For a variety of technical and social reasons the rapier became shorter and lighter during the late 17th century, relying more and more on the thrust over the cut. Eventually, edges were abandoned alltogether and the smallsword was born, initially in France it seems, but spreading across Europe reasonably quickly (the Italians seem to have kept up the use of older weapons for a long time though). The abandonment of the edge meant that strength of the blade could be increased by the adoption of a stiff triangular blade.
These were as much male jewellery as defensive weapon and typically had elaborately chased and engraved guards. Their social importance can be intimated by alternative names such as "court sword".