The construction of the wonderful canon of logarithms

72 Trigonometrical Propositions.
14449; their half difference is 8° 59', and its logarithm
1856956. Add these logarithms and you have
1 87 1 405; subtract 693 1 47 and there remains 11 78258.
The arc corresponding to this logarithm is 17° 56',
which arc we call the third found.
From the logarithm of the third found, subtract
the logarithms of the given sides, namely 581260
and 312858, and there remains 283533; halve this
and you have 141 766 for the logarithm of the half
vertical angle 60° 12' 24-^'''. The whole vertical
angle sought is therefore 120° 24' 49".
Another rule forfinding the base by prosthaphceresis.—
N'
\Given the sides and vertical angle, to find the base.\
Ote the half difference between the versed sines
of the sum and difference of the sides, and also
the half-versed sine of the vertical angle. Look
among the common sines for the values noted, and
find the arcs corresponding to them in the table.
Then write for the second found the half difference
of the versed sines of the sum and difference of these
arcs.
Also, as before, take for the first found the halfversed
sine of the difference of the sides.
Add the first and second found, and you will
obtain the half-versed sine of the base sought for.
Conversely— \given the sides and the base, to find the vertical angle.']
The first found will
be, as before, the half-versed
sine of the difference of the sides.
From the half-versed sine of the base subtract the
first found and you will have the second found.
Multiply the latter by the square of radius ; divide
by