Without wishing to sound pedantic, the wings of this stunning jewel are not invisibly set, that is a whole other different technique, what you are looking at here are (pretty spectacularly depicted) 'raised grain' settings.
A hole are pierced into the metal, a bevel is created to seat the gem, and the jeweller then (using just the right one from a huge selection of engraving tools) digs or slide the tool into the surrounding metal to create a "whisper" of metal that is then forced into a rounded ball just over the edge of the gem and the hole locking it securely in place.
The cutting of the hole, the bevelling of the edge and the selection of the engraving tool to create the optimum sized grains is the pure technical skill and one that far surpasses our estimation. In the hands of a Master, the gems seem to float, held together with gossamer, barely held in place but secure enough for a century or more's delight