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Alexandre Eremenko you wrote:
"Sextants are not designed to take the angle between the Sun and a garden fence."

Its perfectly possible to take the angle between a terestial object and a garden fence using either the blank tube or no tube at all. Try it.  It's only when you start to introduce lenses that images start to get wobbly.  I wish I still had a "steam camera" operational to take a photograph.  Using a smart phone needs a minimum of three steady hands.

You also said "When you focus on wires (so that they look as sharp as possible), then you automatically focus on any remote object (Sun, Moon, a star or horizon)."
I wish that was true because then I could anounce that it must be so, because lines coming from the distant object are near parallel.  In fact, with my draw, you can't alter focus on the wires.  They're always in focus.  They're in focus looking through the draw alone or with any position of the draw in the telescope.  I know because there's a tiny flake of black paint where two wires cross, and the picture of the two wires and the flake is always in focus.  Try it, but be careful not to punch yourself in the eye when the last bit of the slide comes away from the telescope with a jump. 

Incidentally, I had a feeling that this approach tied in with King Charles 2nd's attitude to "hard" v "theoretical" science, but every time I tried to Google it, AI? just came up with pages on either Charle's Law or prostate problems.  DaveP