# NICOLE (Francis)

, a very celebrated French mathematician, was born at Paris December the 23d, 1683. His early attachment to the mathematics induced M. Montmort to take the charge of his education: and he opened out to him the way to the higher geometry. He first became publicly remarkable by detecting the fallacy of a pretended quadrature of the circle. This quadrature a M. Mathulon so assuredly thought he had discovered, that he deposited, in the hands of a public notary at Lyons, the sum of 3000 livres, to be paid to any person who, in the judgment of the Academy of Sciences, should demonstrate the falsity of his solution. M. Nicole, piqued at this challenge, undertook the task, and exposing the paralogism, the Academy's judgment was, that Nicole had plainly proved that the rectilineal figure which Mathulon had given as equal to the circle, was not only unequal to it, but that it was even greater than the polygon of 32 sides circumscribed about the circle.—The prize of 3000 livres, Nicole presented to the public hospital of Lyons.

The Academy named Nicole, Eleve-Mechanician, March 12, 1707; Adjunct in 1716, Associate in 1718, and Pensioner in 1724; which he continued till his death, which happened the 18th of January 1758, at 75 years of age.

His works were all inserted in the different volumes of the Memoirs of the Academy of Sciences; and are as follow:

1. A General Method for determining the Nature of Curves formed by the Rolling of other Curves upon any Given Curve; in the volume for the year 1707.

2. A General Method for Rectifying all Roulets upon Right and Circular Bases; 1708.

3. General Method of determining the Nature of those Curves which cut an Insinity of other Curves given in Position, cutting them always in a Constant Angle; 1715.

4. Solution of a Problem proposed by M. de Lagny; 1716.

5. Treatise of the Calculus of Finite Differences; 1717.

6. Second Part of the Calculus of Finite Differences; 1723.

7. Second Section of ditto; 1723.

8. Addition to the two foregoing papers; 1724.

9. New Proposition in Elementary Geometry; 1725.

10. New Solution of a Problem proposed to the English Mathematicians, by the late M. Leibnitz; 1725.

11. Method of Summing an Infinity of New Series, which are not summable by any other known method; 1727.

12. Treatise of the Lines of the Third Order, or the Curves of the Second Kind; 1729.

13. Examination and Resolution of some Questions relating to Play; 1730.

14. Method of determining the Chances at Play.

15. Observations upon the Conic Sections; 1731.

16. Manner of generating in a Solid Body, all the Lines of the Third Order; 1731.

17. Manner of determining the Nature of Roulets formed upon the Convex Surface of a Sphere; and of determining which are Geometric, and which are Rectifiable; 1732.

18. Solution of a Problem in Geometry; 1732.

19. The Use of Series in resolving many Problems in the Inverse Method of Tangents; 1737.

20. Observations on the Irreducible Case in Cubic Equations; 1738.

21. Observations upon Cubic Equations; 1738.

22. On the Trisection of an Angle; 1740.

23. On the Irreducible Case in Cubic Equations; 1741.

24. Addition to ditto; 1743.

25. His Last Paper upon the same; 1744.

26. Determination, by Incommensurables and Decimals, the Values of the Sides and Areas of the Series in a Double Progression of Regular Polygons, inscribed in and circumscribed about a Circle; 1747.