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Table from the Imperial Essence of Mathematical Sciences
These tables are numerical data. In this translation, Chinese numerals (e.g., 一, 二, 三) have been converted to Arabic numerals (1, 2, 3) for modern readability. The first five digits in the left-hand column represent the "argument" or the number being looked up, while the following digits provide the mantissa (the decimal part) of the logarithm.
| 3 | 0 | 2 | 5 | 0 | 4 | 4 | 8 | 0 | 7 | 3 | 9 | 7 | 3 | 5 | 6 | 3 | 0 | 2 | 0 |
| 3 | 0 | 2 | 5 | 1 | 4 | 4 | 8 | 0 | 7 | 5 | 4 | 0 | 9 | 1 | 7 | 3 | 0 | 2 | 0 |
| 3 | 0 | 2 | 5 | 2 | 4 | 4 | 8 | 0 | 7 | 6 | 8 | 4 | 4 | 7 | 4 | 3 | 0 | 2 | 0 |
| 3 | 0 | 2 | 5 | 3 | 4 | 4 | 8 | 0 | 7 | 8 | 2 | 8 | 0 | 2 | 6 | 3 | 0 | 2 | 0 |
| 3 | 0 | 2 | 5 | 4 | 4 | 4 | 8 | 0 | 7 | 9 | 7 | 1 | 5 | 7 | 3 | 3 | 0 | 2 | 0 |
| 3 | 0 | 2 | 5 | 5 | 4 | 4 | 8 | 0 | 8 | 1 | 1 | 5 | 1 | 1 | 5 | 3 | 0 | 2 | 0 |
| 3 | 0 | 2 | 5 | 6 | 4 | 4 | 8 | 0 | 8 | 2 | 5 | 8 | 6 | 5 | 3 | 3 | 0 | 2 | 0 |
| 3 | 0 | 2 | 5 | 7 | 4 | 4 | 8 | 0 | 8 | 4 | 0 | 2 | 1 | 8 | 5 | 3 | 0 | 2 | 0 |
| 3 | 0 | 2 | 5 | 8 | 4 | 4 | 8 | 0 | 8 | 5 | 4 | 5 | 7 | 1 | 0 | 3 | 0 | 2 | 0 |
| 3 | 0 | 2 | 5 | 9 | 4 | 4 | 8 | 0 | 8 | 6 | 8 | 9 | 2 | 3 | 7 | 3 | 0 | 2 | 0 |
| 3 | 0 | 2 | 6 | 0 | 4 | 4 | 8 | 0 | 8 | 8 | 3 | 2 | 7 | 5 | 5 | 3 | 0 | 2 | 1 |
| 3 | 0 | 2 | 6 | 1 | 4 | 4 | 8 | 0 | 8 | 9 | 7 | 6 | 2 | 6 | 9 | 3 | 0 | 2 | 1 |
| 3 | 0 | 2 | 6 | 2 | 4 | 4 | 8 | 0 | 9 | 1 | 1 | 9 | 7 | 7 | 8 | 3 | 0 | 2 | 1 |
| 3 | 0 | 2 | 6 | 3 | 4 | 4 | 8 | 0 | 9 | 2 | 6 | 3 | 2 | 8 | 3 | 3 | 0 | 2 | 1 |
| 3 | 0 | 2 | 6 | 4 | 4 | 4 | 8 | 0 | 9 | 4 | 0 | 6 | 7 | 8 | 2 | 3 | 0 | 2 | 1 |
| 3 | 0 | 2 | 6 | 5 | 4 | 4 | 8 | 0 | 9 | 5 | 5 | 0 | 2 | 7 | 7 | 3 | 0 | 2 | 1 |
