I am doing some research on the egyptian mathematics. The so called Moscow papyrus, from 1850 bc, the famous problem 14 shows how to calculate the volume of a frustum. The most authoritive translation i have been able to find on the internet so far, describes it like this:
"If you are told: a truncated pyramid of 6 for the vertical height by 4 on the base by 2 on the top: You are to square the 4; result 16. You are to double 4; result 8. You are to square this 2; result 4. You are to add the 16 and the 8 and the 4; result 28. You are to take 1/3 of 6; result 2. You are to take 28 twice; result 56. See, it is of 56. You will find (it) right"
All sources i have found derives this formula from the text:
V = h/3 (a^2 + a*b +b^2)
which is, to everyones amazement, the correct formula.
I am on track with the "h/3", the "a^2" and the "b^2", but if the translation above is correct, the "a*b" is not correct, but should rather be "2*b" according to the text which says ".. you are to double 4" not "multiply 2 and 4".
Could it be that it has been mistaken since a=2 in the example? Or is the translation above flawed?
Thanks for any comments and help