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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.
by simplicio 3y ago
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.
- bee_rider 3y agoI 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.
- simplicio 3y agoA, 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.
- Someone 3y ago> 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”)