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LX. Notices respecting New Books. 



A Letter from Alexandria on the Evidence of the practical Application 

 of the Quadrature of the Circle in the Configuration of the Great 

 Pyramids of Gizeh. By H. C. Agnew, Esq. London : Longman 

 and Co., 1838, 4to. pp. 57 ; Plates 9. 



THE author conceives that while the principal purpose which 

 the ancient Egyptians had in view, in the construction of the 

 pyramids, was that of their serving as sepulchral monuments, they 

 at the same time intended to perpetuate, by their means, the know- 

 ledge they had acquired of certain geometrical relations between 

 lines appertaining to the circle ; and that, conformably with tliis 

 intention, they proceeded upon a regular system of geometrical con- 

 struction, in selecting those relative dimensions in regard to the 

 length of the sides of their bases, their perpendicular altitudes, the 

 length of their edges, and their respective angles of inclination of 

 the faces to one another, and to the horizontal plane, which ex- 

 pressed various geometrical relations, derived from the quadrature of 

 the circle, and the proportions between its area and that of squares 

 inscribed within, or circumscribed about the circle, according to 

 certain methods. 



He has taken great pains to obtain the most accurate measure- 

 ments of the lengths of the sides, and the inclinations of the faces 

 and edges to the horizon, of each of the three great pyramids of 

 Gizeh, both by collecting and comparing the statements of former 

 travellers, and by verifying and correcting them from his own per- 

 sonal observation: and he presents the whole of his numerous 

 measurements in a tabular form. 



In the development of his hypothesis, the author proceeds on the 

 principle that the three pyramids were all parts of one system ; all 

 their dimensions being derivable from one and the same parent 

 circle, which he terms the holy circle, and the properties of which 

 they were all intended to represent. Then describing an inscribed, 

 and a circumscribed square, and also a square, partly the one and 

 partly the other, (that is, having one of its sides tangent to the 

 circle, and the angular points terminating the opposite side being 

 situated in the circumference of the same circle,) he infers from his 

 measurements that the three pyramids are constructed with refer- 

 ence to these squares ; inasmuch as he finds that the perpendicular, 

 or altitude of the second pyramid, is the radius of a second circle, 

 of which the circumference, joined to the circumference of the great 

 circle, is equal to the united perimeters of the two squares ; and 

 that, in the third pyramid, the perpendicular is the radius of a circle, 

 whose circumference is equal to the perimeter of its base. 



The author enters at great length into the investigation of various 

 other recondite geometrical properties of these congenerous squares 

 and circles, which he conceives are exemplified and illustrated by 

 the several proportions existing among the lines and angles of the 

 system of pyramids of Gizeh. 



