Is it wrong that I want to make a replica and write a user manual for this?

Yes, for folks who are curious about this sort of thing see:

https://wiki.shapeoko.com/index.php/List_of_Tools#Sector

and the book A Treatise of Mathematical Instruments by John Robertson.

The full title is:

A
Treatise
of such
Mathematical Instruments,
as are usually put into a
portable case
Showing some of their uses in
Arithmetic, Architecture, Geometry, Surveying, Trigonometry, Geography, Spherics, Perspective, &c.
with
An Appendix
containing
The Description and Use of the
Gunners Calipers
and
The Description and Precepts for the Delineation of
Ship-Guns and Sea Mortars

My current reading is also topical: The Perfectionists: How Precision Engineers Created the Modern World by Simon Winchester — highly recommended.

and c.f., my first project on my Shapeoko 3:

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