Le Cam, L. The central limit theorem around 1935. Т. 1. 1986. DOI:10.1214/ss/1177013818. с. 78 – 96 [p. 81]. The result, obtained using a formula originally proved by de Moivre but now called Stirling's formula, occurs in his `Doctrine of Chances' of 1733.}
Pearson, Karl. Historical note on the origin of the normal curve of errors. Т. 16. 1924. DOI:10.2307/2331714. с. 402 – 404 [p. 403]. I consider that the fact that Stirling showed that De Moivre's arithmetical constant was √2π does not entitle him to claim the theorem, [...]