As to the results of the whole investigation, perhaps many theorists will agree with an American who was a warm believer in Pyramid theories when he came to Gizeh. I had the pleasure of his company there for a couple of days, and at our last meal together he said to me in a saddened way: “Well, sir! I feel as if I had been to a funeral. By all means let the old theories have a decent burial, though we should take care that in our haste none of the wounded ones are buried alive.” As regards the late J. A. Parker’s calculation in general, and his third proposition especially, we have consulted some eminent mathematicians, and this is the substance of what they say: Parker’s reasoning rests on sentimental, rather than on mathematical, considerations, and is logically inconclusive. Proposition III, namely, that: The circle is the natural basis or beginning of all area, and the square being made so in mathematical science, is artificial and arbitrary. —is an illustration of an arbitrary proposition, and cannot safely be relied upon in mathematical reasoning. The same observation applies, even more strongly, to Proposition VII, which states that: Because the circle is the primary shape in nature, and hence the basis of area; and because the circle is measured by, and is equal to the square only in ratio of half its circumference by the radius, therefore, circumference and radius, and not the square of diameter, are the only natural and legitimate elements of area, by which all regular shapes are made equal to the square, and equal to the circle. Proposition IX is a remarkable example of faulty reasoning, though it is the one on which Mr. Parker’s Quadrature mainly rests. It states that: The circle and the equilateral triangle are opposite to one another in all the elements of their construction, and hence the fractional diameter of one circle, which is equal to the diameter of one square, is in the opposite duplicate ratio to the diameter of an equilateral triangle whose area is one, etc., etc. Granting, for the sake of argument, that a triangle can be said to have a radius, in the sense in which we speak of the radius of a circle—for what Parker calls the radius of the triangle, is the radius of a circle inscribed in a triangle, and therefore not the radius of the triangle at all—and granting for the moment the other fanciful and mathematical propositions united in his premisses, why must we conclude that, if the equilateral triangle and circle are opposite in all the elements of their construction, the diameter of any defined circle is in the opposite duplicate ratio of the diameter of any given equivalent triangle? What necessary connection is there between the premisses and the conclusion? The reasoning is of a kind not known in geometry, and would not be accepted by strict mathematicians.