The construction of the wonderful canon of logarithms

74 Trigonometrical Propositions.
Again, add together the logarithm of the half difference,
the logarithm of the complement of the half
sum, and the logarithm of the tangent of half the base;
subtract the logarithm of the sum and the logarithm
of half radius, and you will have the second found.
Proceed as above with the first and second found,
and you will obtain the sides.
[d]
Another way of the same.
Multiply the secant of the complement of the
sum of the angles at the base by the tangent
of half the base.
Multiply the product by the sine of the greater
angle at the base, and you will have the first found.
Multiply the same product by the sine of the less
angle, and you will have the second found,
Then divide the sum of the first and second found
by the square of radius, and you wiU have the tangent
of half the sum of the sides.
Also subtract the less from the greater and you will
have the tangent of half the difference of the sides.
Whence add the arcs corresponding to these two
tangents, and the greater side will be obtained ; subtract
the less arc from the greater and you have the
less side.
Of the five consecutive parts of a spherical triangle, s^ven
the three intermediate, to find both extremes by one oper^
ation and without the need ofdiscriminating between the
several cases.
(*) '^^ angles at the base, the sine of the half
f^^
^-^ difference is to the sine of the half sum, as the
sine of the difference is to a fourth which is the sum
of the sines.
And