The Collected Mathematical Papers of James Joseph Sylvester

Table of Contents

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

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