>I think according to Lou and Wayne, "segments" did not exist in Euclid's time. At least, not our version of them.
Of course they did, and of course they are not precisely the same (as "our" version,) because that level of precision didn't exist back then.
I'm still curious as to whether "Neighbor" is being totally straight (ahem..) with us.
When he says: "but I want you to explain me the nature of a straight-line in Euclid's geometry, not putting numbers on the straight-line, and not saying that what for numbers is true is also true for straight-lines. Just now I want to deal only with straight-lines and points on them, as Euclid does in the Elements, without putting numbers on them."
I think he has some axe to grind with Euclid or something, and is explicitly not interested in modern understandings.