CHAPTER IV. 



ON COMBIjSTATIONS. 



87. The theory of combinations is closely connected witli the 

 theory of probability ; so that we shall find it convenient to imi- 

 tate Montucla in giving some account of the writings on the 

 former subject up to the close of the seventeenth century. 



88. The earliest notice we have found respecting combinations 

 is contained in Wallis's Algebra as quoted by him from a work by 

 William Buckley; see Wallis's Algebra 1693, page 489. Buckley 

 was a member of King's College, Cambridge, and lived in the time 

 of Edward the Sixth. He wrote a small tract in Latin verse con- 

 taining the rules of Arithmetic. In . Sir John Leslie's Pliilosophj 

 of Arithmetic full citations are given from Buckley's work; in 

 Dr. Peacock's History of A rithmetic a citation is given ; see also 

 De Morgan's Arithmetical Books from the invention of Printing .. . 



Wallis quotes twelve lines which form a Regula Comhinationis, 

 and then explains them. We may say briefly that the rule 

 amounts to assigning the whole number of combinations which can 

 be formed of a given number of things, when taken one at a time, 

 or two at a time, or three at a time,. . . and so on until they are taken 

 all together. The rule shews that the mode of proceeding was 

 the same as that which we shall indicate hereafter in speaking 

 of Schooten ; thus for four things Buckley's rule gives, like Schoo- 

 ten's, 1 + 2 + 4 + 8, that is 15 combinations in all. 



By some mistake or misprint Wallis apparently overestimates 

 the age of Buckley's work, when he says *' . . . in Arithmetica sua, 



