> Good. So If the two lines (the "bisects"?) are > disjoint, then you have either of the following two > cases: > > 1. The intersection point is left behind, neither of > the two bisects has it as a member. Therefore the > original line hasn't been bisected, its been > trisection into two lines plus one lone point. If you > try to put the two lines back together without that > third component, you don't get back the original > line, you get a line with a single point missing... > > 2. The intersection point goes with one of the lines > but not the other. They are not symmetrical, not > equal in every way (though they could be equal in > length,) they are not equal in other properties.
My notion now is that a line is made of smaller lines and these of smaller and so on. If we want to cut a line into smaller lines, I dare say, we literally "break" the original line into smaller lines, but if we want to keep them together we use a point (between any two lines) as "glue" that keeps them together. And this point is dimensionless (having neither length nor width), therefore when we break (divide) a line in smaller ones, and put them together again with the help of points, the whole will be identically equal (i.e. will coincide) with the initial line that we had before the break, for points (being dimensionless) will add no length to the whole. The inference is that when we cut a straight-line in half by means of another straight-line (when they meet), the halves are attached by means of a point that serves as glue, and the whole (the two halves + the point) will coincide with the initial straight-line. And when we want to disjoint them again, the point which attaches them (i.e. "the glue") will either remain on one of the two straight-lines or neither (i.e. we leave the point). When the point remain on either straight-line, it will not change the length of that straight-line (i.e. the line itself), being dimensionless, but will only remain as glue on it, and the straight-line is the same as when without glue (i.e. the point), and therefore will coincide with the other half, and the two together will make the former straight-line again. Now, when we leave the point, the case will be the same as the previous, the two straight-lines will coincide, but as you said, without the point they will not be able to make the former straight-line again (that which has been divided in half), because they need the glue (the point) to be attached again.
Inasmuch as I'm very eager to reach a conclusion, maybe all this story with the glue is nonsense.
> Neighbor says: > >A line has length,which we can notice, but a point > is dimensionless, without both length and width, so > we can't see a point , therefore I'm disposed to use > the term "imagine" for a point. > > You couldn't see an infinitely thin line with your > eyes any more than you could a point. With you mind > you can see both. > > Cheers, > Joe N
You're right, since a line has only length and no width, we couldn't see it, and therefore when we draw a line , we draw it with a little bit of width, but actually we do not consider that width, what we consider is only the length.