These legs are accessories for mining instruments. Each of the three sections is made up of two mobile parts which are free to slide over each other in order to achieve the required length.
The instrument is finished in exquisitely engraved and worked gilded brass, in the same style as the mining instruments belonging to the Medicean collection.
This object was brought from Germany by Prince Mattias de' Medici, together with the other German instruments intended to enrich the Grand Ducal collection. Like the other instruments, they remained the personal property of the Grand Duke, until they passed into the Uffizi Gallery in 1654, when they were placed in the Stanza delle Matematiche and inventoried.
See M. Miniati, Museo di Storia della scienza: Catalago (Florence, 1991), p. 26.