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Quadratrix of Hippias
Hippias of Elis, 5th century BC; Dinostratus, 4th century BC
A line falls evenly down a square while a radius turns evenly about one corner; they start together and arrive together, and the quadratrix is where they cross. It is credited to Hippias of Elis, who may have used it to trisect angles, and Dinostratus later used it to square the circle. With a copy of the curve, compass and straightedge can do both, which they cannot do alone.
x = (2a/π) t cot t, y = (2a/π) t
On mathcurve.com as Quadratrice de Dinostrate