e values being measurements, they are also regarded as the formulae by which any other module is classified.
That is, any of the listed feet could occupy the Root position in the above table, and all of its variants would be subject to
the multiplications of the tabulated values. As an example, the Persian foot when subjected to this process:
|1.040461 ||1.046406 ||1.052386 ||1.0584 ||1.064448
Thus, whichever of the measures shows a direct fractional link to the English foot, such as the one and one twentieth, as above,
is Root, then the maximum value of 1.064448ft is both the Hashimi foot and the original pied de roi, both could be
classified as a Standard Geographic Persian foot (1.05 x 1.01376). Or the given length of the Mycenaen foot at .910315ft could
be classified as a Root Geographic Assyrian foot (.9 x 1.0114612ft) and so forth. Then, whenever one is making cultural
comparisons of modules, the correct classification must be selected, Root Reciprocal to Root Reciprocal etc. otherwise one is
looking at a compound fraction, i.e. the fraction separating the distinctive foot plus the fraction of the variation(s), which
may then show no apparent rational relationship.
These fractional separations of the rows and columns have a practical purpose; they are designed to maintain integers in
circular structures and artefacts such as storage and measuring vessels. If a diameter is multiple of four or a decimal,
by using 22/7 as pi this results in a fractured number perimeter. Therefore 3.125 or 25/8 would be used to give an
integer or rational fraction for the perimeter. Accuracy is maintained by using the longer version -- by the 176th part -- of
the measure in the perimeter; this is because 25/8 differs from 22/7 as 175 to 176. Similarly, the fraction 441 to 440 maintains
integrity of number in diameter and perimeter, but of different modules. If one has a canonical perimeter number such as
360 English feet, then the diameter will be exactly 100 royal Egyptian feet, but, the royal Egyptian foot that is directly
related by a ratio 8 to 7 of the English at 1.142857ft (Root), is supplanted in the diameter by the foot that is the 440th part
longer at 1.145454ft (Standard). Another example is to use as a diameter 100 Standard common Greek feet, then the perimeter is
360 Assyrian feet but of the Root classification -- the 440th part less. This is clearly indicative of the integrated nature of
the original system, the purpose of which was the maintenance of integers in what would mostly be fractured numbers were a
single standard measure used, which is what we have today. Ancient metrology is very simply based upon how number itself