My research paper is on John Napier and the invention of logarithms. I know that his motivation for inventing logs was to simplify some of the trigonometric calculations being done in astronomy, but while everyone says that, I can find no example of such a problem. What kinds of problems were astronomers solving? What calculations were they doing circa 1595? And how the hell did they even do trigonometry the way they did, where the "sine" of a 60 degree angle on a circle of radius=100 is entirely different from the "sine" of a 60 degree angle on a circle of radius=1000?
It seems silly to try to write a paper on a topic and not be able to have a single example problem, but that is the quandary in which I find myself.