The construction of the wonderful canon of logarithms

Trigonometrical Propositions. 69
Let the arcs be 38° i' and ^f. Their complements
are 51° 59' and 13°. The half sum of the
complements is 32° 29', the half difference 19° 29',
and the logarithms are 621656 and 1098014 respectively.
Adding these, you have 17 19670, from
which, subtracting 693147, the logarithm of half
radius, there will remain 1026523, the logarithm of
21°, or thereabout. Whence the sine of 21°, namely
358368, is equal to the difference of the sines of the
arcs ']f and 38° i', which sines are 974370 and
6 1
589 1, more or less.
4. Given an arc, to find the Logarithm of its versed sine. [a]
Let the arc be 13°; its half is 6° 30', of which the
logarithm is 2178570. From double this, namely
4357140, subtract 693147, and there will remain
3663993. The arc corresponding to this is 1° 28',
and the number put for the sine is 25595 ; but this
is also the versed sine of 13°.
*^5.*
5. Given two arcs, to find a third whose sine shall be equal to
the sum of the sines of the given arcs.
Let the arcs be 38° i' and 1° 28'; their sum is 39°
29' and their difference 36° 33', also the half sum is
19° 44' and the half difference 18° 16'. Wherefore
add the logarithm of the half sum, viz. 1085655, to
the logarithm of the difference, viz. 5 183 13, and you
have 1603968; from this subtract the logarithm of
the half difference, namely 11 60 177, and there will
remain the logarithm 443791, to which correspond
the arc 39° 56' and sine 641896. But this sine is
equal, or nearly so, to the sum of the sines of 38° i'
and 1° 28', namely 615661 and 25595 respectively.
6. Given an arc & the Logarithm of its sine, to find the arc
whose versed sine shall be equal to the sine of the given
arc,
I 3 Let