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A comment on The propagation of error in classical geometry constructions (2018). Parent comment

Re:The propagation of error in classical geometry constructi... by simplicio on Wednesday March 06, 2024 @11:08AM (#39617379)
I think the construction is usually phrased: "given a line, to..", so it assumes a pre-existing line segment, rather then that being part of the construction itself.
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Re:The propagation of error in classical geometry constructi... by bee_rider on Wednesday March 06, 2024 @11:18AM (#39617480)
A line is defined by a pair of points, isn’t it? It is literally the line AB, wherever A and B are, they define the line.
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Re:The propagation of error in classical geometry constructi... by simplicio on Wednesday March 06, 2024 @11:44AM (#39617792)
But you start the construction with the line already drawn. Then you have to place the arms of the compass on the points, so you have error on both ends.
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Re:The propagation of error in classical geometry constructi... by bee_rider on Wednesday March 06, 2024 @11:53AM (#39617905)
I must be missing something; I don’t see how you can rigorously define the line without A and B, so I don’t see how it can exist before A and B are marked.

I think it is possible that part of what’s missing in your “given a line to..” is that the description of the line in the .. refers to A and B, or possibility the phrasing is just informal.

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Re:The propagation of error in classical geometry constructi... by simplicio on Wednesday March 06, 2024 @12:20PM (#39618263)
A, B and the line connecting them exist before you start the construction, and the author assumes there's no error there.

Then to start the construction, you have to put one arm of your compass on the point A, and one on the point B. These points exist and are already marked, but you incur error when you place your compass down on each one. These are the represented by the blue and yellow circles in the diagram.

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Re:The propagation of error in classical geometry constructi... by Someone on Wednesday March 06, 2024 @06:01PM (#39622876)
> I don’t see how you can rigorously define the line without A and B

That line segment isn’t defined, it’s postulated (“there somehow is a line segment with endpoints A and B; you needn’t care how it came about”)

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