REVIEWS 



MATHEMATICS 



Constructive Text-book of Practical Mathematics. Vol. Hi., Technical 

 Geometry, by H. W. Marsh. [Pp. xiv + 244] (New York : John Wiley 

 & Sons, Inc. ; London : Chapman & Hall, Ltd , 1914. Price 5J. 6d. net.) 



It would be easy to misjudge this book. If indeed it is regarded as a book, 

 it would be impossible to judge it leniently : it is only by considering it as a 

 text subsidiary to the course of instruction at the Pratt Institute that one can 

 give any estimate of it. There is no difficulty in discerning the author as a 

 man who has worked out with great persistence, and perhaps ingenuity, a system 

 of his own ; but the printed matter which he places before us conveys to the 

 reader little more than a grotesque travesty of his earnest and devoted labours 

 with the 2,000 students who, he tells us, have passed through his hands. The 

 author's system of teaching is heuristic, and this system has always failed, apart 

 from strong personality in the teacher, to achieve results of value in geometry. 

 At the best there are but few geniuses in the world at any one time who can, 

 as Pascal is said to have done, discover the system of geometry for themselves ; 

 when the heuristic system is applied with students who are not Pascals, it de- 

 generates into a system of suggestion in which the students attempt to supply 

 answers which they think will please their instructor. 



The book begins with a preface, which is perhaps its best part. Then 

 follows a section in which the " work-book " is dealt with, a section which is of 

 value for the student of the Pratt Institute, but worthless to the student of 

 geometry. We have then shorthand contractions by which axioms are referred 

 to — thus "Thru Pt 1 ||" denotes Playfair's axiom. Thereupon 120 definitions 

 succeed, which introduce the ten books in which the subject is developed in 

 skeleton form, or, as the work goes on, with enunciation only. Each book is 

 prefaced by a contracted list of contents of the enunciations ; some of these 

 are intelligible, others are not. Here is one which some readers might like to 

 guess : 



Ea Leg M P Hyp and Adj Seq. 



The plan of the author seems to be to get the student to make certain 

 measurements of figures and then to form a guess at a theorem ; when guessed 

 successfully, the proof of the theorem is roughed out. The method of pro- 

 ceeding is unsound, as it subordinates reason to measurement. One feature of 

 interest is that while all figures in plane geometry are omitted, representations 

 in two dimensions are yet given of solid figures. There are good reasons for 

 omitting figures altogether if the author is, as a French geometer puts it, 

 convaincu que des notations convenablement choisies permettent de suivre une 

 demonstration mieux qu'une figure qui detourne forcement l'attention ; but 

 enough has been given to show that this can hardly be the conviction of the 

 author of Technical Geometry, nor does this apology for the absence of figures 

 constitute a defence of the figures which exist. 



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