It seems like you'd get a lot deeper understanding by doing it that way, and be much more able to adapt the knowledge to the real world, vs only knowing how to solve problems in the exact form they were presented to you. I had so many semesters of undergrad math, did fine, but feel like I took basically nothing from it.
Sorry, author's name was Van Brummelen, not Van Bremmelen.
This is a very entertaining hobby to have. Wishing you a lot of fun.
Next stop, making sundials and reading astrolabe.
I was so surprised to know that Chaucer had such interest in the workings of an Astrolabe. It's not much of a surprise if you think that Astrolabe were the pocket GPS, pocket watch, pocket star chart of those times.