Two of Galileo's fingers, removed from his corpse by admirers in the 18th century, have gone on display in a Florence museum now named after the astronomer.

The Museum of the History of Science had shut down for two years for renovations. It reopened on Tuesday, calling itself the Galileo Museum.

Last year, the museum director announced that the thumb and middle finger from Galileo's right hand had turned up at an auction and were recognised as being the fingers of the scientist, who died in 1642. The fingers are now displayed in slender, glass cases. Also on display is his tooth. A third finger was already in the museum.

In 1737, admirers of Galileo Galilei removed the three fingers, plus the tooth and a vertebra, from his body as it was being moved from a storage place to a monumental tomb – opposite that of Michelangelo, in Santa Croce Basilica in Florence.

The vertebra is kept at the University of Padua, where Galileo taught for many years.

The tooth, thumb and middle finger were held in a container passed from generation to generation in the same family, but in the early 20th century all traces of the relics disappeared. The container turned up at auction late last year, and detailed historical documents and the family's own records helped experts to identify them, according to museum officials.

A wooden bust of Galileo tops the container in which the relics had long been kept.

Visitors can also view what the museum says are the only surviving instruments designed and built by Galileo, including two telescopes and a lens he used to discover Jupiter's moons.

The Vatican condemned Galileo for contradicting church teaching, which held at the time that the Earth, not the sun, was the centre of the universe. Two decades ago, Pope John Paul II rehabilitated the astronomer, saying the church had erred.