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Davies' Logic of Mathematics.


The Logic and Utility of Mathematics, with the best methods of Instruction, explained and illustrated. By CHARLES DAVIES, L. L. D.

"One of 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 intended as a treatise on any special branch of mathematical science, and demands for 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. It 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 essential 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 impress of the intellect of the writer; his style is for the most part chaste, simple, transparent, and in admirable harmony with the dignity of the subject, and his condensed generalizations are often profound and always suggestive."-Harper's New Monthly Magazine.

"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 improvement, 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 of 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 institutions but what is directly practical'; nowhere have we seen a finer illustration of 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 Mathemetical Science, and the third, of the Utility of Mathematics."-Independent.

"The author's style is perspicuous and concise, and he exhibits a mastery of the abstruse topics which he attempts to simplify. For the mathematical student, who 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's mathematical works, we believe, have become quite popular with educators, and this discloses quite as much research and practical scholarship as any we have seen from his pen." --New-York Evangelist.

Page's Theory and Practice of Teaching.






"I received a few days since your "Theory and Practice, &c.,' and a capital theory and capital practice it is. I have read it with unmingled delight. Even if I should look through a critic's microscope, I should hardly find a single sentiment to dissent from, and certainly not one to condemn. The chapters on Prizes and on Corporal Punishment are truly admirable. They will exert a most salutary influence. So of the views sparsim on moral and religious instruction, which you so earnestly and feelingly insist upon, and yet within true Protestant limits. IT IS A GRAND BOOK, AND I THANK HEAVEN THAT YOU HAVE WRITTEN IT."-Hon. Horace Mann, Secretary of the Board of Education in Massachusetts.

"Were it our business to examine teachers, we would never dismiss a candidate without naming this book. Other things being equal, we would greatly prefer a teacher who has read it and speaks of it with enthusiasm. In one indifferent to such a work, we should certainly have little confidence, however he might appear in other respects. Would that every teacher employed in Vermont this winter had the spirit of this book in his bosom, its lessons impressed upon his heart!"-Vermont Chronicle.

"I am pleased with and commend this work to the attention of school teachers, and those who intend to embrace that most estimable profession, for light and instruction to guide and govern them in the discharge of their delicate and important duties.”— N. S. Benton, Superintendent of Common Schools, State of New York.

Hon. S. Young says, "It is altogether the best book on this subject I have ever soen."

President North, of Hamilton College, says, "I have read it with all that absorbing bing self-denying interest, which in my younger days was reserved for fiction and poetry. am delighted with the book."

Hon. Marcus S. Reynolds says, "It will do great good by showing the Teacher what should be his qualifications, and what may justly be required and expected of him.”

"I wish you would send an agent through the several towns of this State with Page's Theory and Practice of Teaching,' or take some other way of bringing this valuable book to the notice of every family and of every teacher. I should be rejoiced to see the principles which it presents as to the motives and methods of good school keeping carried ut in every school-room; and as nearly as possible, in the style in which Mr. Page illustrates them in his own practice, as the devoted and accomplished Principal of your State Normal School."-Henry Barnard, Superintendent of Common Schools for the State of Rhode Island.

"The "Theory and Practice of Teaching,' by D. P. Page, is one of the best books of the kind I have ever met with. In it the theory and practice of the teacher's duties are clearly explained and happily combined. The style is easy and familiar, and the suggestions it contains are plain, practical, and to the point. To teachers especially it will furnish very important aid in discharging the duties of their high and responsible profession."—Roger S. Howard, Superintendent of Common Schools, Orange Co., Vt.


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