180 METHODS IN SECONDARY PROPOSITIONS. [CHAP. XII. 



Cicero terms this form of proposition, "Conjunctio ex repug- 

 nantibus ;" and he remarks that Chrysippus thought in this way 

 to evade the difficulty which he imagined to exist in contingent 

 assertions respecting the future : " Hoc loco Chrysippus aestuans 

 falli sperat Chaldaeos caeterosque divinos, neque eos usuros esse 

 conjunctionibus ut ita sua percepta pronuntient : Si quis natus 

 est oriente Canicula is in mari non morietur ; sed potius ita dicant: 

 Non et natus est quis oriente Canicula, et in mari morietur. 

 O licentiam jocularem ! . . . . Multa genera sunt enuntiandi, nee 

 ullum distortius quam hoc quo Chrysippus sperat Chalda3os con- 

 tentos Stoicorum causa fore." Cic. De Fato, 7, 8. 



5. To reduce the given proposition to a disjunctive form. 

 The constituents not entering into the first member of (2) are 



Whence we have 



y (!-*) + *(! -y) + (1 -*) (1 -y) - 1. (3) 



The interpretation of which is : Either Fabius was born at the 

 rising of the dogstar, and will not perish in the sea; or he was not 

 born at the rising of the dog star, and will perish in the sea; or he 

 was not born at the rising of the dog star, and will not perish in 

 the sea. 



In cases like the above, however, in which there exist consti- 

 tuents differing from each other only by a single factor, it is, as 

 we have seen (VII. 15), most convenient to collect such consti- 

 tuents into a single term. If we thus connect the first and third 

 terms of (3), we have 



(l-y)#+l-tf=l; 



and if we similarly connect the second and third, we have 

 y(l-x)+ l-,y= 1. 



These forms of the equation severally give the interpretations 

 Either Fabius was not born under the dogstar, and will die in 



the sea, or he will not die in the sea. 



Either Fabius was born under the dogstar, and will not die in 



the sea, or he was not born under the dog star. 



