# Nicole, Francis

, a very celebrated French mathematician, was born at Paris, December 23, 1683. His early attachment to the mathematics induced M. Montmortto take the charge of his education, and initiate him in the higher geometry. He first distinguished himself by detecting the fallacy of a pretended quadrature of the circle. A M. Mathulon was so confident that he had discovered this quadrature, as to deposit 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 having undertaken the task, the academy’s judgment was, that he 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. It was the love of science, however, and not of money, which inspired Nicole on this occasion, for he presented the prize of 300O livres 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 January 18, 1758, at seventy-five years of age.

His works, which were all inserted in the different vo^ lumes of the Memoirs of the academy of sciences, are: 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 infinity 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, 172*. 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 tliird order, or the curves of the second kind, 172.9. 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 aproblem 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. Ob.
servations 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. ^{1}