From the PREFACE. The following work is not a series of speculations. It is but an analysis of that system of mathematical instruction which has been steadily pursued at the Military Academy nearly half a century, and which has given to that institution its celebrity as a school of mathematical science. It is of the essence of that system that a principle be taught before it is applied to practice; that general principles and general laws be taught, for their contemplation is far more improving to the mind than the ...
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From the PREFACE. The following work is not a series of speculations. It is but an analysis of that system of mathematical instruction which has been steadily pursued at the Military Academy nearly half a century, and which has given to that institution its celebrity as a school of mathematical science. It is of the essence of that system that a principle be taught before it is applied to practice; that general principles and general laws be taught, for their contemplation is far more improving to the mind than the examination of isolated propositions; and that when such principles and such laws are fully comprehended, their applications be then taught, as consequences, or practical results. This view of education led, at an early day, to the union of the French and English systems of Mathematics. By this union the exact and beautiful methods of generalization, which distinguish the French school, were blended with the practical methods of the English system. The fruits of this new system of instruction have been abundant. The graduates of the Military Academy have been sought for wherever science of the highest grade has been needed. Russia has sought them to construct her railroads;* the Coast Survey needed their aid; the works-of internal improvement of the first class in our country, have mostly been conducted under their direction; and the war with Mexico afforded ample opportunity for showing the thousand ways in which science--the highest class of knowledge--may be made available in practice. All these results are due to the system of instruction. In that system, Mathematics is the basis--Science precedes Art -- Theory goes before Practice--the general formula embraces all the particulars. Although my official connection with the Military Academy was terminated many years since, yet the general system of Mathematical instruction has not been changed. Younger and able professors have extended and developed it, and it now forms an important element in the education of the country. The present work is a modification, in many important particulars, of the Logic and Utility of Mathematics, published in the year 1850. The changes in the Text, seemed to require a change in the Title....
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