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The Ancients had an idea that numbers must be sympathetic possessing a hidden natural connection or mystical affinity, because the number 9, which closes the first decade a group of ten; here referring to the return to a zero-ending number like 10 from 0 to 0, has the special property that, no matter what number you multiply it by, it produces a result of two digits which, when added together, produce the number nine again; for example:
| Multiplier | Number | Result | Digits added | ||
|---|---|---|---|---|---|
| 9 | multiplied by | 2 | gives | 18 | (1+8 = 9) |
| 9 | — | 3 | — | 27 | (2+7 = 9) |
| 9 | — | 4 | — | 36 | (3+6 = 9) |
| 9 | — | 5 | — | 45 | (4+5 = 9) |
| 9 | — | 6 | — | 54 | (5+4 = 9) |
| 9 | — | 7 | — | 63 | (6+3 = 9) |
| 9 | — | 8 | — | 72 | (7+2 = 9) |
| 9 | — | 9 | — | 81 | (8+1 = 9) |
Likewise in addition:
| First Number | Added to | Result | ||
|---|---|---|---|---|
| 1 | 8 | — | 9 | |
| 2 | 7 | — | 9 | |
| 3 | 6 | — | 9 | |
| 4 | 5 | — | 9 | |
| 5 | 4 | — | 9 | |
| 6 | 3 | — | 9 | |
| 7 | 2 | — | 9 | |
| 8 | 1 | — | 9 |