The construction of the wonderful canon of logarithms

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Trigonometrical Propositions. 65
4. Given the side h. T>, & the angles T> & V>, to find the
side B D.
D ;
Multiply radius by the sine of the complement of
divide by the tangent of the complement of
A D, and you will obtain the tangent of the arc
C D :
then multiply the sine of C D by the tangent
of D ; divide the product by the tangent of B, and
the sine of B C will result :
C D, and you have B D.
add or subtract B C and
5. Given the side A D, df the angles D cSf B, /c find the
angle A.
Multiply radius by the sine
of the complement of
divide by the tangent of' the complement of
A D ;
D, and the tangent of the complement of C A D
will be produced ; whence we have CAD itself.
Similarly multiply the sine of the complement of B
by the sine of C A D ;
divide by the sine of the
complement of D, and the sine of B A C will be
produced ;
which being added to or subtracted from
CAD, you will obtain the required angle BAD.
6. Given KTi, & the angle D with the side B D, to find
the angle B.
Multiply radius by the sine of the complement of
divide by the tangent of the complement of
D ;
A D, and the tangent of C D will be produced ;
arc C D subtract from, or add to, the side B D, and
you have B C : then multiply the sine of C D by
the tangent of D ; divide the product by the sine of
B C, and you have the tangent of the angle B.
7. Given A D, cSj' the angle D with the side B D, to find
the side A B.
Multiply radius by the sine of the complement of
D ;
divide the product by the tangent of the com-
be
I
produced
plement of A D, and the tangent of C D will
its