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The Collegiate Course. 1. DAVIES' BOURDON'S ALGEBRA. II. DAVIES' LEGENDRE'S GEOMETRY AND TRIGONOMETRY. III. DAVIES' ANALYTICAL GEOMETRY. IV. DAVIES' DESCRIPTIVE GEOMETRY. V. DAVIES' SHADES, SHADOWS, AND PERSPECTIVE. VI. DAVIES' DIFFERENTIAL AND INTEGRAL CALCULUS.

The works embraced under the head of the “ Collegiate Course," were originally prepared as text-books for the use of the Military Academy at West Point, where, with a single exception, they are still used. Since their introduction into many of the colleges of the country, they have been somewhat modified, so as to meet the wants of collegiate instruction. The general plan on which these works are written, was new at the time of their appearance. Its main feature was to unite the logic of the French School of Mathematics with the practical methods of the English, and the two methods are now harmoniously blended in most of our systems of scientific instruction.

The introduction of these works into the colleges was for a long time much retarded, in consequence of the great deficiency in the courses of instruction in the primary schools and academies : and this circumstance induced Professor Davies to prepare his Elementary Course.

The series of works here presented, form a full and complete course of mathematical instruction, beginning with the first combinations of arithmetic, and terminating in the higher applications of the Differential Calculus. Each part is adapted to all the others. The Definitions and Rules in the Arithmetic, have reference to those in the Elementary Algebra, and these to similar ones in the higher books. A pupil, therefore, who begins this course in the primary school, passes into the academy, and then' into the college, under the very same system of scientific instruction.

The methods of teaching are all the same, varied only by the jature and difficulty of the subject. He advances steadily from one grade of knowledge to another, seeing as he advances the con nection and mutual relation of all the parts : and when he reaches the end of his course, he finds indeed, that “science is but know ledge reduced to order."

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