Arithmetical Series.

BY GEORGE R. PERKINS, LL.D.

This Series embraces four text-books, which cover the whole ground, from the first lesson of the beginner in counting to the most abstruse and intricate operations embraced in the science. Their distinguishing features, as a whole, and the points on which their claim to superiority rests, are as follows:

1. They are complete. Nothing connected with the subject is omitted.

2. Each number follows that which precedes it naturally and easily, the step from one to another not being too great for the pupil's comprehension. The teacher is not obliged to look up a work by some other author to fill up an annoying gap.

3. They are consistent with each other. The definitions and rules in the different numbers are, as far as practicable, in the same words, and similar modes of reasoning are employed throughout.

4. They are philosophically arranged.

The easier parts take precedence of the

mere difficult; and nothing is anticipated to the bewilderment of the pupil.

5. They are inductive. General laws are deduced from individual cases. A rule is not arbitrarily laid down; but an example is first given and worked out by analysis. 6. They are practical, constructed with direct reference to the wants of the pupil when he shall enter on the actual business of life. All the branches connected with mercantile transactions receive special attention, and are impressed on the mind in a way that insures their retention.

7. Rules and explanations are given tersely. Their point is not lost in a mass of words.

8. They present an unusually large number of examples. The, space saved by stating rules and principles in a condensed form is thus used to the greatest practical advantage.*

9. The examples, particularly those given first under the rules, do not involve tedious operations. A principle may be illustrated with simple numbers, as well as with combinations of ten or twelve figures, while, by using the former, the pupil is saved from discouragement and a waste of time and labor.

10. Each rule is illustrated by every variety of example that can fall under it; and, to accustom the scholar to every possible application, the language of the examples is varied as much as practicable.

11. The examples are so constructed as to require thought on the part of the pupil. The mind is thus developed and disciplined, and gradually prepared for the study of the higher mathematics.

12. A principle once taught is not allowed to be forgotten. In one form or other it is made the subject of constant review, and is so interwoven in the examples successively presented that it cannot escape the mind.

13. Finally, these Arithmetics teach the shortest, simplest, and most easy to be remembered modes of performing the different operations of which they. treat,

Arithmetical Series.

By GEORGE R. PERKINS, LL.D.

I. Primary Arithmetic. 18mo, 160 pages.

This work presupposes no knowledge of Arithmetic.

It commences

with Elementary principles, and lays a sure foundation for what is to follow. From the four fundamental rules it proceeds to Fractions. Next come Decimals and Federal Money.

II. Elementary Arithmetic. 16mo, 347 pages.

From the Primary the pupil proceeds to the Elementary, in which it is aimed to discipline the mind, to develop the reasoning powers, and to prepare the pupil for the advanced departments of Mathematics. In the author's treatment of Vulgar Fractions, Percentage, and Interest, his new method of finding the cash balance in Equation of Payments, and his improved method of Extracting the Cube Root, he has certainly made a great advance on the other Elementary Arithmetics now before the public.

III. Practical Arithmetic. 12mo, 356 pages.

This work covers nearly the same ground as the Elementary, differing from it principally in presenting a greater number of examples. It may, therefore, either follow the Elementary, or be substituted for it. No other work offers the scholar such facilities for practice as this, no less than 3,926 sums being given. All of the Examples or Problems are strictly practical, made up, as they are, in a great measure, of important statistics and valuable facts in history and philosophy, which are thus unconsciously learned in acquiring a knowledge of the Arithmetic.

IV. Higher Arithmetic. 12mo, 324 pages.

This is intended as a finishing book for those who would complete a thorough arithmetical course. It embraces all the more abstruse parts of the science, and develops its principles to a greater extent than is usual with school-books on this subject.

** A copy of any of Dr. PERKINS's works, for examination, will be sent by mail, post-paid, to any Teacher or School Officer, remitting one-half its price.

Algebraic Series.

BY GEORGE R. PERKINS, LL.D.

Elements of Algebra. 12mo, 244 pages.-The want of a text-book on Algebra sufficiently simple for common schools was long and seriously felt; it is now supplied by this work of Prof. Perkins. Many years' experi ence in training the youthful mind, and instilling into it the principles of mathematical science, has enabled the author to adapt himself to the dullest comprehension, and to remove the difficulties that have hitherto impeded the scholar's progress. Among the peculiar merits of this work, besides its simplicity, are the conciseness of its rules and definitions; its close and logical reasoning, which calls the powers of the learner into active exercise; and the great number and variety of its examples, which afford every opportunity for extended practice.

