Expanded demonstrations of two Q.E.D. proofs are seriously needed. The first expands a common Egyptian and Greek rational number system recorded in concise unit fraction series. The second expands square root examples also recorded in concise unit fraction series.
On the rational number level n/144, n/145, n/146 and a few other table of unit fraction series calculations will be discussed. The n/144 table will be easy, 2/144 = 1/72, 3/144 = (2 + 1)/144 = 1/72 + 1/144 and so forth. The n/p cases will show that divisible denominators were created by LCM m as Ahmes created his 2/n table.
On the square root level, the square root of 144 = 12; the square root of 145 began with (12 + 1/25)^2 with a rational error EI = 21/625; increased 1/24 by 1/625 to 1/24 such that (12 + 1/24)^2 found an irrational error E2 = (1/24)^2, following the method used to solve the square root of 164. About a half dozen of these example betweem 144 and 169 will be shown.