NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Gary LaPook
Date: 2021 Mar 15, 01:12 -0700
Number two is the correct understanding.
It is nothing radical since it is the same as the ancient menthod of "latitude sailing." Without a chronometer one could always determain their latitude by noon observation, travel north or south until reaching the latitude of the destination (to windward or the destination) and then sail straight east or west to the destination checking being on course by subsequent noon sights.
After the Sumner line technique was developed then a navigator was no longer limited to the one course line, east-west, but could use any LOP.
See:
https://sites.google.com/site/fredienoonan/topics/landfall-procedure
https://sites.google.com/site/fredienoonan/topics/precomputed-altitude-curves
https://sites.google.com/site/fredienoonan/discussions/navigation-to-howland-island
gl