Arithmetic

In the Middle Ages, arithmetic was one of the seven liberal arts taught in universities.

If the minuend is larger than the subtrahend, the difference D is positive.
If the minuend is smaller than the subtrahend, the difference D is negative.

The fundamental theorem of arithmetic states that any integer greater than 1 has a unique prime factorization (a representation of a number as the product of prime factors), excluding the order of the factors. For example, 252 only has one prime factorization:

Knowledge of the relationship between the various units of measure, their multiples and their submultiples forms an essential part of compound unit arithmetic.

The addition operation is carried out from right to left; in this case, pence are processed first, then shillings followed by pounds. The numbers below the "answer line" are intermediate results.

The total in the pence column is 25. Since there are 12 pennies in a shilling, 25 is divided by 12 to give 2 with a remainder of 1. The value "1" is then written to the answer row and the value "2" carried forward to the shillings column. This operation is repeated using the values in the shillings column, with the additional step of adding the value that was carried forward from the pennies column. The intermediate total is divided by 20 as there are 20 shillings in a pound. The pound column is then processed, but as pounds are the largest unit that is being considered, no values are carried forward from the pounds column.

For the sake of simplicity, the example chosen did not have farthings.

The book begins with the foundations of mathematics and proceeds to its application in the later chapters.