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CHAPTER I—EGYPTIAN ARITHMETIC
[38
Problem 38
I have gone three times into the hekat-measure, my 1⁄7 has been added to me, and I return having filled the hekat-measure. What is it that says this?
Assume 1. Multiplying by the given expression we have
\ | 1 | 1 |
\ | 2 | 2 |
\ | 1⁄7 | 1⁄7 |
Total | 31⁄7 |
Get 1 by operating on 31⁄7.
1 | 31⁄7 | |
1⁄22 | 1⁄7 |
for 1⁄7 of 22 is 31⁄7,
1⁄1⁄41⁄28 | ||
1⁄61⁄66 | 1⁄21⁄14 | |
Total | 1. |
Therefore the answer is 1⁄61⁄111⁄221⁄66.
Proof.
1 | 1⁄61⁄111⁄221⁄66 | |
2 | 1⁄21⁄111⁄331⁄66 | |
1⁄7 | 1⁄22 |
for 1⁄22 of 7 is the expression that we have obtained.
Total | 1. |
Express the result in ro.
1 | 320 | |
2⁄3 | 2131⁄3 | |
1⁄3 | 1062⁄3 | |
\ | 1⁄6 | 531⁄3 |
\ | 1⁄11 | 291⁄11 |
\ | 1⁄22 | 141⁄21⁄22 |
\ | 1⁄66 | 42⁄31⁄61⁄66 |
Total | 1012⁄31⁄111⁄221⁄66 |
Proof of the result as expressed in ro.
\ | 1 | 1012⁄31⁄111⁄221⁄66 |
\ | 2 | 2031⁄21⁄111⁄331⁄66 |
\ | 1⁄7 | 141⁄21⁄22 |
Total | 320, |
or 1 hekat.
It amounts in grain to 1⁄41⁄16 hekat12⁄31⁄111⁄221⁄66ro.