| 3 | 0 | 2 | 6 | 6 | 4 | 4 | 8 | 0 | 9 | 6 | 9 | 3 | 7 | 6 | 8 | 3 | 0 | 2 | 1 |
| 3 | 0 | 2 | 6 | 7 | 4 | 4 | 8 | 0 | 9 | 8 | 3 | 7 | 2 | 5 | 3 | 3 | 0 | 2 | 1 |
| 3 | 0 | 2 | 6 | 8 | 4 | 4 | 8 | 0 | 9 | 9 | 8 | 0 | 7 | 3 | 4 | 3 | 0 | 2 | 1 |
| 3 | 0 | 2 | 6 | 9 | 4 | 4 | 8 | 1 | 0 | 1 | 2 | 4 | 2 | 1 | 0 | 3 | 0 | 2 | 2 |
| 3 | 0 | 2 | 7 | 0 | 4 | 4 | 8 | 1 | 0 | 2 | 6 | 7 | 6 | 8 | 1 | 3 | 0 | 2 | 2 |
| 3 | 0 | 2 | 7 | 1 | 4 | 4 | 8 | 1 | 0 | 4 | 1 | 1 | 1 | 4 | 7 | 3 | 0 | 2 | 2 |
| 3 | 0 | 2 | 7 | 2 | 4 | 4 | 8 | 1 | 0 | 5 | 5 | 4 | 6 | 0 | 9 | 3 | 0 | 2 | 2 |
| 3 | 0 | 2 | 7 | 3 | 4 | 4 | 8 | 1 | 0 | 6 | 9 | 8 | 0 | 6 | 6 | 3 | 0 | 2 | 2 |
| 3 | 0 | 2 | 7 | 4 | 4 | 4 | 8 | 1 | 0 | 8 | 4 | 1 | 5 | 1 | 8 | 3 | 0 | 2 | 2 |
| 3 | 0 | 2 | 7 | 5 | 4 | 4 | 8 | 1 | 0 | 9 | 8 | 4 | 9 | 6 | 6 | 3 | 0 | 2 | 2 |
| 3 | 0 | 2 | 7 | 6 | 4 | 4 | 8 | 1 | 1 | 1 | 2 | 8 | 4 | 0 | 8 | 3 | 0 | 2 | 2 |
| 3 | 0 | 2 | 7 | 7 | 4 | 4 | 8 | 1 | 1 | 2 | 7 | 1 | 8 | 4 | 6 | 3 | 0 | 2 | 2 |
| 3 | 0 | 2 | 7 | 8 | 4 | 4 | 8 | 1 | 1 | 4 | 1 | 5 | 2 | 8 | 0 | 3 | 0 | 2 | 2 |
| 3 | 0 | 2 | 7 | 9 | 4 | 4 | 8 | 1 | 1 | 5 | 5 | 8 | 7 | 0 | 8 | 3 | 0 | 2 | 3 |
| 3 | 0 | 2 | 8 | 0 | 4 | 4 | 8 | 1 | 1 | 7 | 0 | 1 | 3 | 3 | 2 | 3 | 0 | 2 | 3 |
| 3 | 0 | 2 | 8 | 1 | 4 | 4 | 8 | 1 | 1 | 8 | 4 | 5 | 5 | 5 | 1 | 3 | 0 | 2 | 3 |
| 3 | 0 | 2 | 8 | 2 | 4 | 4 | 8 | 1 | 1 | 9 | 8 | 8 | 9 | 6 | 6 | 3 | 0 | 2 | 3 |
| 3 | 0 | 2 | 8 | 3 | 4 | 4 | 8 | 1 | 2 | 1 | 3 | 2 | 3 | 7 | 5 | 3 | 0 | 2 | 3 |
| 3 | 0 | 2 | 8 | 4 | 4 | 4 | 8 | 1 | 2 | 2 | 7 | 5 | 7 | 8 | 0 | 3 | 0 | 2 | 3 |
| 3 | 0 | 2 | 8 | 5 | 4 | 4 | 8 | 1 | 2 | 4 | 1 | 9 | 1 | 8 | 0 | 3 | 0 | 2 | 3 |
| 3 | 0 | 2 | 8 | 6 | 4 | 4 | 8 | 1 | 2 | 5 | 6 | 2 | 5 | 7 | 6 | 3 | 0 | 2 | 3 |
| 3 | 0 | 2 | 8 | 7 | 4 | 4 | 8 | 1 | 2 | 7 | 0 | 5 | 9 | 6 | 6 | 3 | 0 | 2 | 3 |
