Constructing a fourth point D on line AB from 3 collinear points A, B, C using a ruler only.

Start with 3 points like this.

Randomly pick a point O and also a point A' on OA and draw these lines. B' is the intersection.

Now intersect lines AB' and BA' to get point P.  Finally, intersect line OP with line AB to get point D, which is our goal.