was done with the first figure; observing to advance the terms of the different columns as many places to the right as the number expressing the order of the column ; that is, advancing the terms of the FIRST COLUMN one place, those of the SECOND COLUMN two places, and so for the succeeding columns.

After completing the requisite number of terms in the different columns, by means of this second figure of the root, then proceed to obtain the third figure of the root in the same way as the second figure was obtained; and in this way the operation can be continued until all the periods are brought down. If there is still a remainder, the process can be extended by forming periods of ciphers.

11(1.2436, nearly, which is a trifle too great.

4. What is the fifth root of 5?

5. What is the seventh root of 2?

CHAPTER X.

ARITHMETICAL PROGRESSION.

81. A SERIES of numbers which succeed each other regularly by a common difference, is said to be in arithmetical progression.

When the terms are constantly increasing, the series is an arithmetical progression ascending.

When the terms are constantly decreasing, the series is an arithmetical progression descending.

Thus, 1, 3, 5, 7, 9, &c., is an ascending arithmetical progression; and 10, 8, 6, 4, 2, is a descending arithmetical progression.

In arithmetical progression, there are five things to be considered:

1. The first term.

2. The last term.

3. The common difference.

4. The number of terms.

5. The sum of all the terms.

These quantities are so related to each other, that any three of them being given, the remaining two can be found.