A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Sean C
Date: 2019 Jan 18, 21:19 -0800
"...can you use [Napier's] Rule 8 to calculate the longitude of the vertex without first using Rule 2 to calculate its latitude, and can you solve Rule 2 without first knowing the starting course? To calculate this, won’t you need an end point and a bit more magic?"
To be honest, I don't have the slightest idea. I'm about the farthest thing from a mathematician that you can find. The formulas I quoted are from a list of formulas I have collected from various sources over the years for my own use. Math was my least favorite subject in school. I understood geometry because, being an amateur artist, I could relate it to actual shapes I could draw. Algebra was a mystery to me and I did very poorly in that class. I didn't even consider taking trigonometry - and calculus was right out. This is a shame because had I known that trig and spherical trig also related directly to shapes, I probably would have enjoyed them as much as I did geometry. And now that I'm older, I wish I had studied math more. Not just for the purposes of celnav, but because I believe math to be the language of the structure of the universe itself. And it's pretty handy for solving a lot of problems. But I barely graduated high school and never went to college.
Oh, well. Like Jackson McDonald I have resolved to learn more about spherical trig. There are quite a few schools near where I live. Perhaps I can pick up a textbook or two - or even sign up for a few classes. I don't know. Until then, you'll have to wait for someone who knows more about math than I do to answer your question. Apologies.