60 REMARKS ON APPENDIX.
but they agree in this, that tn both, the Logarithm of unity is 0; and consequently the Logarithms of the same numbers are either equal or at least proportional to each other.
The first must divide the third, and the quotient of the third, and each quotient of a quotient successively as many times as possible, until the last quotient becomes less than the divisor. Then let the number of these divisions be noted, but not the value of any quotient, unless perhaps the least, to which we shall refer presently. In the same manner let the second divide the same third. And so also let the fourth be divided by each.
| Thus let the | first | sine | be | 2 | |
| second | sine” | be” | 4 | ||
| third | sine” | be” | 16 | ||
| fourth | sine” | be” | 64 |
The first, 2. divides the third, 16. four times; and the quotients are 8, 4, 2, 1. The second, 4. divides the same third, 16. two times; and the quotients are 4, 1. Therefore A will be 4, and B will be 2.
In the same manner the first, 2. divides the fourth, 64. six times; and the quotients are 32, 16, 8, 4, 2, 1. The second, 4. divides the fourth, 64. three times; and the quotients are 16, 4, 1. Therefore C will be 6, and D will be 3.
Hence I say that, as A, 4. is to B, 2. so is C, 6. to D, 3. and so ts the Logarithm of the second to the Logarithm of the first.
If in these divisions the last and smallest quotient be everywhere unity, as in these four cases, the numbers of
