THE NATIONAL SERIES OF STANDARD SCHOOL-BOOKS. 



Algebra. The student's progress in Algebra depends very largely upon the proper treat- 

 ment of the four Fundamental Operations, The terms Addition, Subtraction, Multiplication, 

 and Division in Algebra have a wider meaning than in Arithmetic, and these operations 

 have been so denned as to include their arithmetical meaning ; so that the beginner 

 is simply called upon to enlarge his views of those fundamental operations. Much 

 attention has been given to the explanation of the negative sign, in order to remove the 

 well-known difficulties in the use and interpretation of that sign. Special attention 'is 

 here called to " A Short Method of Removing Symbols of Aggregation," Art. 76. On 

 account of their importance, the subjects of Factoring, Greatest Common Dirisor, and 

 L<-(ist Common Multiple have been treated at greater length than is usual in elementary 

 works. In the treatment of Fractions, a method is used which is quite simple, and, 

 at the same time, more general than that usually employed. In connection with Radical 

 Quantities the roots are expressed by fractional exponents, for the principles and rules 

 applicable to integral exponents may then be used without modification. The Equation 

 is made the chief subject of thought in this work. It is denned near the beginning, 

 and used extensively in every chapter. In addition to this, four chapters are devoted 

 exclusively to the subject of Equations. All Proportions are equations, and in their 

 treatment as such all the difficulty commonly connected with the subject of Proportion 

 disappears. The chapter on Logarithms will doubtless be acceptable to many teachers 

 who do not require the student to master Higher Algebra before entering upon the 

 study of Trigonometry. 



HIGHER MATHEMATICS. 

 Peck's Manual of Algebra. 



Bringing the methods of Bourdon within the range of the Academic Course. 



Peck's Manual of Geometry. 



By a method purely practical, and unembarrassed by the details which rather confuse 

 than simplify science. 



Peck's Practical Calculus. 

 Peck's Analytical Geometry. 

 Peck's Elementary Mechanics. 

 Peck's Mechanics, with Calculus. 



The briefest treatises on these subjects now published. Adopted by the great Univer- 

 sities : Yale, Harvard, Columbia, Princeton, Cornell, &c. 



Macnie's Algebraical Equations. 



Serving as a complement to the more advanced treatises on Algebra, giving special 

 attention to the analysis and solution of equations with numerical coefficients. 



Church's Elements of Calculus. 



Church's Analytical Geometry. 



Church's Descriptive Geometry. With plates. 2 vols. 



These volumes constitute the " West Point Course " in their several departments. 

 Prof. Church was long the eminent professor of mathematics at West Point Military 

 Academy, and his works are standard in all the leading colleges. 



Courtenay's Elements of Calculus. 



A standard work of the very highest grade, presenting the most elaborate attainable 

 survey of the subject. 



Hackley's Trigonometry. 



With applications to Navigation and Surveying, Nautical and Practical Geometry, 

 and Geodesy. 



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