Further to my previous comments, I have come across an interesting approximate relationship which could have helped Napier in constructing his log tables. This is cos30 equals (cos15)^4. This seems approximately to apply to angles below 30 degrees, and in particular should be helpful in calculating the logarithms of cosines below 30 degrees and of sines of angles above 60 degrees that is sin60 equals (sin75)^4. submitted by Peter L. Griffiths.