〈NUMBER IN EACH PILE.〉
It will be observed at p. 49 that in order to find {56} independently any number of the Table of the price of butchers’ meat, the following rule was observed:—
Take the number whose tabular number is required.
Multiply it by the first difference.
This product is equal to the required tabular number.
Again, at p. 53, the rule for finding any triangular number was:—
| Take the number of the group | 5 |
|---|---|
| Add 1 to this number, it becomes | 6 |
| Multiply these numbers together | 2)30 |
| Divide the product by 2 | 15 |
This is the number of marbles in the 5th group.
Now let us make a bold conjecture respecting the Table of cannon balls, and try this rule:—
| Take the number whose
tabular number is required, say | 5 |
|---|---|
| Add 1 to that number | 6 |
| Add 1 more to that number | 7 |
| Multiply all three numbers together | 2)210 |
| Divide by 2 | 105 |