The proposed scaled aspect of the square root of 6, and most numbers less than 1,000 need not have used 6/6 at any time. Updates to the Planetmath writeup will contibue until the project is complete.
Planetmath will also be updated to show that Egyptian scribes commonly mentioned inverse relationships in shorthand discussions of square roots of perfect squares 4, 25, 36, 49, 64, 81, 100 and higher, an important historical point will be reviewed on another level.
What was used focused upon were remainders(R). Remainders were often estimated in n/5 parts such that n/5 was scaled by 24/24 = 24n/120 as discussed by:
1/5(24/24) = 24/120 = (20 + 3 + 1)/120
2/5(24/24).= 48/120 = (40 + 5 + 3)/120
3/5(24/24) = 72/120 = (60 + 8 + 3 + 1)/120
4/4(24/24) = 96/120 = (80 + 8 + 5 + 3)/120
and other partitions.
Initial estimated square root of N statements, with Quotient (Q) used the form
(Q + n/5)^2
The raw square root data was processed in shorthand formats that considered a rational error E1 that scribes reduced to a lower acceptable error E2.
The complete historical method (found by Occam's Razor, and historical data) will be posted to a Planetmath page in the next few days, and maybe weeks. The final method will likely describe selections of (irrational) errors E2 associated with adding or subtracting from the last term (1/40, most often, and as I suspect, at other times 1/120).
Thanks to Peter D. for the prodding. This unresolved topic had been running around in my head for far too many years, over 20 to be sure.