Graduation and scale in astronomical instruments

The pursuit on subdivision precision 

Length:

Diagonal scale (Gunter rule)

Widely used on cartography and maps

Vernier scale

Angles:

Cross staff

Astrolabe

Tycho Brahe's armillary sphere and quadrant 

Idea from Levi ben Gerson

10” accuracy 

Nonius scale

Mariner's quadrant

original nonius scale

I guess in practice, the observer just read off the angle as  900/87 degrees, and later on convert it to DMS.

元史四海測驗

由晷影轉換成角度.北宋 sub degree 用 

半 = 1/2

小 = 1/3

強 = 2/3

半小= 1/6？

半強=5/6？

太強=？

太= 3/4=6/8？

太弱=5/8？

渾天儀: 0.1古度, linear

沒有用“magnification of scale"

Cf: 郭守敬把數據精確到1/20度（how?)，晷影轉換到角， 時的角度單位？averaging?

永樂大典(失傳？），分度矩（估計是舶來品）：WeChat 

Reference:

Curiosite geometrique internet archive

元史

四海

元史天文志疏漏

163 

Astronomiae Instauratae mechanica Tycho Brahe

Pansci 

Chapman , YouTube 

Dividing circle by Henry Hindley 

Wiki