NavList:

Frank, you wrote:  “Aha. So the methods you were investigating were intended for extrapolating great circles! […] Our celestial lines of position are short sections of small circles on the globe. Extrapolating them as great circles would be fine over short distances (apart from being overkill), but technically that's incorrect”.

I may be missing something, but as far as I can tell, the method I mentioned on August 29th (https://NavList.net/m2.aspx/Navigate-Skyline-Caruso-aug-2022-g53183), and that Lars Bergman elucidated so clearly, was developed to find the intersection point of two straight lines in two-dimensional space, determined by points on a zero-volume plane in Euclidean geometry, as stated in the attached file. In our application, these straight lines may be used to approximate short sections of (small) circles of position, as you point out. 

If this is correct, then I fail to see why this method is intended for extrapolating circles in spherical geometry.  But then again, this may not be correct, and I’ll welcome an explanation of why this is so, from you, Lars Bergman, or any other NavList contributor.

Best regards, Rafael