Can any rational number be found using a straight edge only?

Question

This is being reposted by request. Given an infinite straight line on a plane, and 3 points at x = 0, 1, 2, and using only a straight edge, construct any rational location on the line. For example, 355/113 is a famous rational approximation for π, construct the point x = 355/113. For a simpler problem, construct the point x = 1/2.

The rules of "straight edge only" construction are:
1. The straight edge may be infinitely long, but is not and cannot be marked as a ruler
2. No other points with known coordinates are given on the plane
3. No other lines with known slopes (like the y-axis) are given
4. You may arbitrarily chose points or lines with unknown coordinates or slopes

If you begin by drawing arbitrary lines, you will have intersection points, which may be incorporated in further construction. However, "constructed" intersections with rational locations on the x-axis has to be mathematically provable.

The original posting of this question is:
http://answers.yahoo.com/question/index;_ylt=Ai.ZMUsFzF7oOq7UciA_UNbsy6IX?qid=20070315101958AA1bHGR

I'm not asking for actual details of how the point 355/113 would be found, but only that whether or not it's even possible to be constructed.

james k----the Greek method of constructing "all rational numbers" involves the use of the compass

curt monash---that's why I gave the 3 coordinates x = 0, 1, 2, so that all the rational points on the line are relative to those. For example, the rational point 1/2 would be exactly halfway between 0 and 1, while the rational point 3/2 halfway between 1 and 2, etc.

Answer 1

Yes, it is possible to construct any rational number--the Greeks proved this.

Answer 2

It's not possible in the slightest. You've constructed the problem so that there's no metric or form of measurement whatsoever.

For example, if you constructed a number, even a number as simple as 2 -- how would you know??