The construction of the wonderful canon of logarithms

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28 Construction of the Canon.
THUS, let
Example.
the greater of the given sines be
9999975.5000000, and the less 9999975-
0000300, the difference of these ,4999700 being
multiplied into radius (cyphers to the eighth place
after the point being first added to both for the
purpose of demonstration, although otherwise
seven are sufficient), if you divide the product by
the greater sine, namely 9999975.5000000, there
will come out for the less limit .49997122, with
eight figures after the point ; again, if you divide
the product by the less sine, namely 9999975.
0000300, there will come out for the greater limit
.49997124; and, as already proved, the difference
of the logarithms of the given sines lies between
these. But since the extension of these fractions
to the eighth figure beyond the point is greater
accuracy than is required, especially as only seven
figures are placed after the point in the sines
therefore, that eighth or last figure of both being
deleted, then the two limits and also the difference
itself of the logarithms will be denoted by the
fraction .4999712 without even the smallest particle
of sensible error.
41. To find the logarithms of sines or natural numbers not
proportionals in the First table, but near or between them;
or at least, tofind limits to them separated by an insensible
difference.
Write down the sine in the First table nearest
to the given sine, whether less or greater. Seek
out the limits of the table sine (by 33), and when
found note them down. Then seek out the limits
of the difference of the logarithms of the given
sine