| 3 | 0 | 2 | 8 | 8 | 4 | 4 | 8 | 1 | 2 | 8 | 4 | 9 | 3 | 5 | 2 | 3 | 0 | 2 | 3 |
| 3 | 0 | 2 | 8 | 9 | 4 | 4 | 8 | 1 | 2 | 9 | 9 | 2 | 7 | 3 | 3 | 3 | 0 | 2 | 4 |
| 3 | 0 | 2 | 9 | 0 | 4 | 4 | 8 | 1 | 3 | 1 | 3 | 6 | 1 | 1 | 0 | 3 | 0 | 2 | 4 |
| 3 | 0 | 2 | 9 | 1 | 4 | 4 | 8 | 1 | 3 | 2 | 7 | 9 | 4 | 4 | 2 | 3 | 0 | 2 | 4 |
| 3 | 0 | 2 | 9 | 2 | 4 | 4 | 8 | 1 | 3 | 4 | 2 | 2 | 8 | 4 | 9 | 3 | 0 | 2 | 4 |
| 3 | 0 | 2 | 9 | 3 | 4 | 4 | 8 | 1 | 3 | 5 | 6 | 6 | 2 | 1 | 1 | 3 | 0 | 2 | 4 |
| 3 | 0 | 2 | 9 | 4 | 4 | 4 | 8 | 1 | 3 | 7 | 0 | 9 | 5 | 8 | 3 | 3 | 0 | 2 | 4 |
| 3 | 0 | 2 | 9 | 5 | 4 | 4 | 8 | 1 | 3 | 8 | 5 | 2 | 9 | 2 | 1 | 3 | 0 | 2 | 4 |
| 3 | 0 | 2 | 9 | 6 | 4 | 4 | 8 | 1 | 3 | 9 | 9 | 6 | 2 | 6 | 9 | 3 | 0 | 2 | 4 |
| 3 | 0 | 2 | 9 | 7 | 4 | 4 | 8 | 1 | 4 | 1 | 3 | 9 | 6 | 1 | 3 | 3 | 0 | 2 | 4 |
| 3 | 0 | 2 | 9 | 8 | 4 | 4 | 8 | 1 | 4 | 2 | 8 | 2 | 9 | 5 | 1 | 3 | 0 | 2 | 4 |
| 3 | 0 | 2 | 9 | 9 | 4 | 4 | 8 | 1 | 4 | 4 | 2 | 6 | 2 | 8 | 5 | 3 | 0 | 2 | 5 |
The second column continues the mathematical data, likely representing "Proportional Parts." These smaller tables allowed the user to find values between the main entries (interpolation), significantly increasing the precision of calculations.
| 1 | 4 | 4 | 8 | 0 | 0 | 2 | 1 | 3 | 2 | 2 | 3 | 3 | 0 | 2 | 0 | 2 | 4 | 4 | 8 |
| 2 | 4 | 4 | 8 | 0 | 0 | 3 | 5 | 10 | 0 | 3 | 2 | 3 | 0 | 2 | 0 | 3 | 4 | 4 | 8 |
| 3 | 4 | 4 | 8 | 0 | 0 | 5 | 0 | 0 | 8 | 2 | 7 | 3 | 0 | 2 | 0 | 4 | 4 | 4 | 8 |
| 4 | 4 | 4 | 8 | 0 | 0 | 6 | 4 | 4 | 6 | 1 | 6 | 3 | 0 | 2 | 0 | 5 | 4 | 4 | 8 |
| 5 | 4 | 4 | 8 | 0 | 0 | 7 | 8 | 8 | 4 | 0 | 1 | 3 | 0 | 2 | 0 | 6 | 4 | 4 | 8 |
| 6 | 4 | 4 | 8 | 0 | 0 | 9 | 3 | 2 | 1 | 8 | 1 | 3 | 0 | 2 | 0 | 7 | 4 | 4 | 8 |
| 7 | 4 | 4 | 8 | 0 | 1 | 0 | 7 | 5 | 9 | 5 | 6 | 3 | 0 | 2 | 0 | 8 | 4 | 4 | 8 |
