Something very important missing from the video.
FIRST, the two sides being inspected MUST be parallel with each other.
The preferred way to use this method is to first generate perfectly parallel top and bottom.
Then select a right angle side.
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When I originally linked to the video, the purpose was more so show the basic concept or using the gauge to check the squareness of one angle (two adjacent surfaces) relative to a "precision" reference.
Gotcha. I missed that comparison to an already known 'square'.
Following the steps I gave can give a perfect cube, though one can stop at any point after getting the third side square.
I was assuming, as the video did, that surface grinding would be employed.
When comparing to a known 'square', one must assume that that known square is indeed truly square.
Following the procedures that I outlined, one does not need a perfect square for reference but generates that perfection on its own.
Kind of like, "where did the first square come from?"
Incidentally, a shop-made cylindrical square can be utilized as a master if that method is preferred.
First create a straight cylinder with no taper. Say about 2.00 dia by 6.0 long.
Face the end as true as possible with a flat or slightly concave end so the cylinder will sit on its end without any wobble.
Then set up your squareness gage and indicate various places around the cylinder, noting the extremes of the TIR.
Halfway between these extremes will be points that are 'square'.
All this is encouragement to have a good handle on how to generate perfect squareness with no known master reference.
Otherwise, your squareness is only as good as the master.
I think I saw another post by you asking how angle plates were made.
Now you have the answer.