The construction of the wonderful canon of logarithms

58 Remarks on Appendix.
As the quotients of the given Logarithms are
3 and 7, their product is 2 1 , which, multiplied by
84509804 the common divisor, makes 17.74705884
the Logarithm of the number produced.
It should be observed that the cube ofthe second number,
and its equal the seventh power of the first (which some
call secundus solidus), contain eighteen figures, wherefore
its Logarithm has 17. in front, besides the figures following.
The latter represent the Logarithm of the number
denoted by the same digits, but of which 5, the first digit to
the left, is alone integral, the remaining digits expressing
a fraction added to the integer, thus 5 ioooooooooo
'^^•
has for its Logarithm 74705884. Again, iffour places
remain integral, 3. must be placed in front of the Logarithm,
thus ^^^^ \%%%%%%% &c. has for its Logarithm
3.74705884.
Hencefrom two given Logarithms and the
sine of the first we shall be able tofind
the sine of the second.
Take some common divisor of the Logarithms, {the
larger the better') ; divide each by it. Then let the first
sine multiply itself and its products continuously until the
number of these products is exceeded, by unity only, by the
quotient of the second Logarithm ; or until the power is
produced of like name with the quotient of the second Logarithm.
The same number would beproduced if the second
sine, which is sought, were to multiply itself until it became
the power of like name with the quotient of the first
Logarithm, as is evident from the preceding proposition.
Therefore