The construction of the wonderful canon of logarithms

70 Trigonometrical Propositions.
Let the arc be 39° 56', to which corresponds the
logarithm 443791, the sine being unknown. To the
logarithm 443791 add 693147, the logarithm of half
radius, and you have 1 136938. Halve this logarithm
and you have 568469. To this corresponds the arc
34° 30', which being doubled gives 69° for the arc
which was sought. This is the case since the sine
of 39° 56' and the versed sine of 69° are each equal,
or nearly so, to 641800.
[b] Of the spherical triangle A B Ti, given the sides & the
contained angle, to find the base.
LEt
the sides be 34° and 47°, and the contained
angle 1 20° 24' 49". Half the contained angle is
60^12' 24.^4", and its logarithm 141 766. To the double
of the latter, namely 283533, add the logarithms of
the sides, namely 581260 and 312858, and the sum
is II 7765 1. This sum is the logarithm of half the
difference between the versed sine of the base and
the versed sine of the difference of the sides ; it is
also the logarithm of the sine of the arc 17° 56',
which arc we call the "second found," for that which
follows is first found.
Halve the difference of the sides, namely 13°, and
you have 6° 30', the logarithm of which is 2178570,
Double the latter and you have 4357140 for the
logarithm of the half-versed sine of 13°; it is also
the logarithm of the sine of the arc 0° 44', which arc
we call the " first found."
The sum of the two arcs is 1 8° 40', the half sum
9° 20', and their logarithms 1139241 and 1819061
respectively. Also the difference of the two arcs is
17° 12', the half difference 8° 36', and their logarithms
1218382 and 1 9002 2 1 respectively.
Now