| 8 | 4 | 4 | 8 | 0 | 1 | 2 | 1 | 9 | 7 | 2 | 6 | 3 | 0 | 2 | 0 | 9 | 4 | 4 | 8 |
| 9 | 4 | 4 | 8 | 0 | 1 | 3 | 6 | 3 | 4 | 9 | 2 | 3 | 0 | 2 | 1 | 0 | 4 | 4 | 8 |
| 0 | 4 | 4 | 8 | 0 | 1 | 5 | 0 | 7 | 2 | 5 | 3 | 3 | 0 | 2 | 1 | 1 | 4 | 4 | 8 |
| 1 | 4 | 4 | 8 | 0 | 1 | 6 | 5 | 1 | 0 | 0 | 9 | 3 | 0 | 2 | 1 | 2 | 4 | 4 | 8 |
| 2 | 4 | 4 | 8 | 0 | 1 | 7 | 9 | 4 | 6 | 6 | 0 | 3 | 0 | 2 | 1 | 3 | 4 | 4 | 8 |
| 3 | 4 | 4 | 8 | 0 | 1 | 9 | 3 | 8 | 5 | 0 | 7 | 3 | 0 | 2 | 1 | 4 | 4 | 4 | 8 |
| 4 | 4 | 4 | 8 | 0 | 2 | 0 | 8 | 2 | 2 | 4 | 9 | 3 | 0 | 2 | 1 | 5 | 4 | 4 | 8 |
| 5 | 4 | 4 | 8 | 0 | 2 | 2 | 2 | 5 | 9 | 8 | 6 | 3 | 0 | 2 | 1 | 6 | 4 | 4 | 8 |
| 6 | 4 | 4 | 8 | 0 | 2 | 3 | 6 | 9 | 7 | 1 | 8 | 3 | 0 | 2 | 1 | 7 | 4 | 4 | 8 |
| 7 | 4 | 4 | 8 | 0 | 2 | 5 | 1 | 3 | 4 | 4 | 6 | 3 | 0 | 2 | 1 | 8 | 4 | 4 | 8 |
| 8 | 4 | 4 | 8 | 0 | 2 | 6 | 5 | 7 | 1 | 6 | 9 | 3 | 0 | 2 | 1 | 9 | 4 | 4 | 8 |
| 9 | 4 | 4 | 8 | 0 | 2 | 8 | 0 | 0 | 8 | 8 | 7 | 3 | 0 | 2 | 2 | 0 | 4 | 4 | 8 |
| 0 | 4 | 4 | 8 | 0 | 2 | 9 | 4 | 4 | 6 | 0 | 0 | 3 | 0 | 2 | 2 | 1 | 4 | 4 | 8 |
| 1 | 4 | 4 | 8 | 0 | 3 | 0 | 8 | 8 | 3 | 0 | 9 | 3 | 0 | 2 | 2 | 2 | 4 | 4 | 8 |
| 2 | 4 | 4 | 8 | 0 | 3 | 2 | 3 | 2 | 0 | 1 | 2 | 3 | 0 | 2 | 2 | 3 | 4 | 4 | 8 |
| 3 | 4 | 4 | 8 | 0 | 3 | 3 | 7 | 5 | 7 | 1 | 1 | 3 | 0 | 2 | 2 | 4 | 4 | 4 | 8 |
| 4 | 4 | 4 | 8 | 0 | 3 | 5 | 1 | 9 | 4 | 0 | 6 | 3 | 0 | 2 | 2 | 5 | 4 | 4 | 8 |
| 5 | 4 | 4 | 8 | 0 | 3 | 6 | 6 | 3 | 0 | 9 | 5 | 3 | 0 | 2 | 2 | 6 | 4 | 4 | 8 |
| 6 | 4 | 4 | 8 | 0 | 3 | 8 | 0 | 6 | 7 | 8 | 0 | 3 | 0 | 2 | 2 | 7 | 4 | 4 | 8 |
| 7 | 4 | 4 | 8 | 0 | 3 | 9 | 5 | 0 | 4 | 6 | 0 | 3 | 0 | 2 | 2 | 8 | 4 | 4 | 8 |
| 8 | 4 | 4 | 8 | 0 | 4 | 0 | 9 | 4 | 1 | 3 | 5 | 3 | 0 | 2 | 2 | 9 | 4 | 4 | 8 |
| 9 | 4 | 4 | 8 | 0 | 4 | 2 | 3 | 7 | 8 | 0 | 6 | 3 | 0 | 2 | 3 | 0 | 4 | 4 | 8 |
