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THE POPULAR SCIENCE MONTHLY. 



taught by going over demonstrative geometry, then taking up 

 mechanical drawing, and adding to these personal experience. 

 The author has secured all this and much more. He appeals 

 first to the inventive faculty, seeks expression through the hand, 

 and brings before the eye accurate and beautiful forms of the 

 pupil's own constructing. The eye is trained to accuracy and 

 similarity of forms, invention is quickened, comparison and judg- 

 ment are constantly exercised, and inductive growth of mind is 

 directly promoted. Besides the manual skill gained in construct- 

 ing figures, and the power acquired to deal with original ques- 



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tions through the constant appeal to invention, the pupil gains 

 by his own efforts proofs of theorems really conclusive in them- 

 selves, though not the syllogistic form of proof belonging to the 

 deductive science. 



In but one of a great number of schools visited has the writer 

 found inventional geometry used, and in that school quite out of 

 the design of the author. It should precede demonstrative geom- 

 etry, so as to give the pupil many concepts to draw upon when he 

 takes up syllogistic demonstration. Demonstrative geometry then 

 becomes an easier subject, and he is surer of what he is doing, be- 

 cause he has more general notions as a basis. In the school alluded 



