The construction of the wonderful canon of logarithms

Trigonometrical Propositions, 75
And the sine of the sum is to the sum of the sines
as the tangent of half the base is to the tangent of
half the sum of the sides.
Whence the sine of the half sum is to the sine of
the half difference of the angles as the tangent of
half the base is to the tangent of half the difference
of the sides.
Add the arcs of these known tangents, taking
them from the table of tangents, and you will have
the greater side ; in like manner subtract the less
from the greater and the less side will be obtained.
F .1 N I. S.
K 2 SOME