| √2 | = 1 + ... |
| 1 | 1 1 |
| 1 | 1 1 |
| 1 | 2 2 2 2 2 2 |
| 1 | 2 | 5 | 12 | 29 | 70 | &c. |
| 2 | 5 | 12 | 29 | 70 | 169 |
Here it appears that
| 1 | 29 | does not err by | 1 | ; |
| 70 | 70 × 169 |
| consequently, | 99 | or | 100 - 1 | is, |
| 70 | 70 |
considering the ease of the operation, a fair approximation. In fact, ⁹⁹/₇₀ is 1·4142857 ... the truth being 1·4142135 ...
The following is an additional example:
| √ | 19 | = 4 + ... |
| 4 | 2 3 3 2 4 4 2 | |
| 1 | 3 5 2 5 3 1 3 | |
| 4 | 2 1 3 1 2 8 2 1 3 1 2, &c. |
| 1 | 1 | 4 | 5 | 14 | , &c. |
| 2 | 3 | 11 | 14 | 39 |