The folium of Descartes is symmetric with respect to the line y = x, being a direct result of the
René Descartes (1596-1650) was the first to examine this curve, in 1638, so that the curve was named after him.
He (incorrectly) believed that the shape was repeated in each quadrant.
The French mathematician Gilles Personne de Roberval (1602 - 1675) gave the curve the name of the fleur de jasmin, also
the result of a incorrect understanding of the shape of the curve.
Isaac Barrow (1630-1677), a student of Roberval, wrote in 1669 the "Lectiones Opticae et Geometricae", in which he applied his theory on tangents on the curve,
which now was named la galande.
In French the curve is sometimes called the noeud de ruban 2).
1) folium = leaf
2) noeud de ruban: knot of ribbons. Is this true, isn't here a confusion with the strophoid?