Page:The Construction of the Wonderful Canon of Logarithms.djvu/34

10 CONSTRUCTION OF THE CANON.

less of the other, and the greater of the one to the greater of the other.

Thus let the line a b c be divided into two parts, ab and bc. Let ab lie between the limits 123.5 the greater and 123.2 the less. Also let bc lie between the limits 43.2 the greater and 43.1 the less. Then the greater being added to the greater and the less to the less, the whole line ac will lie between the limits 166.7 and 166.3.

9.The two limits of one quantity are multiplied into the two limits of another, when the less of the one is multiplied into the less of the other, and the greater of the one into the greater of the other.

Thus let one of the quantities ab lie between the limits 10.502 the greater and 10.500 the less. And let the other ac lie between the limits 3.216 the greater and 3.215 theless, Then 10.502 being multiplied into 3.216 and 10.500 into 3.215, the limits will become 33.774432 and 33.757500, between which the area of a b c d will lie.

10.Subtraction of limits ts performed by taking the greater limit of the less quantity from the less of the greater, and the less limit of the less quantity from the greater of the greater.

Thus, in the first figure, if from the limits of ac, which are 166.7 and 166.3, you subtract the limits of bc, which are 43.2 and 43.1, the limits of ab become 123.6 and 123.1, and not 123.5 and 123.2, For although the addition of the latter to 43.2

and