CHAPTER VI. 



MISCELLANEOUS INVESTIGATIONS 

 Between the yeaes 1670 and 1700. 



69. The present chapter will contain notices of various con- 

 tributions to our subject, which were made between the publi- 

 cation of the treatise by Huygens and of the more elaborate 

 works by James Bernoulli, Montmort, and De Moivre. 



70. A Jesuit named John Caramuel published in 1670, under 

 the title of Mathesis Bicej^s, two folio volumes of a course of 

 Mathematics ; it appears from the list of the author's works at the 

 beginning of the first volume that the entire course was to have 

 comprised four volumes. 



There is a section called Gomhinatoria which occupies pages 

 921 — 1036, and part of this is devoted to our subject. 



Caramuel gives first an account of combinations in the modern 

 sense of the word; there is nothing requiring special attention 

 here : the work contains the ordinary results, not proved by general 

 symbols but exhibited by means of examples. Caramuel refers 

 often to Clavius and Izquierdus as his guides. 



After this account of combinations in the modern sense Cara- 

 muel proceeds to explain the Ars Lidliana, that is the method of 

 affording assistance in reasoning, or rather in disputation, proposed 

 by Raymond Lully. 



71. Afterwards we have a treatise on chances under the title 

 of Kyheia, quce Combinatorioe genus est, de Alea, et Ludis FortuncB 



