The construction of the wonderful canon of logarithms

Construction of the Canon. 23
way, if you please, continue the logarithms themselves
in an exactly similar progression -with little
and insensible error ; in which case the logarithm
of radius will be o, the logarithm of the first sine
after radius (by 31) will be 1.00000005, of the
second 2.00000010, of the third 3.00000015, and
so of the rest.
34. The difference of the logarithms of radius and a given
sine is the logarithm of the given sine itself
This is evident, for (by 27) the logarithm of
radius is nothing, and when nothing is subtracted
from the logarithm of a given sine, the logarithm
of the given sine necessarily remains entire.
35- The difference of the logarithms of two sines must be
added to the logarithm of the greater that you may have
the logarithm, of the less, and subtracted from, the logarithm
of the less that you may have the logarithm of the
greater.
Necessarily this is so, since the logarithms increase
as the sines decrease, and the less loga-,
rithm is the logarithm of the greater sine, and the
greater logarithm of the less sine. And therefore
it is right to add the difference to the less logarithni,
that you may have the greater logarithm
though, corresponding to the less sine, and on the
other hand to subtract the difference from , the
greater logarithm that you may have the less
logarithm though corresponding to the greater
sine.
36. The logarithms ofsimilarly proportioned sines are equidifferent.
This necessarily follows from the definitions of
a logarithm and of the two motions. For since by
C 4 these