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.

Pappus turns then to a consideration of certain properties of Archimedes's spiral, the **conchoid** of Nicomedes (already mentioned in book i.

The Greek geometers invented other curves; in particular, the **conchoid**, which is the locus of a point such that its distance from a given line, measured along the line drawn through it to a fixed point, is constant; and the cissoid, which is the locus of a point such that its distance from a fixed point is always equal to the intercept (on the line through the fixed point) between a circle passing through the fixed point and the tangent to the circle at the point opposite to the fixed point.