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Euclidean proposition 8 of Book I

I'm reading about the Euclidean Elements. What does this proposition mean?

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With a "modern compass" you can put the two ends down at two points in the plane, pick the compass up without having it fold, and put it down with one point somewhere else, to draw a circle there with the radius you want. That allows you to lay off a segment of given length on a given line.

With Euclid's compass, when you pick it up you lose the angle between the legs. Proposition 2 cleverly shows you that even with that restriction you can lay off a segment determined in one place on a line somewhere else. Once it's been proved you can proceed as if compasses didn't collapse when they left the plane.

(No one told me about this when I studied geometry in high school many years ago. I only discovered it when teaching the history of mathematics, read the start of Euclid, and wondered why we even needed Book I Proposition 2.)

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In modern compasses with distance retained tightly after setting it or geometrical software like Geogebra where you get radial distance exactly what you wanted it is unthinkable that the compass distance can change after you first set it to the circle radius.

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