LITERARY NOTICES. 



53 



well in our smooth-running educational sys- 

 tem not a machine that can be belted on 

 in some convenient corner of our education- 

 al cotton-mills. In the objects it aims to 

 secure, and in the method of attaining 

 them, it is outside of the customary school 

 routine. It is a contribution to the momen- 

 tous and much-neglected work of self-educa- 

 tion to which the school-room, as common- 

 ly managed, is not very favorable. 



The author of this little work, the late 

 W. G. Spencer, of Derby, England, was a 

 mathematical teacher, and a gentleman of 

 wide cultivation and independent opinions. 

 He had been for many years an instructor, 

 and entertained quite unconventional views 

 on the subject of education. He maintained 

 that, of all that passes under the name, only 

 that is truly education which calls out men- 

 tal exertion, trains the pupil to the exer- 

 cise of his own faculties, develops the judg- 

 ment, and gives the student the ready use 

 and command of his own mind. It is, there- 

 fore, necessary constantly to throw the pu- 

 pil back upon himself, and, while encour- 

 aging and guiding him, leave him at the 

 same time to do his own work. For the 

 usual occupations of the school-room, explan- 

 atory instruction, loading the memory with 

 the contents of books, and helping the pupil 

 rapidly along by all kinds of facilities and 

 devices, Mr. Spencer had but little respect ; 

 and he measured the excellence of the teach- 

 er by his faculty and resources for awaken- 

 ing the pupil's interest, keeping him judi- 

 ciously occupied, and inciting him to use, 

 cultivate, and strengthen his own powers. 



In the later years of his teaching, Mr. 

 Spencer was much occupied in giving pri- 

 vate instruction in mathematics, and he was 

 therefore brought into constant contact 

 with individual minds, and enabled to study 

 them much more critically than if he had 

 been dealing with classes in the usual way. 

 In these circumstances he devised a course 

 of exercises in elementary geometry for the 

 use of beginners, designed to lay the foun- 

 dation for mathematical study, and at the 

 same time to cultivate the faculties of in- 

 vention and construction, which are of the 

 highest importance, and almost totally neg- 

 lected in the common methods of the schools. 

 As this course of exercises began with the 

 simplest problems, and was skillfully graded 



so that the pupil could do the whole work 

 himself, there seemed to be no reason why 

 the benefits of the method should not be 

 extended to all who might wish to avail 

 themselves of it, and it was so highly ap- 

 preciated by those who had used it that the 

 author was at length induced to print it, 

 although he had no such intention at the 

 time of its preparation. The " Inventional 

 Geometry" is now republished, and being a 

 very suitable book for companionship with 

 the " Science Primers," now being issued 

 from time to time, the publishers have 

 thrown it into the same form, and included 

 it among the reprints in this elementary 

 series. But in one respect the "Inventional 

 Geometry " differs from the little books with 

 which it is associated. The Science Prim- 

 ers are highly estimated. They fall in with 

 the stereotyped habits of the class-room, and 

 may be easily learned by heart like histo- 

 ry, grammar, or the catechism. This book 

 will, however, enforce a different treatment, 

 and if the object of education be the disci- 

 pline of the mental faculties through honest 

 effort, and if thorough familiarity with geo- 

 metrical conceptions be desirable, and the 

 training of the inventive and constructive 

 faculties be valuable and important, the 

 Primer of Geometry will be worth more 

 than all its associates put together. We 

 recommend it to those who are thoughtful 

 and conscientious in educational matters. 

 Any fair-minded boy or girl cf twelve or 

 fourteen years of age can go through it 

 without difficulty, and cannot get through 

 it without gaining the advantages it aims to 

 secure. Those who work their way through 

 it will be certain to know one thing thor- 

 oughly, and, as Goethe said to Eckermann, 

 " It is always an advantage to have any 

 clear bit of knowledge." 



The author of this book was the father 

 of Herbert Spencer, who testifies from ob- 

 servation and experience to the excellence 

 of the method, as will be seen by the fol- 

 lowing note to the publishers : 



" London, June 3, 1876. 

 "Messes. D. Appleton & Co.: I am glad that 

 you are ahout to republish, in the United States, 

 my father's little work on ' Inventional Geom- 

 etry.' Though it received but little notice when 

 first issued here, recognition of its usefulness 

 has been gradually spreading, and it has been 

 adopted by some of the more rational science- 



