Ruler and compass mathematics : possibility and Impossibility

What can be done with straight-edge and compass? We will now address math in the way that the Greeks did: with very few numbers involved. Culturally different from the way we approach math currently, Greek math included no direct concept of measurement. Solutions, instead of measured or calculated, were drawn and physically constructed with the equivalent of pencil and paper and, of course, ruler and compass. We define ruler to be a movable straight-edge. It cannot directly transfer distances, nor directly make parallel or perpendicular lines. We define compass to be a mechanism for drawing a circle of some radius around a fixed point. It also cannot directly transfer distances or angles