The construction of the wonderful canon of logarithms

6o
Remarks on Appendix.
but they agree in this, that in both, the Logarithm of unity
is o ; and consequently the Logarithms of the same numbers
are either equal or at least proportional to each other.
[B] If a first sine divide a third, )
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 num,ber 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.
i first sine be 2
Thus let the i !^"°r^ " "
\ third „ J
„ 16
(fourth „ „ 64
The first, 2. divides the third, 16. four times; and the
quotients are 8, 4, 2, i. The second, 4. divides the same
third, 1 6. two times ; and the quotients are 4, i . Therefore
A will be 4, and B will be 2.
In the same m,anner the first, 2, divides the fourth, 64.
six times ; and the quotients are 32, 16, 8, 4, 2, i. The
second, 4. divides thefourth, 64. three times ;
and the quotients
are 16, 4, i. 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 is 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
the