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that exist between the sciences of quantity. I would not m 

 the first place precede these simple demonstrations by any 

 definitions. Where necessary when a scientific word is first 

 used I would define it, but as the definition would then be 

 erven with the thing defined bodily before the eyes of the 

 learner it would be more easily learnt and understood, and 

 more indelibly fixed in the mind." But generally it is better 

 at first to trust to the general knowledge possessed by most 

 learners, however young, of the names of elementary forms 

 when they see them, rather than add to the bulk of material set 

 forth as having to be learnt. 



But, to my mind, the greatest advantage of the system is 

 that it renders the understanding of mathematical reasoning so 

 easy as also to render easy the understanding of all other logical 

 reasoning. It visibly puts before the eye the lines upon which 

 all reasoning proceed. It thus increases the usefulness _ of 

 mathematics as a promoter of exactness in reasoning, and assists 

 learners in all their other studies by giving them clearer and 

 larger powers of apprehension. It not only simplifies geometry, 

 but makes the acquirement of all other science more easy. 



