In math world, I'm scooting around the edges of what there is to know about the above chart, from Synergetics 453.01. Where did Bucky get those numbers? How did he compute them in other words, way back when?
David Koski was wondering if he was using primes in some way, to work with minimum integers, e.g. the arcsin or arctan of what n/d ratio would agree with the above to the digits computed? In every case, he found a match.
More background:
Great Circles of the VE on Synergeo