Problem 45
A rectangular granary into which there have gone 7500 quadruple hekat of grain. What are its dimensions?
Multiply 75 times 20; it makes 1500. Take 1⁄10 of 1500, namely, 150, 1⁄10 of its 1⁄10, 15,2⁄3 of 1⁄10of its 1⁄10, 10. Therefore the dimensions are 10 by 10 by 10.
The working out:
| 1 | 75 | |
| 10 | 750 | |
| 20 | 1500, |
its contents in khar.
| 1 | 1500 | |
| 1⁄10 | 150 | |
| 1⁄10 of 1⁄10 | 15 | |
| 2⁄3 of 1⁄10 of 1⁄10 |
Instead of taking 2⁄3 at the beginning to reduce the contents to cubed cubits, as he would have done if he had exactly reversed the process of the preceding solution, the author takes 2⁄3 of the last quotient to find the third dimension.
Problem 46
A rectangular granary into which there have gone 2500 quadruple hekat of grain. What are its dimensions?
Multiply 25 times 20; it makes 500, its contents in khar. Take 1⁄10 of 500, namely, 50, its 1⁄20, 25, 1⁄10 of 1⁄10, 5, 2⁄3 of 1⁄10 of its {{frac|}, 31⁄3. Therefore the dimensions are 10 by 10 by 31⁄3.
Its working out:
| 1 | 25 | |
| 10 | 250 | |
| 20 | 500 |
its contents in khar.
| 1 | 500 | |
| 1⁄10 | 50 | |
| 1⁄10 of 1⁄10 | 5 | |
| 2⁄3 of 1⁄10 of 1⁄10 | 31⁄3 |
The dimensions of the granary are therefore in cubits 10 by 10 by 31⁄3.
The 1⁄20 that the author takes in this solution is not necessary and is not used.
