The person having chosen any number from one to fifteen, he is to add twenty-one to that number, and triple the amount. Then,
1st. He is to take half of that triple, and triple that half.
2nd. To take the half of the last triple, and triple that half.
3rd. To take the half of the last triple.
4th. To take the half of the last half.
In this operation there are four distinct cases or stages where the half is to be taken. The three first are denoted by one of the eight following Latin words, each word being composed of three syllables, and the syllables containing the letter i corresponding in numerical order with the cases where the half cannot be taken without a fraction; consequently, in those cases the person who makes the deduction is to add one to the number to be divided. The fourth case shows which of the two numbers corresponding to each word has been chosen. For if the fourth half can be taken without adding one, the number chosen is in the first, or left-hand column; but if not, it is in the second column to the right.
| The words. | The numbers denoted. | |
| Mi-ser-is | 8 | 0 |
| Ob-tin-git | 1 | 9 |
| Ni-mi-um | 2 | 10 |
| No-tar-i | 3 | 11 |
| In-fer-nos | 4 | 12 |
| Or-di-nes | 13 | 5 |
| Ti-mi-di | 6 | 14 |
| Te-ne-ant | 15 | 7 |
Example.—Suppose the number chosen to be nine, to which is to be added one, making ten, and which last, being tripled, gives thirty. Then:
| 1st case. | The half of the triple is | 15 |
| which tripled, makes | 45 | |
| 2nd case. | The half of that triple, 1 being added to make an even number, is | 23 |
| and that tripled, makes | 69 | |
| 3rd case. | The half of the last triple, 1 being added, is | 35 |
| 4th case. | The half of the last half, 1 being again added, is | 18 |