result is 82⁄31⁄101⁄2190 This makes for a day 1⁄64 hekat 32⁄31⁄101⁄2910 ro.
Do it thus:
| 1 | 365 | |
| 2 | 730 | |
| 4 | 1460 | |
| 8 | 2920 | |
| 2⁄3 | 2432⁄3 | |
| 1⁄10 | 361⁄2 | |
| 1⁄2190 | 1⁄6 | |
| Total | 82⁄31⁄101⁄2190. |
Do the same thing in any example like this.
Here, as in Problem 61, our author generalizes, suggesting that the method can be applied in any case like this.
Problem 67
Example of reckoning the cattle of a herd. How many cattle are there in a herd when 2⁄3, of 1⁄3 of them make 70, the number due as tribute to the owner?
The herdsman came to the stock-taking with 70 cattle. The accountant said to the herdsman, Very few tribute-cattle art thou bringing; pray where are all thy tribute-cattle? The herdsman replied to him, What I have brought is 2⁄3 of 1⁄3 of the cattle that thou hast committed to me. Count and thou wilt find that I have brought the full number.
Do it thus:
| 1 | 1 | |
| 2⁄3 | 2⁄3 | |
| 1⁄3 | 1⁄3 | |
| 2⁄3 of 1⁄3 | 1⁄61⁄18 |
Get 1 by operating on 1⁄61⁄18.
| 1 | 1⁄61⁄18 | |
| 2 | 1⁄31⁄9 | |
| \ | 4 | 2⁄31⁄61⁄18 |
| \ | 1⁄2 | 1⁄9 |
| Total | 41⁄2. |
Multiply 70 by 41⁄2 it makes 315. These are those committed to him.
