NavList:

There seem to have been several "aha" moments in the growing understanding of spherical geometry.  For instance, there was an "aha" regarding the Sumner line in the first half of the 19th century, and the St. Hilaire method in the second half.

At what point did people realize that the observed height of a celestial object equated, at the rate of 60 nm per degree, to the distance to the geographic point?

I read Lecky's "Wrinkles..." and it seems that in the late 1800s, there were still sailors who were skeptical about great circle routes being the shortest distance between two points.  Lecky had a section where he seemed to be engaging in a sort of "great-circle evangelism".

Given that you can do a great circle calculation with Pub. 229 from where you are to any point on earth, treating your destination's latitude and longitude as though it were the "geographic point" of some celestial object, it would seem that there was some sort of leap that people needed to make in equating Hc with "miles remaining for us to sail in this trip".

Was there in fact an "aha" moment here?  Or was this obvious to people as soon as they worked out the basic mechanics of celestial navigation?

I find that in talking to novice navigators today, the relation between height-of-celestial-object and distance-to-GP-in-nautical-miles seems to come as a bit of an eyebrow-raiser...it seems to produce an "aha" moment when it is first introduced to them. 

And though I can't remember exactly what I was thinking 35 years ago when I first got a sextant, I think that I also had a bit of an aha moment...with a sense that I would not have figured this out on my own if somebody else had not told me.

Bob