Treatise on Algebra: Embracing, besides the elementary principles, all the higher parts usually taught in Colleges; containing, moreover, the new method of Cubic and Higher Equations, as well as the development and application of the more recently discovered Theorem of Sturm. 8vo, sheep, 420 pages.-What the Elements are to Common Schools, this Trea tise is to Academies and Colleges. It will be seen, from the title given above, that it is comprehensive and complete. The principles of the science are combined and arranged on a new plan, which renders the increase in difficulty exceedingly gradual. The method of finding the numerical values of the roots of Cubic and Higher Equations,.and the application of Sturm's Theorem, open up to the student new fields as interesting as they are important. Nothing valuable found in other text-books is omitted; while much that has been gleaned by extensive reading from the later treatises of France and Germany is presented-and that in a form which bears the impress of a master's hand.

The numerous institutions in which the Treatise has been adopted as the standard text-book on Algebra, speak of its practical workings in the highest terms.

Geometrical Series.

BY GEORGE R. PERKINS, LL.D.

Elements of Geometry, with Practical Applications. 12mo, 82C pages. In these Elements it is aimed to strip Geometry of its difficulties, and render it an attractive study. This is effected by giving a practical bearing to every thing that is taught. The pupil is not allowed to grope in the dark, and ask, "What is the use of these demonstrations?" As soon as a principle is explained, it is applied to the practical purposes of life by means of remarks, suggestions, and questions, added in smaller type. This original feature invests Geometry with an interest of which its apparently abstract character has heretofore deprived it.

An Appendix, containing the solution of some geometrical problems by means of Algebra, shows the facility with which difficult cases yield to the analytical method of investigation. The relation between the branches of mathematical science is also made clear by the exhibition of some curious Theorems, evolved by translating the results of algebraic deductions into geometrical language.

Plane and Solid Geometry: To which are added, Plane and Spherical Trigonometry and Mensuration, accompanied with all the necessary Logarithmic and Trigonometric Tables. Large 8vo, 443 pages.-This work is intended to follow the Elements, and gives an extended course in the higher as well as the more rudimental departments of the science, adapted for advanced schools and colleges. It is based on the admirable work of Vincent, revised by Bourdon, which has long been the geometrical standard in the French schools. All that is valuable in Vincent has been taken; but the mathematical attainments and practical skill of Professor Perkins are everywhere exhibited in adapting, modifying, rearranging and adding.

Plane Trigonometry, and its application to Mensuration and Land Surveying, accompanied with all the necessary Logarithmic and Trigonome tric Tables. 8vo, 328 pages. Sheep.-This work is remarkable for its simplicity, and bears throughout the marks of its practical origin.

Works of Herbert Spencer published by D. Appleton & Co.

These discussions are able, vigorous, and suggestive.-American Journal of Science.

They are undoubtedly among the most philosophical and important of the recent issues of the American Press.--Dr. John W. Draper.

It is masterly and valuable beyond all other books on the theme.-Rev. T. Starr King.

These papers are clearly and gracefully written, and illustrate the author's fresh and vigorous spirit, his power of separating the essential from the accidental, as well as his success in grasping the main features of the subject.-Atlantic Monthly.

His book contains more good sense in a small compass, than any book on Education we have ever seen.-Rev. Dr. Hill, Pres. Harvard College.

In breadth of philosophical view, for depth of research in all directions, and for surprising familiarity with the details of nearly every department of science, Mr. Spencer has no competitor among English writers on Education.-Prof. W. F. Phelps, Prin. N. J. Normal School.

It is a mighty book.-Anson Smyth, State School Com. of Ohio.

The most philosophical and able discussion of the principles of Education that has yet appeared.-D. H. Cochran, Prin. N. Y. State Normal School.

It happily illustrates the importance of an intelligent knowledge of physical science as an element of education, I have read it with much pleasure and profit.-Prof. B. Silliman, Jr.

The entire volume claims diligent study, and is replete with suggestions that intimately concern all parents and Educators. Its author is one of the great thinkers of the age.-North American Review.

Its subjects are treated with profound ability and remarkable clearness of thought and extent of research.-N. Y. Observer.

We think it the most important book on the education of children ever written.American Agriculturist.

Profound in analysis, practical in suggestion, and sagacious in theory.-inde pondent.

It throws a rare light upon the importance of studying the natural unfolding of the powers, and ministering to them the proper food at the proper time.-Albion. Rarely have we seen a book of more cogent reasoning than this.-—N. Y. Evening

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