# Florimond de Beaune

Florimond de Beaune (7 October 1601, Blois – 18 August 1652, Blois) was a French jurist[1] and mathematician, and an early follower of René Descartes.[2] R. Taton calls him "a typical example of the erudite amateurs" active in 17th-century science.[1]

In a 1638 letter to Descartes, de Beaune posed the problem of solving the differential equation

${\displaystyle {\frac {\operatorname {d} y}{\operatorname {d} x}}={\frac {\alpha }{y-x}}}$

now seen as the first example of the inverse tangent method of deducing properties of a curve from its tangents.[3][4]

His Tractatus de limitibus aequationum was reprinted in England in 1807;[5] in it, he finds upper and lower bounds for the solutions to quadratic equations and cubic equations, as simple functions of the coefficients of these equations.[2] His Doctrine de l'angle solide and Inventaire de sa bibliothèque were also reprinted, in Paris in 1975.[1] Another of his writings was Notae breves, the introduction to a 1649 edition of Descartes' La Géométrie.[6]

## References

1. ^ a b c Taton, R. (1977), "Review of Doctrine de l'angle solide", Revue d'histoire des sciences (in French), 30 (1): 82–84.
2. ^ a b Cajori, Florian (1907), "A history of the arithmetical methods of approximation to the roots of numerical equations of one unknown quantity", Science Series, Colorado College Publication, 12: 171–289. The material on de Beaune is on p. 187.
3. ^ Goldstine, Herman Heine (1991), Die Streitschriften, Springer, p. 20, ISBN 9783764323486.
4. ^ Cajori, Florian (1898), A History of Elementary Mathematics, Macmillan, p. 189.
5. ^ Reprinted in Scriptores Logarithmici: Or, A Collection of Several Curious Tracts on the Nature and Construction of Logarithms, Mentioned in Dr. Hutton's Historical Introduction to His New Edition of Sherwin's Mathematical Tables: Together with Some Tracts on the Binomial Theorem and Other Subjects Connected with the Doctrine of Logarithms, Francis Maseres, collected by Charles Hutton and printed by J. Davis, 1807, p. 217ff.
6. ^ Sasaki, C. (2003), Descartes's Mathematical Thought, Boston Studies in the Philosophy of Science, 237, Springer, p. 235, ISBN 9781402017469.