278 PROCEEDINGS OF THE AMERICAN ACADEMY 



Short Reduction. Long Reduction. 



B A B A BT 



r B r B A B 



AT r A AT 



The verses of Shyreswood show how Celantes and Dabitis are to be 

 reduced in the short way, and Frisesoinorurn in the long way. Celan- 

 tes and its long reduction are as follows : — 



Any X is not Y, Any not- A 7 " is not Z, 



Any Z is A; Any Y is not-A; 



.'. Any Y is not Z. .: Any Y is not Z. 



" Any X is not Y" becomes, by conversion, " Any Y is not X." 

 The term " not-A" is then introduced, being defined as that which Y 

 is when it is not X. Then " ^is X" becomes " Any not-A is not Z" ; 

 and, the premises being transposed, the reduction is effected. 



Dabitis and its long reduction -are as follows : — 



Any Z is X, Any some-Z is Y, 



Some Y is Z; Some X is some-^; 



.*. Some A is Y. .*. Some X is J". 



" Some J" is Z" becomes, by conversion, " Some Z is Y." Then 

 the term "some-^" is introduced, being defined as that Z which is 

 Y if « some Z is Y" Then "Any Z is A" becomes " Some X is 

 some-Z" and, the premises being transposed, the reduction is effected. 



Frisesomorum is, 



Let some-Z be that Y which is Z when some Y is Z; and then 

 we have, 



