In this paper using elementary Galois Theory, we give a detailed explanation of the calculation of the radical expression for which was first discussed by Vandermonde decades before Galois and we point out and correct a minor correction in his work which was also observed by Lagrange.
References
[1]
Vandermonde, A.T. (1771) Mémoire sur la résolution des équations, Histoire de l'Acad. Royale des Sciences (avec les mémoires de Math. & Phys. pour la même année, tirés des registres de cette Acad.), 365-416.
[2]
Tignol, J.-P. (2001) Galois’ Theory of Algebraic Equations. World Scientific, Singapore, 348 p. https://doi.org/10.1142/4628
[3]
Jones, P.S. (1976) Vandermonde, Alexandre-Théophile, Dictionary of Scientific Biography, Vol. 8, Charles Scribner’s Sons, New York, 571-572.
[4]
Neumann, O. (2007) Cyclotomy: From Euler through Vandermonde to Gauss. In: Bradley, R.E. and Sandifer, C.E., Eds., Leonhard Euler: Life, Work and Legacy, Elsevier, Amsterdam, 323-361. https://doi.org/10.1016/S0928-2017(07)80018-1
[5]
Hamburg, R.R. (1976) The Theory of Equations in the 18th Century: The Work of Joseph Lagrange. Archive for the History of Exact Sciences, 16, 17-36.
[6]
Lagrange, J. (1869) Oeuvres. Notes sur la théorie des équations, Note XIV (Où l’on donne la résolution générale des équations à deux termes), Gauthier-Villars, Paris, 354-355.
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which was first discussed by Vandermonde decades before Galois and we point out and correct a minor correction in his work which was also observed by Lagrange.
