What mathematics were age-of-sail naval officers expected to know?

by thecatfoot

The Aubrey-Maturin and Hornblower series feature many mentions of spherical trigonometry, as well as captains' understandings of how to calculate the physical forces at work on their ships.

Was there a standard navigational math/physics curriculum put forth by various countries' navies? Or was it more of a de facto curriculum based on pretty universal needs at sea? Either way, what was the required knowledge?

jschooltiger