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Topic:
Egyptian algebra, RMP 21 thru RMP 34
Replies:
10
Last Post:
May 14, 2011 12:00 PM




Re: Egyptian algebra, RMP 21 thru RMP 34
Posted:
Apr 30, 2011 11:23 AM


Ahmes solved the RMP 32 algebraic statement:
1 + x/3 + x/4 = 2
by LCM 144 and solved
144x + 144x/3 + 144x/4 = 288
144x + 48x + 36x = 288
228x = 288
x = 288/228
x = 1 + 60/228 = 1 + (57 + 3)/228 = 1 + 1/4 + 1/76
Ahmes wrote out duplication calculations of 48x and 36x and proofs on a lower arithmetic level.
Ahmes can be fairly translated as
x = 1 + 5/19(4/4) = 1 + 20/76 = 1 + (19 + 1)/76 = 1 + 1/4 + 1/76
as the actual unit fraction answer.
footnote: Clagett's 1999 review of the arithmetic and algebraic facts and proof omitted discussions of numerators 288 and 60 and the final answer. Clagett did mention the correct denominator 228.



