81]
FRACTIONS OF A HEKAT
113
Problem 80
Express the "Horus eye" fractions in terms of the hînu. The following vessels are used[1] in measuring grain by the functionaries of the granary:
| 1 | hekat | makes | 10 | hînu |
| 1⁄2 | " | " | 5 | " |
| 1⁄4 | " | " | 21⁄2 | " |
| 1⁄8 | " | " | 11⁄4 | " |
| 1⁄16 | " | " | 1⁄21⁄8 | " |
| 1⁄32 | " | " | 1⁄41⁄16 | " |
| 1⁄64 | " | " | 1⁄81⁄32 | " |
Problem 81
Another reckoning. Expressfraetions of a hekat as "Horus eye" fractions and in term: of the hînu.
Now
| 1⁄2 | hekat | makes | 5 | hînu | |
| 1⁄4 | " | " | 21⁄2 | " | |
| 1⁄8 | " | " | 11⁄4 | " | |
| 1⁄16 | " | " | 1⁄21⁄8 | " | |
| 1⁄32 | " | " | 1⁄41⁄16 | " | |
| 1⁄64 | " | " | 1⁄81⁄32 | " |
a now
| 1⁄21⁄41⁄8 | hekat | 'ro | makes | 81⁄21⁄4 | 'hînu | |||||||
| 1⁄21⁄4 | hekat | 31⁄3 | " | 81⁄21⁄4 | 'hînu | |||||||
| 1⁄21⁄81⁄32 | " | " | 62⁄3 | " | it | is | 2⁄3 | of | a | hekat | ||
| 1⁄21⁄8 | " | " | 61⁄4 | " | " | " | 1⁄21⁄8 | " | " | " | ||
| 1⁄41⁄8 | " | " | 31⁄21⁄4 | " | " | " | 1⁄41⁄8 | " | " | " | ||
| 1⁄41⁄161⁄64 | " | 12⁄3 | " | " | 12⁄3 | " | " | " | 1⁄8 | " | " | " |
| 1⁄4 | " | " | 21⁄2 | " | " | " | 1⁄4 | " | " | " | ||
| 1⁄81⁄16 | " | 31⁄3 | " | " | 12⁄3 | " | " | " | 1⁄6 | " | " | " |
| 1⁄81⁄32 | " | 31⁄3 | " | " | 12⁄3 | " | " | " | 1⁄8 | " | " | " |
b Now
| 1⁄81⁄16 | " | 4 | " | " | 2 | " | " | " | 1⁄5 | " | " | " |
| 1⁄161⁄32 | " | 2 | " | " | 1 | " | " | " | 1⁄10 | " | " | " |
| 1⁄321⁄64 | " | 1 | " | " | 1⁄2 | " | " | " | 1⁄20 | " | " | " |
| 1⁄64 | " | 3 | " | " | 1⁄4 | " | " | " | 1⁄40 | " | " | " |
| 1⁄16 | " | 11⁄3 | " | " | 2⁄3 | " | " | " | 1⁄15 | " | " | " |
- ↑ This interpretation is suggested by Gunn (page 136).
