Page:On the economy of machinery and manufactures - Babbage - 1846.djvu/231

Rh very extensive use, which has been printed and reprinted very frequently in many countries, and is called a Table of Square Numbers.

Any number in the table, column A, may be obtained, by multiplying the number which expresses the distance of that term from the commencement of the table by itself; thus, 25 is the fifth term from the beginning of the table, and 5 multiplied by itself, or by 5, is equal to 25. Let us now subtract each term of this table from the next succeeding term, and place the results in another column (B), which may be called first-difference column. If we again subtract each term of this first difference from the succeeding term, we find the result is always the number 2, (column C;) and that the same number will always recur in that column, which may be called the second-difference, will appear to any person who