Galileo's last pupil, Vincenzo Viviani (1622-1703), collected and made mathematical instruments. He left his collection to the Hospital of Santa Maria Nuova, which in turn donated it to the Florentine Imperial and Royal Museum of Physics and Natural History. From here the collection went on to the University of Florence, and lastly to the Museo Galileo. A collection within a collection, it includes a variety of artifacts that reveal Viviani's particular interest in astronomy: the measurement of time and the structure of the universe according to the different cosmological systems debated in the 17th century.