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RMP 53, and its setat and mh^2 units
Posted:
May 16, 2009 9:15 AM
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Dear Forum members:
Removing Ahmes Egyptian fractions, and replacing them with readable Ahmes intermediate rational numbers, the arithmetic, algebraic and geometric statements and operations in RMP 53 are reported by two columns of data.
The first colum has not been fully read in terms of Ahmes hand written diagram (in Chace) and likely by other transliterators. Chace did not report the diagram of a triangle sliced into three sections, annotated by Ahmes. The total of the first (top section) of the triangle, written in red, is 7 1/2 1/4 1/8.
The second column of RMP 53 reports the derivation (proof) of the sum of the area 63/8 setat, by :
9 x (7/4)
which Ahmes places in a formula for an area of a triangle:
1/2 the base times the altitude, such that:
9 x 7/4 x 1/2 = 63/8
written as an Egyptian fraction
7 1/2 1/4 1/8
meaning,
quotient: 7
remainder 7/8 = 1/2 + 1/4 + 1/8
The first column of confusing data provides unclear discussions:
4 1/2 setat
\9
2 1/4
1 1/8
dmd 5 1/2 1/8 setat
followed by another total
1 1/4 1/8 mh^2
with mh^2 being a cubit strip (100 cubit unity is a term that may connects to Ahmes' hekat units terminology).
Chace's comment
" 1/0 of it is : to be taken away; then this: the amount:"
may refer to 1 1/4 1/8 mh^2?
One of several questions: how is column 2's 63/8 sum connected to column 1's confusing sums(s)( please suggest connections to the triangle diagram, its notes, and 5 3/8 setat sum, and 1 3/8 mh^2 sum and/or subtraction?)
In other words, which number was reduced by 1/10 to obtain 1 3/8 mh^2, and so forth?
Best Regards,
Milo Gardner
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