A ruler without marks and a compass: with just these two tools, the Greeks constructed midpoints, perpendiculars and parallels with total precision. Who discovered The classical constructions are in The Elements of Euclid (c. 300 BC): the perpendicular bisector and the midpoint (proposition I.10), the angle bisector (I.9), the perpendicular by one point (I.11 and I.12) and the parallel by one point (I.31). The rule of using only a ruler without marks and a compass comes from Euclid’s first three postulates: draw a straight line through two points, extend it and draw a circle with any center and radius.