Use of GUNTER'S Line. 1. To find the product of two numbers. From 1 extend the compasses to the multiplier; and the same extent, applied the same way from the multiplicand, will reach to the product. Thus, if the product of 4 and 8 be required, extend the compasses from 1 to 4, and that extent, laid from 8, the same way, will reach to 32, their product. 2. To divide one number by another. The extent from the divisor to unity will reach from the dividend to the quotient. Thus, to divide 36 by 4, extend the compasses from 4 to 1, and the same extent will reach from 36 to 9, the quotient sought. 3. To three given numbers, to find a fourth proportional. Suppose the numbers 6, 8, 9; extend the compasses from 6 to 8; and this extent, laid from 9 the same way, will reach to 12, the fourth proportional required. 4. To find a mean proportional between any two given numbers. Suppose 8 and 32; extend the compasses from 8, on the left-hand part of the line, to 32 on the right; then bisecting this distance, its half will reach from 8 forward, or from 32 backward, to 16, the mean proportional sought. 5. To extract the square-root of any number. Suppose 25. Bisect the distance between 1 on the scale and the point representing 25; then the half of this distance, set off from 1, will give the point representing the root 5. In the same manner the cube root, or that of any higher power, may be found by dividing the distance on the line between 1 and the given number into as many equal parts as the index of the power expresses; then one of those parts, set from 1, will find the point representing the root required.