NOTES ON TRIGONOMETRICAL PROPOSITIONS. 81
whether there be given two angles with the interjacent side or two sides with the contained angle. In each oe the important point is what occupies the third place in the proportion, In the former it is the tangent of half the base, in the latter the tangent of the complement of half the vertical angle. In these examples, if the tangent or the sum of the sines be greater than radius, the logarithm is negative and has a dash preceding, for example −8328403.
Another way of the same ]
[d]Then divide the sum of the first and second found by the square of radius, and you will have )
To make the sense clearer, I should prefer to write this as follows:—
Then divide both the first and second found by the square of radius, add the quotients, and you will have the tangent, &c.
This proposition ts absolutely true, as well as the one
preceding; but while the former may most conveniently be
solved by logarithms, the latter will not admit of the use
of logarithms throughout, as the quotients must be added
and subtracted to find the tangents; for the utility of
Logarithms ts seen in proportionals, and there-
fore in multiplication and division,
and not in addition or
subtraction.
THE END.
