At the bottom of the original image are the words: "Alexis Claude Clairault—born in 1713. Elected by the Académie des Sciences on September 4, 1729."
If these dates are anything to go by, he entered the Académie des sciences at 16, not 18 as his biographies usually state.
Clairaut was indeed elected to the Académie in September 1729—on the 7th, not the 4th as stated on the image—but the academicians' choice still had to be approved by the king, which did not happen until nearly two years later, on July 11, 1731. And it was indeed his manuscript on skew curves, presented in 1729, that won him election, a decision the king confirmed when the manuscript was published... in 1731.
Clairaut was therefore elected by the Académie at 16, but did not become a full member until he was 18.
One final comment on the spelling of his name: Clairaut himself spelled his surname "Clairaut"; the form "Clairault" never appears in his own hand. That is why the former spelling has been retained.
