only 3 thousand; but we do not say that C, who has 107 thousand pounds, is much richer than D, who has 100 thousand, though the difference of fortune is the same in both cases, viz. 7 thousand pounds. In comparing numbers we take into our reckoning not only the differences, but the numbers themselves. Thus, if B and D both received 7 thousand pounds, B would receive 233 pounds and a third for every 100 pounds which he had before, while D for every 100 pounds would receive only 7 pounds. And though, in the view taken in (170), 3 is as near to 10 as 100 is to 107, yet, in the light in which we now regard them, 3 is not so near to 10 as 100 is to 107, for 3 differs from 10 by more than twice itself, while 100 does not differ from 107 by so much as one-fifth of itself. This is expressed in mathematical language by saying, that the ratio or proportion of 10 to 3 is greater than the ratio or proportion of 107 to 100. We proceed to define these terms more
- When we use the term part of a number or fraction in the remainder of this section, we mean, one of the various sets of equal parts into which it may be divided, either the half, the third, the fourth, &c.: the term multiple has been already explained (102). By the term multiple-part of a number we mean, the abbreviation of the words multiple of a part. Thus, 1, 2, 3, 4, and 6, are parts of 12; ½ is also a part of 12, being contained in it 24 times; 12, 24, 36, &c., are multiples of 12; and 8, 9, ⁵/₂, &c. are multiple parts of 12, being multiples of some of its parts. And when multiple parts generally are spoken of, the parts themselves are supposed to be included, on the same principle that 12 is counted among the multiples of 12, the multiplier being 1. The multiples themselves are also included in this term; for 24 is also 48 halves, and is therefore among the multiple parts