Comment by throwway120385

Maybe something similar to a vernier caliper.

From Wikipedia:

> The first caliper with a secondary scale, which contributed extra precision, was invented in 1631 by the French mathematician Pierre Vernier (1580–1637).[1] Its use was described in detail in English in Navigatio Britannica (1750) by mathematician and historian John Barrow.[2] While calipers are the most typical use of vernier scales today, they were originally developed for angle-measuring instruments such as astronomical quadrants.

https://en.wikipedia.org/wiki/Vernier_scale

So it would have been a contemporaneous technique with that initial angle measurement, and the use of a Vernier scale for angular measurements would have itself been common.