TERMINOLOGY AND NOMENCLATURE. 295 



.ymbols) without an image annexed to them. It is only 

 ifter ascertaining that the solution of a question con- 

 jerning lines can be made to depend upon a previous 

 question concerning numbers, or in other words after 

 the question has been (to speak technically) reduced to 

 an equation, that the unmeaning signs become avail- 

 able, and that the nature of the facts themselves to 

 which the investigation relates can be dismissed from 

 the mind. Up to the establishment of the equation, 

 the language in which mathematicians carry on their 

 reasoning does not differ in character from that em- 

 ployed by close reasoners on any other kind of 

 subject. 



I do not deny that every correct ratiocination, 

 when thrown into the syllogistic shape, is conclusive 

 from the mere form of the expression, provided none 

 of the terms used be ambiguous; and this is one of 

 the circumstances which have led some philosophers 

 to think that if all names were so judiciously con- 

 structed and so carefully defined as not to admit of 

 any ambiguity, the improvement thus made in lan- 

 guage would not only give to the conclusions of every 

 deductive science the same certainty with those of 

 mathematics, but would reduce all reasonings to the 

 application of a technical form, and enable their con- 

 clusiveness to be rationally assented to after a merely 

 mechanical process, as is undoubtedly the case in 

 algebra. But, if we except geometry, the conclusions 

 of which are already as certain and exact as they can 

 be made, there is no science but that of number, 

 in which the practical validity of a reasoning can 

 be apparent to any person who has looked only 

 at the form of the process. Whoever has assented 

 to all that was said in the last Book concerning the 

 case of the Composition of Causes, and the still 



