The construction of the wonderful canon of logarithms

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Trigonometrical Propositions. 67
CAD will be produced, giving us C A D.
10. Given A D, cS^ the angle D with the side A B, to find
the angle A.
Multiply radius by the sine of the complement of
A D, divide the product by the tangent of the complement
of D, and the tangent of the complement of
Again,
multiply the tangent of A D by the sine of the complement
of C A D, divide the product by the tangent
of A B, and the sine of the complement of
B A C will be produced, giving B A C. Then the
sum or difference of the arcs B A C and CAD
will be the required angle BAD.
1 1. Given KY), & the angle D with the angle A, to find the
side A B.
Multiply radius by the sine of the complement of
A D, divide the product by the tangent of the complement
of D, and you have the tangent of the complement
of C A D CAD ; being thus known, the
difference or sum of the same and the whole angle
A is the angle B A C. Multiply the tangent of
A D by the sine of the complement of C A D
divide the product by the sine of the complement of
B A C, and you will have the tangent of A B.
1 2. Given A D, dr" the angle D with the angle A, to find the
third angle B.
Multiply radius by the sine of the complement of
A D, divide the product by the tangent of the complement
of D, and the sine of the complement of B
will be produced, from which we have the angle
required.
Given A D, & the angle D with the angle A,
to find the side B D.
This follows from the above, but in this form the
problem would require the " Rule of Three" to be
I 2 three