Nearly three dozen Italians, including the Oscar-nominated director Franco Zeffirelli, have received word they may be descendants of Leonardo da Vinci – a claim met with surprise and joy.

“How does it feel to be descended from Leonardo da Vinci? Obviously I’m surprised, but happy, happy also for my grandmother who is no more, who was proud to have the name Vinci,” Elena Calosi, an architect from Empoli told La Repubblica. “Who has not studied Leonardo or seen his paintings?”

The findings were unveiled in Florence this week by Alessandro Vezzosi and Agnese Sabato, historians who claim to have reconstructed the genealogy of Leonardo – perhaps the most famous Renaissance painter, inventor and mathematician – and the lives and burial spots of some of his direct descendants.

The researchers said they had based their work on a study of documents in Italy, France and Spain, including estate papers, and did not have access to DNA evidence, because the body of the master who painted the Mona Lisa was lost in the 16th century.

Among the alleged descendants was Giovanni Calosi, who told La Stampa that his mother used to talk of having documents and letters that were written backwards and could only be read in a mirror, recalling Leonardo’s use of mirrored script.

Leonardo da Vinci’s remains were lost in the 16th century. Photograph: Bettmann/Corbis

“We never gave any importance to those documents, which were lost and sold. What we thought was a legend passed down through generations turns out to be the truth,” said Calosi.

The researchers said they would next try to trace Leonardo’s DNA through the descendants they believed they had identified.

The revelation may not have come out of the blue for Zeffirelli, who directed films of Romeo and Juliet and The Taming of the Shrew, which starred Elizabeth Taylor and Richard Burton. Zeffirelli is the son of Ottorino Corsi, who was born and raised in Vinci in Tuscany, before moving to Florence.

In 2007, when he accepted the Leonardo award from the then Italian president, Giorgio Napolitano, Zeffirelli is said to have quipped: “The Corsis, who are my family, were also descendants of Leonardo.” It was thought at the time to be a joke.