Notices respecting New Books. 149 



Elementary Plane Geometry. By Julius Petersen - . Translated 

 into English by R. Steenberg, Jun. {Authorized English Edition.) 

 Sampson Low, Marston, Searle and Rivington. 72 pages. 

 Considering the great number of elementary books on Plane 

 G-eometry which have been published during the past twelve years 

 (many better and few worse than the one now before us), the raison 

 d'etre of an English edition of M. Petersen's work is not very ap- 

 parent. It consists of 72 pages, and contains 228 exercises, the 

 latter being unquestionably the best part of the book, certainly as 

 regards quality, if not quantity. Could the accomplished and 

 amusing author of ' Euclid and his Modern Rivals ' have seen 

 it before publishing his work, he would certainly have found mate- 

 rial for his piquant criticism. 



Congruent figures are badly defined, if defined at all in the true 

 sense of a definition ; and the sign for congruence is simply grotesque. 

 He, too, would be a sharp boy indeed who could understand that 

 the exterior angles of any convex polygon are together equal to 

 four right angles from the explanation given in art. 16, or make 

 out what is meant by "-parallels all over are at the same distance 

 from each other." 



The translation is undoubtedly creditable to a foreigner ; but we 

 would suggest to the author and translator the advisability of get- 

 ting an Englishman to correct the proofs of the next edition ; for 

 the present contains from beginning to end many very unenglish 

 expressions. Just twelve years ago a well-known ' Athenaeum ' 

 Reviewer (Jan. 9, 1869, No. 2150) wrote, "After a score of 

 attempts to overthrow Euclid, we shall have a chance of a good 

 attempt to amend the ' Elements.' " We have seen the score 

 attempts exceeded ; but the chance of getting a book worthy of 

 supplanting Euclid seems as far off as ever. 



Mathematical Formula. Edited by R. M. Milbtjrn, M.A. Long- 

 mans and Co. 100 pages. 

 The title does not do the book full justice. "We opened it expect- 

 ing to find formulae only, but found a number of definitions which 

 are models of clearness and succinctness. Besides tables of Squares 

 and Cubes and their reciprocals of numbers from 1 to 100, there 

 are excellent rules and definitions in Commercial Arithmetic. In 

 Algebra, comprising ratio, proportion, variation, and permutations, 

 the definitions are perfect and the formulae all that could be desired. 

 The same may be said of every other branch of Mathematics. 

 Besides this system of memoria technica, several well-executed 

 figures add to the value of the book. We repeat, the title is defec- 

 tive; " Definitions, Rules, Hints, and Formulae " would be more 

 appropriate. The book is only a compilation ; but it is manifestly 

 the work of an excellent judge of the subjects treated, as the 

 various definitions and hints throughout the book testify. 



