 

 beyond the Fourth Book. 



t It ought in fairness to be stated that Rober's interpretation of Egyp- 

 tian antiquities included a vast deal more than what is here described, and 

 that he probably considered the geometrical part of it to be the least inter- 

 esting, although still, in his view, an essential and primary element. 



K2 



