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LI I. Notices respecting New Books. 



Recent Te.vt-books of Determinants. 



Teoria elemental de las Determinants, y sus principals aplicaciones 

 al Algebra y la Geometria. For Felix Amorstti y Carlos M. 

 Morales. (Buenos Ayres : M. Biedma, 1888.) 



Elementary Treatise on Determinants. By Wtlliajm G. Peck, 

 Ph.D., LL.D. (New York and Chicago: A. S. Barnes & Com- 

 pany, 1887.) 



r pHE first of these books is a fresh and pleasing indication that 

 -*- mathematical studies have taken vigorous root in the University 

 of Buenos Ayres. The change for the better, due in great part to 

 the energy and enthusiasm of Professor Valentin Balbin, deserves 

 cordial recognition in this country, whose financial and trade rela- 

 tions with the Argentine Republic are yearly becoming more and 

 more important. To the supply of text-books Professor Balbin 

 has made important contributions ; and the present work, though 

 not bearing his name on the titlepage, claims him as godfather. 



As a specimen of printers' handicraft it is very satisfactory; the 

 page is large (larger than that of Salmon's works), the margin 

 is wide, and the type clear and generously spaced. The subject is 

 treated of in three Sections, viz. : — Determinants in General, occu- 

 pying 71 pages ; Determinants of Special Form, occupying 43 

 pages ; and Applications of Determinants, occupying Q6 pages. 

 In all three the arrangement is most methodical : definition, 

 theorem, and corollary following in order, with sufficient illustra- 

 tions and examples interspersed to satisfy any ordinary student. 



With the first section very little fault can be found. The his- 

 torical indications are rather seriously inaccurate— a venial weakness, 

 considering the rarity of such accuracy, and bearing in mind the 

 fact that the authors do not profess to have made any original 

 research on the subject. The reviewer, however, cannot too often 

 point out how misleading it is to say, for example, that Gauss 

 notably advanced the theory of determinants, that the notation 



a. b. c, \ 



is due to Cauchv, that Leibnitz's notation was 



a n a x 



or, indeed, that Leibnitz had any notation for determinants at all. 

 These and other such statements the authors should try to verify, 

 Phil Mag. S. 5. Vol. 26. No. 162. Nor. 1888. 2 I 



