MATHEMATICAL SOCIETY. 285 



and the grocer's is the Post-Office, it follows that the grocer's is 1865. 

 the chandler's, another place, by hypothesis ; which is absurd ; Inaugural 

 and so with every other place except the grocer's. Therefore 

 the Post-Office is at the grocer's. 



Is not this mode of proof in the third book of Euclid, being 

 the way in which proposition 19 is deduced from proposition 18 ? 

 Yet any body who should use it out of geometry would be laughed 

 at, though Euclid used it, and all those who have studied his 

 Elements have been proving things in this manner for two thou- 

 sand years. 



There is no doubt about the matter, I say and it will appear 

 more distinctly on further thought that you are proving by 

 help of a syllogism what must be admitted before syllogism 

 itself is valid. 



As to the chances of the Society finding for itself 

 lines of original work, he says : 



The higher Mathematics may be carried on with much greater 

 effect by elementary students if they will but study points of 

 Logic, History, Language, and perception of propositions by 

 simple common sense. Mathematics is becoming too much of 

 a machinery, and this is especially the case with reference to the 

 elementary students. They put the data of the problems into a 

 mill, and expect them to come out ground at the other end 

 an operation which bears a close resemblance to putting in hemp- 

 seed at one end of a machine, and taking out ruffled shirts ready 

 for use at the other end. This mode is, no doubt, exceedingly 

 effective in producing results, but it is certainly not so in teach- 

 ing the mind and in exercising thought. If it should chance 

 that we find a disposition among the members of this Society to 

 leave the beaten track and cut out fresh paths, or mend the old 

 ones, we make this Society exceedingly useful. But if not, if it 

 be our fate only to become problem makers and problem solvers, 

 there is no harm done ; we shall but add one more association to 

 the list of journals, colleges, &c., devoted to this object. The 

 only objection is that this branch of the subject is sufficiently 

 well appreciated and more than sufficiently well practised 

 already. 



Original papers by both its first President and Secre- 

 taries appear in the first pages of its earliest reports, and 



