REVIEWS 



MATHEMATICS 



The Theory of Plane Curves: Parts I and II. By Surendramohan 

 Ganguli, M.Sc, Lecturer in Pure Mathematics, University of Cal- 

 cutta. [Part I, pp. X + 138 ; Part II. pp. xiii + 350 ; with dia- 

 grams.] (Calcutta : University Press, 1919.) 



These two small books comprise a set of lectures on the " Theory of Plane 

 Curves," delivered to post-graduate students in the University of Calcutta. 

 They are intended as an introductory course simply, and consequently little 

 beyond the general theorems of the Calculus and the simpler results in 

 analytical geometry are assumed. Much use has been made of the stan- 

 dard works of Salmon and Scott, but the interesting novelty of the present 

 treatment of plane curves is the introduction of geometrical methods in 

 many cases where those of analysis have formerly been generally used. 

 The author states that this scheme has been introduced to avoid otherwise 

 tedious and lengthy investigations. Various criticisms of this procedure 

 might be made. These books are expressly designed to follow on an ele- 

 mentary course on the theory of plane curves. But even an elementary 

 course must necessarily introduce the fundamental ideas involved in the 

 subject. In general it seems to be better to allow familiarity with the rough 

 outline of a notion to prompt students to a further inquiry into its logical 

 ancestry and relations when interest has been aroused by interesting appli- 

 cations, rather than to endeavour to introduce each logical conception such 

 as the length of a curve or the circular points in a logically unobjectionable 

 way. If the notions are to be intelligently investigated — and this is obviously 

 a different kind of inquiry from the study of the properties of the notion — 

 this must be done at some stage after the introductory one. A book, there- 

 fore, which is designed to follow on an elementary course should make some 

 attempt to deal with this aspect, or give good reason why it is to be further 

 postponed. In these lectures no attempt is made, and it is clear, from 

 the mSlange of geometrical methods and analytical methods, that it was not 

 considered necessary by the author to make such an attempt. As the book 

 is designed for post-graduate students of mathematics, this, on the whole, 

 seems a mistake. But, important as this side is, it is only one part of any 

 branch of mathematics, and it would be a great error to overestimate its 

 value. At some point or other concepts must be used which we cannot 

 further analyse. 



The second volume applies the general treatment of curves in vol. i 

 to cubics and quartics. An exhaustive treatise was obviously impossible 

 in the limits of a small book, and the author has singled out various pro- 

 minent characteristics of the curves to discuss. 



Dorothy Wrinch. 



Differential Equations. By H. T. H. Piaggio, M.A., D.Sc, Professor of 



Mathematics, University College, Nottingham. [Pp. xvi -f- 216 -}- 



xxv.] (London : G. Bell & Sons, 1920. Price 12s. net.) 



This book on Differential Equations will be very welcome for teaching 



purposes. It assumes no previous knowledge of the subject, and covers a 



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