The first vase with the Muse Erato (the companion painting was the Muse Clio), is decorated after Boucher's original painting for Mme de Pompadour. It was engraved by Jean Daullé in 1756. See Pierrette Jean-Richard, L'Oeuvre gravé de François Boucher, dans la Collection Edmond de Rothschild, vol. I, fig. 560 for the engraving from the Rothschild Collection, now in the Louvre.
The two scenes of the putti emblematic of Autumn and Water on the second vase are also after François Boucher, see Pierrette Jean-Richard, op. cit., figs. 905 and 913, respectively, both engraved by Claude Daflos, le Jeune.