The quadratrix of Dinostratus was well known to the ancient Greek geometers, and is mentioned by Proclus, who ascribes the invention of the curve to a contemporary of Socrates, probably Hippias of Elis.
Then the locus of the intersection of PQ and OM is the quadratrix of Dinostratus.
The quadratrix of Tschirnhausen is constructed by dividing the arc and radius of a quadrant in the same number of equal parts as before.
Its properties are similar to those of the quadratrix of Dinostratus.
Thus Nicomedes invented the conchoid; Diodes the cissoid; Dinostratus studied the quadratrix invented by Hippias; all these curves furnished solutions, as is also the case with the trisectrix, a special form of Pascal's limacon.