CONTENTS. 



PAGE 



Chapter I. Cardan. Kepler. Galileo . . l 



Commentary on Dante, i. Cardan, Be Ludo Alece, i, Kepler, De Stella 

 Nova, 4. Galileo, Considerazione sopra il Giuco del Dadi, 4 ; Lettcre, 5. 



Chapter II. Pascal and Fermat .... 7 



Quotations from Laplace, Poisson, and Boole, 7. De Mare's Problems, 7, 

 Problem of Points, 9. De Merc's dissatisfaction, 11. Opinion of Leib- 

 nitz, 12. Fermat's solution of the Problem of Points, 13. Roberval, 13. 

 Pascal's error, 14. The Arithmetical Triangle, 17. Pascal's design, 20. 

 Contemporary mathematicians, 21. 



Chapter III. Huygens 22 



De liatiodniis in Ludo Alece, 22. English translations, 23. Huygens's solu- 

 tion of a problem, 24 ; Problems proposed for solution, 25. 



Chapter IV. On Combinations . . . .20 



"William Buckley, 26. Bernardus Bauhusius and Erycius Puteanus, 27. Quo- 

 tation from James Bernoulli, 28. Pascal, 29. Schooten, 30. Leibnitz, 

 Dissertaiio de Arte Comhinatoria, 31 ; his fruitless attempts, 33. Wallis'3 

 Algebra, 34; his errors, 35. 



Chapter V. Mortality and Life Insurance . 37 



John Graunt, 37. Van Hudden and John de Witt, 38, Sir William Petty, 39. 

 Correspondence between Leibnitz and James Bernoulli, 40. Halley, 4 1 ; 

 his table, 42 ; geometrical illustration, 43. 



Chapter YI. Miscellaneous Investigations between 



THE YEARS 1670 AND 1700 -ii 



Caramuel's Matliesis Biceps, 44 ; his errors, 45, 46. Sauveur on Bassette, 46. 

 James Bernoulli's two problems, 47. Leibnitz, 47; his error, 48. Of 

 the Laws of Chance, ascribed to Motte, 48 ; really by Arbuthnot, 49 ; 

 quotation from the preface, 50 ; error, 52 ; problem proposed, 53. 

 Francis Roberts, An Arithmetical Paradox, 53, Craig's Theologies Chris- 

 tiance Principia Maihematica, 54. Credihility of Human Testimony, 55. 



Chapter YII. Jaihes Bernoulli . . . .56 



Correspondence with Leibnitz, 56 ; Ars Conjectandi, 57. Error of Montucia, ^S. 

 Contents of the Ars Conjectandi, 58. Problem of Points, 59. James 

 Bernoulli's own method for problems on chances, 60; his solution of a 



