2. If two uneven numbers be added or subtracted, their sum or difference will be an even number.
3. The sum or difference of an even and an uneven number added or subtracted will be an uneven number.
4. The product of two even numbers will be an even number, and the product of two uneven numbers will be an uneven number.
5. The product of an even and uneven number will be an even number.
6. If two different numbers be divisible by any one number, their sum and their difference will also be divisible by that number.
7. If several different numbers, divisible by 3, be added or multiplied together, their sum and their product will also be divisible by 3.
8. If two numbers divisible by 9, be added together, their sum of the figures in the amount will be either 9 or a number divisible by 9.
9. If any number be multiplied by 9, or by any other number divisible by 9, the amount of the figures of the product will be either 9 or a number divisible by 9.
10. In every arithmetical progression, if the first and last term be each multiplied by the number of terms, and the sum of the two products be divided by 2, the quotient will be the sum of the series.
11. In every geometric progression, if any two terms be multiplied together, their product will be equal to that term which answers to the sum of these two indices. Thus, in the series: