> One of the notions of Euclidean Geometry is that a > point has no length. Therefore all four lines [A,C], > [B,C] [A,C) and [B,C) have the same length. The fact > that point C "has no parts" has no bearing whatsoever > on this.
Look, is not a straight-line that which has length without width and is made up of points? But if, as you pointed out, a point has no length, how can points make up a straight-line (i.e. something that has length) if they have no length? Therefore, I cannot help thinking that a point has a length which is the smallest possible, indeed a point cannot be decomposed (I think that this is the meaning of "A point is that of which there is no part")