The method by the little castle was much practiced at Florence. Why the name was given to it is not very clear.

Example 5. Multiply 9876 by 6789.

The method by the square was regarded as elegant, not requiring the operator to attend to the places of the figures.

Some authors wished to elevate the character of the study, so as to save the labor of carrying tens. Here are two processes, or rather one process under different forms, which save that labor:

Example 6. Multiply 234 by 234.

Example 7. Multiply 5142 by 43.