| 0 | 4 | 4 | 8 | 0 | 4 | 3 | 8 | 1 | 4 | 7 | 2 | 3 | 0 | 2 | 3 | 1 | 4 | 4 | 8 |
| 1 | 4 | 4 | 8 | 0 | 4 | 5 | 2 | 5 | 1 | 3 | 3 | 3 | 0 | 2 | 3 | 2 | 4 | 4 | 8 |
| 2 | 4 | 4 | 8 | 0 | 4 | 6 | 6 | 8 | 7 | 8 | 9 | 3 | 0 | 2 | 3 | 3 | 4 | 4 | 8 |
| 3 | 4 | 4 | 8 | 0 | 4 | 8 | 1 | 2 | 4 | 4 | 1 | 3 | 0 | 2 | 3 | 4 | 4 | 4 | 8 |
| 4 | 4 | 4 | 8 | 0 | 4 | 9 | 5 | 6 | 0 | 8 | 7 | 3 | 0 | 2 | 3 | 5 | 4 | 4 | 8 |
| 5 | 4 | 4 | 8 | 0 | 5 | 0 | 9 | 9 | 7 | 2 | 9 | 3 | 0 | 2 | 3 | 6 | 4 | 4 | 8 |
| 6 | 4 | 4 | 8 | 0 | 5 | 2 | 4 | 3 | 3 | 6 | 7 | 3 | 0 | 2 | 3 | 7 | 4 | 4 | 8 |
| 7 | 4 | 4 | 8 | 0 | 5 | 3 | 8 | 6 | 9 | 9 | 9 | 3 | 0 | 2 | 3 | 8 | 4 | 4 | 8 |
| 8 | 4 | 4 | 8 | 0 | 5 | 5 | 3 | 0 | 6 | 2 | 7 | 3 | 0 | 2 | 3 | 9 | 4 | 4 | 8 |
| 9 | 4 | 4 | 8 | 0 | 5 | 6 | 7 | 4 | 2 | 5 | 0 | 3 | 0 | 2 | 4 | 0 | 4 | 4 | 8 |
| 0 | 4 | 4 | 8 | 0 | 5 | 8 | 1 | 7 | 8 | 6 | 8 | 3 | 0 | 2 | 4 | 1 | 4 | 4 | 8 |
| 1 | 4 | 4 | 8 | 0 | 5 | 9 | 6 | 1 | 4 | 8 | 2 | 3 | 0 | 2 | 4 | 2 | 4 | 4 | 8 |
| 2 | 4 | 4 | 8 | 0 | 6 | 1 | 0 | 5 | 0 | 9 | 1 | 3 | 0 | 2 | 4 | 3 | 4 | 4 | 8 |
| 3 | 4 | 4 | 8 | 0 | 6 | 2 | 4 | 8 | 6 | 9 | 5 | 3 | 0 | 2 | 4 | 4 | 4 | 4 | 8 |
| 4 | 4 | 4 | 8 | 0 | 6 | 3 | 9 | 2 | 2 | 9 | 9 | 3 | 0 | 2 | 4 | 5 | 4 | 4 | 8 |
| 5 | 4 | 4 | 8 | 0 | 6 | 5 | 3 | 5 | 8 | 8 | 8 | 3 | 0 | 2 | 4 | 6 | 4 | 4 | 8 |
| 6 | 4 | 4 | 8 | 0 | 6 | 6 | 7 | 9 | 4 | 7 | 8 | 3 | 0 | 2 | 4 | 7 | 4 | 4 | 8 |
| 7 | 4 | 4 | 8 | 0 | 6 | 8 | 2 | 3 | 0 | 6 | 3 | 3 | 0 | 2 | 4 | 8 | 4 | 4 | 8 |
| 8 | 4 | 4 | 8 | 0 | 6 | 9 | 6 | 6 | 6 | 4 | 4 | 3 | 0 | 2 | 4 | 9 | 4 | 4 | 8 |
| 9 | 4 | 4 | 8 | 0 | 7 | 1 | 1 | 0 | 2 | 1 | 9 | 3 | 0 | 2 | 5 | 0 | 4 | 4 | 8 |
| 0 | 4 | 4 | 8 | 0 | 7 | 2 | 5 | 3 | 7 | 9 | 0 |
Use ← → arrow keys to navigateSwipe left/right to navigate·Produced by SourceLibrary.org in Amsterdam, 2026