The Collected Mathematical Papers of James Joseph Sylvester: Volume 2, 1854–1873

Prefatory note; 1. On the double square representation of prime and composite numbers; 2. A probationary lecture on geometry, 1854; 3. Note on Sir John Wilson's theorem; 4. On the calculus of forms, otherwise the theory of invariants; 5. Théorème sur les déterminants; 6. Note on a point of notation; 7. Note on the 'enumeration of the contacts of lines and surfaces of the second order; 8. Note on the formula by aid of which and of a table of single entry the continued product of any set of numbers (or at least a given constant multiple thereof) may be effected by additions and subtractions only without the use of logarithms; 9. On some new theorems in arithmetic; 10. Note on Burman's law for the inversion of the independent variable; 11. On differential transformation and the reversion of serieses; 12. A trifle on projectiles; 13. A note on an intuitive proof of the existence of twenty-seven conics of the closest contact with a curve of the third degree; 14. Letter on professor Galbraith's construction for a range of projectiles; 15. Recherches sur les solutions en nombres entiers positifs ou négatifs de l'equation cubique homogène á trois variables; 16. On the change of systems of independent variables; 17. On a discovery in the partition of numbers; 18. On the partition of numbers; 19. Note on a formal property of a latent integer; 20. Note on a principle in the theory of numbers and the resolubility of any number into the sum of four squares; 21. Development of an idea of Eisenstein; 22. Note on the algebraical theory of derivative points of curves of the third degree; 23. Note on the equation in numbers of the first degree between any number of variables with positive coefficients; 24. On the problem of the virgins, and the general theory of compound partition; 25. On a generalization of Poncelet's theorems for the linear representation of quadratic radicals; 26. Outlines of seven lectures on the partitions of numbers; 27. Théorie des nombres; 28. Théorie des nombres; 29. Note sur certaines séries qui se presentent dans la théorie des nombres; 30. Sur la fonction E (x);, 31. On Poncelet's approximate linear valuation of surd forms; 32. Meditation on the idea of Poncelet's theorem; 33. Notes to the meditation on Poncelet's theorem, including a valuation of two new definite integrals; 34. On the pressure of earth on revetment walls; 35. On an equation in the theory of numbers; 36. Sur une propriété des nombres premiers qui se rattache au théorème de Fermat; 37. Addition á la note insérée dans la précédent compte rendu; 38. Note relative aux communications faites dans les séances des 28 Janvier et 4 Février 1861; 39. Sur l'involution des lignes droites dand l'espace considérées comme des axes de rotation; 40. Note sur l'involution de six lignes dans l'espace; 41. Note sur les 27 droites d'une surface du 3e degré; 42. Generalisation d'un théorème de M. Cauchy; 43. Addition á la note intitulée: 'Généralisation d'un théorème de M. Cauchy'; 44. Démonstration directe du théorème de Lagrange, sur les valeurs numériques minima d'une fonction linéaire á coefficients entiers d'une quantité irrationelle; 45. Note on the numbers of Bernoulli and Euler and a new theorem concerning prime numbers; 46. Note on the historical origin of the unsymmetrical six-valued function of six letters; 47. On a problem in tactic which serves to disclose the existence of a four-valued function of three sets of three letters each; 48. Concluding paper on tactic; 49. Remark on the tactic of nine elements; 50. On a generalization of a theorem of Cauchy on arrangements; 51. Note on a direct method of obtaining the expansion of the sine or cosine of multiple arcs in terms of powers of the sines or cosines of the simple arc by means of De Moivre's theorem; 52. Note on certain definite integrals; 53. On the involution of axes of rotation; 54. Addition á l