The construction of the wonderful canon of logarithms

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66 Trigonometrical Propositions.
produced ; its arc C D subtract from, or add to, the
given side B D, and you have B C. Then multiply
the sine of the complement of A D by the sine of
the complement of B C ; divide the product by the
sine of the complement of C D, and the sine of the
complement of A B will be produced; hence you
have A B itself.
Given A D, & the angle D with the side B D, to
find the angle A.
This follows from the above, but the problem
would require the " Rule of Three " to be applied
thrice. Therefore substitute A for B and B for A,
and the problem will be as follows :
Given B D c2f D, with the side A D, to find the
angle B.
This is exactly the same as the sixth problem, and
is solved by the " Rule of Three " being applied
twice only.
8. Given A D, cSr" the angle D with the side A B, to find
tlie angle B.
Multiply the sine of A D by the sine of D ; divide
the product by the sine of A B, and the sine of the
angle B will be produced.
9. Given K Vi, & the angle D with the side A B, to find
the side B D.
Multiply radius by the sine of the complement of
D, divide the product by the tangent of the complement
of A D, and the tangent of the arc C D will be
produced. Then multiply the sine of the complement
of C D by the sine of the complement of A B,
divide the product by the sine of the complement of
A D, and you have the sine of the complement of
B C. Whence the sum or the difference of the arcs
B C and C D will be the required side B D.
10. Given