according to Theological, Arithmetical, Geometrical, and Harmonical Computation. Pleasing to read, profitable to understande, opening themselves to the capacities of both learned and unlearned; being no other than a Key to lead Man to any Doctrinal Knowledge whatsoever."
But, in addition, there was difficulty and complexity in the science as practiced then that made it no boy's play. Even making allowance for the great advantage of "being used to a thing," the middle-age processes in the fundamental rules were often much more intricate than those practiced nowadays. In his incomparable history of the science of arithmetic, in the "Encyclopædia Metropolitana," Dr. Peacocke gives many interesting illustrations, some of which will doubtless strike the reader as novel. Some of their steps are easily explained, but others are by no means so simple. It might prove of interest and advantage to test the higher grades in some modern schools in regard to their actual comprehension of the first four rules by requiring them to explain the philosophy, not the process merely, of a few of these mediæval "sums." Explanations further than a description of the process are purposely omitted.
In subtraction they usually began at the left hand instead of the right. Inconvenient as it is, the method was continued as late as the end of the sixteenth century. The difference was placed above the numbers instead of below.
| Process | ||
| 18769 | remainder. | |
| 54612 | minuend. | |
| 35843 | subtrahend. | |
| 1111 | ||
Process | ||
| 06779 | remainder | |
| 2991 | ||
| 30024 | minuend. | |
| 23245 | subtrahend. | |
Example 1. Subtract 35843 from 54612. When the digits in the subtrahend are greater than those in the minuend, units are placed beneath them as in the example; 3 being increased by the unit the next place to the right, and similarly for 5, 8, and 4.
Example 2. Subtract 23245 from 30024. Of course with such an arrangement it is of no consequence whether the operation proceeds from right to left or from left to right. It will be easily seen how the substituted minuend is obtained, with the exception of the one ten. Suppose the figure 4 in the subtrahend had been 1; then to what device would the boys and girls of the time of Luther and of Queen Elizabeth have had to resort to save their credit?
There is reason for thinking that the modern method of subtraction was the invention of an English mathematician of the first part of the seventeenth century, by the name of Gath.
In multiplication there were some ten or twelve different processes in practical use; but, strange to say, our present mode is not found among them. A few of the subjoined examples are easily intelligible. A little study will make the others plain:
Example 1. Multiply 135 by 12.
