John Napier

“ In finding the base we may pursue another method, namely:—
Add the logarithm of the versed sine of the given angle to the logarithms of the given sides, and the sum will be the logarithm of the difference between the versed sine of the difference of the sides and the versed sine of the base required. This difference being consequently known, add to it the versed sine of the difference of the sides, and the sum will be the versed sine of the base required. ”

“ 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. ”

“ This proposition appears to be identical with the one which ts inserted at the end, and distinguished like the former by (*) . The latter proposition I consider much the superior. There are, however, three operations in it, the first two of which I throw into one, as they ave better combined. ”