| Processes. | ||
| Ex. 6. | Ex. 7. | |
Though the multiplication-table was in use by the Arabians and Italians at an early date, no notice was taken of it during the middle ages in the rest of Europe. It may give us more charity for the boys and girls who are now wrestling with it—although nowadays it does not seem to require the struggle that it used to—to know that grown men, and wise men probably, sought for devices by which the labor might be avoided which we go through in childhood. Outside of Italy, many writers considered it necessary to relieve the memory from retaining the products of digits above five. The principal rule—known as the "sluggard's rule"—given for this purpose during the last half of the sixteenth century, the half century after the time of Luther, Melanchthon, and Erasmus, was this: Subtract each digit from ten, and write down the differences; multiply the differences together and add as many tens to their product as the first digit exceeds the second difference, or the second digit the first difference.
| Examples. | 7 8 (3 2) | (7 2 5) tens | 56. |
| 6 9 (4 1) | 5 tens | 54. |
The method which we call short division was largely used in the middle ages, as was also the method of dividing by using the factors of the divisor. The process by long division was known, but was not so commonly used as others. It was called the process "by giving," since after subtraction we give or add (bring down) one or more figures to the remainder. Here is an example set down after the fashion of those times:
Example 8. Divide 97335376 by 9876.
| Divisior. | Proveniens. |
