Davies' System of Mathematics. 



DAVIES" LOGIC OF MATHEMATICS. 

 "Rie Logic and Utility of Mathematics, with the best methods of Inatrao 

 tion, explained and illustrated. By Charles Datles, L. L. D. 



"One <>f the most remarkable books of the month, is ' The Logic and Utility of 

 Mathematics, by Charles Davies, L. L. D.,' published by Barnes &. Co. It is not in- 

 tended as a treatise on any special branch of mathematical science, and demands foi 

 its full appreciation a general acquaintance with the leading methods and routine of 

 mathematical investigation. To tho?e who have a natural fondness for this pursuit 

 and enjoy the leisure for a retrospect of their favorite studies, the present volume will 

 possess a charm, not surpassed by the fascinations of a romance. U is an elaborate 

 and lucid exposition of the principles which lie at the foundation of pure mathematics 

 with a highly ingenious application of their results to the development of the essen- 

 tial idea of Arithmetic, Geometry, Algebra, Analytic Geometry, and the Differential 

 and Integral Calculus. The work is preceded by a general view of the subject of Logic, 

 mainly drawn from the writings of Archbishop Whately and Mr. Mill, and closes with 

 an essay on the utility of mathematics. Some occasional exaggerations, in presenting 

 the claims of the science to which his life has been devoted, must here be pardoned 

 to the professional enthusiasm of the author. In general, the work is written with 

 singular circumspection ; the views of the best thinkers on the subject have been 

 thoroughly digested, and are presented in an original form ; every thing bears the im- 

 press of the intellect of the writer ; his style is for the most part chaste, simple, trans- 

 parent, and in admirable harmony with the dignity of the subject, and his condensed 

 generalizations are often profound ai;d always suggestive." — Harper's New Monthly 

 Maffaiine. 



"This work is not merely a mathematical treatise to be used as a text book, but a 

 complete and philosophical unfolding of the principles and truths of mathematical 

 science. 



"It is not only designed for professional teachers, professional men, and students of 

 mathematics and philosophy, but for the general reader who desires mental improve- 

 ment, and would learn to search out the import of language, and acquire a habit of 

 noting of connexion between ideas and their signs ; also, of the relation of ideas to 

 each other.— The Student. 



" Students of the Science will find this volume full of useful and deeply interesting 

 matter." — Albany Evening Journal. 



" Seldom have we opened a book so attractive as this in its typography and style 01 

 execution ; and there is besides, on the margin opposite each section, an index of the 

 subject of which it treats — a great convenience to the student. But the matter is no 

 less to be commended than the manner. And we are very much mistaken if this work 

 shall not prove more popular and more useful than any which the distinguished author 

 has given to the public." — Lutheran Observer. 



" We have been much interested both in the plan and in the execution of the work, 

 and would recommend the study of it to the theologian as a discipline in close and 

 accurate thinking, and in logical method and reasoning. It will be useful, also, to the 

 general scholar and to the practical mechanic. We would specially recommend it to 

 those who would have nothing taught in our Free Academy and other higher instittt 

 tions but what is directly 'practical' ; nowhere have we seen a finer illustration if 

 the connection between the abstractly scientific and the practical. 



"The work is divided into three books; the first of which treats of Logic, mainly 

 upon the basis of Whately; the second, of Mathematical Science; and the third, < f the 

 Utility of Mathematics." — Independent. 



"The authoi's style is perspicuous and concise, and he exhibits a mastery of the 

 abstruse topics which he attempts to simplify. For the mathematical student, wb* 

 desires an analytical knowledge of the science, and who would begin at the beginning, 

 we should suppose the work would have a special utility. Prof Davies* mathemati- 

 cal works, we believe, have become quite popular with "educators, and this disclose! 

 quite as much reasearcfa and practical scholarship as any we have 6een from his pMi. r 

 •-2s eu- Ycrh Evangelist. 



