The construction of the wonderful canon of logarithms

Remarks on Appendix. 59
Therefore take the above power and seek for the root of it
which corresponds to the quotient of the first Logarithm;
thereby you will find the required second sine. Also the
Logarithm of the power itself will be the continued product
of the quotients and the common divisor.
Thus let the given Logarithms be 8 and 14,
and the sine corresponding to the first Logarithm
be 3. A common divisor of the Logarithms is 2 ;
this gives the quotients 4 and 7. If 3 multiply
itself six times, you will have 2187 for the power
which, in a series of continued proportionals from
unity, will occupy the seventh place, and hence it
may, without inconvenience, be called the seventh
power. The same number, 2187, is the fourth
power from unity in another series of continued
proportionals, in which the first power, 6 ]^gg§§§ ^,
is the required second sine. The product of the
quotients 4 and 7 is 28, which, multiplied by the
common divisor 2, makes 56, the Logarithm of
the power 2187.
Continued
Proportionals.
I
3
9
27
81
243
729
2187
o)
I)
^)
(3)
(4)
(5)
(6)
(7)
Logarithms.
O
8
16
24
32
40
48
56
Continued
Proportionals.
I
6 838521
46765372
319 80598
2187
(O)
(X)
(2)
(3)
(4)
Logarithms.
14
28
42
56
// will be observed that these Logarithms differ from
those employed in illustration of the previous Proposition ;
H 2 but