Condottieri and military engineers often invented original measuring instruments for the princes' collections. Among them are refined surveying compasses, such as the one built by Baldassarre Lanci for Cosimo de' Medici (above), or curious dagger-shaped compasses, such as the radio latino invented by the condottiero Latino Orsini (c. 1530-c. 1580) and the "dagger" designed by an unknown captain in the Medicean army. The dagger-shaped compass stands as a symbol of the soldier's new mathematical profile.

The instruments shown here were made especially for the Duke's collection by the engineer Baldassarre Lanci (1510-1571), in the service of Cosimo de' Medici from 1557. They are topographical instruments of military use, sometimes equipped with accessories for perspective drawing (no. 1) or for artillery (no. 2). In the military field, the perspective view of a fortress was used to measure its surface.