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selves to mechanical pursuits, can no longer be dispensed with in our institutions of elementary education. And it is believed, also, that no production of the kind, well calculated and adapted to the wants and capacities of those acquiring an elementary education, has as yet been offered to the public.
Lord Brougham, in his "Practical Observations upon the education of the People,” very judiciously remarks, that“ a most essential service will be rendered to the cause of knowledge by him who shall devote his time to the composition of elementary treatises on mathematics, sufficiently clear, and yet sufficiently compendious to exemplify the method of reasoning employed in that science, and to impart an accurate knowledge of the most useful fundamental propositions with their application to practical purposes." I do not flatter myself that this brief compend will be thought fully adequate to supply even in this department, all the desiderata to which the above writer alludes, yet I could but be gratified after the work was nearly completed, to find that the views which guided me in its execution harmonized with the opinions of others distinguished as mathematicians and experienced as teachers. The author has aimed to present this treatise in the most condensed form which the nature and importance of the work would admit, well knowing that it is a great encouragement to the scholar to proceed when the end of the task is in view, and that
nothing is more discouraging to a beginner, than to be told that the branch of science he is about to learn extends to a great distance. The apparent length of the labor sets proficiency at so distant a view, that their limited time seems altogether too short to accomplish the desired object, and if the natural desire and thirst for knowledge be thus nipped in the bud by such an unneccessary view of the subject, it will be exceedingly difficult afterwards to make any one apply diligently and cheerfully to the study.
As a school book, it is adapted to lead the mind, and to encourage by rules given in terms which it is believed the scholar can easily comprehend; and even those who have not had an opportunity of devoting their time to the study of mathematics will, it is presumed, with the aid the following pages will afford them, be able to perform their part with propriety in this branch of mathematics.
As my design in the publication of this work was not originality of materials, but rather a plan, arrangement and execution adapted to general use, I have freely consulted the valuable works of Day, Hutton, Gregory and Legendre, authors whose works ought to be examined in the preparation of a compend like this; and I freely acknowledge my indebtedness to their labors, for many valuable ideas. I am aware of the great difficulty of preventing errors from creeping into a work of this kind; and should it be found
to contain imperfections, those who may make the discoveries are respectfully solicited to forward any communications or amendments, to the author, which to them may appear necessary to make the work complete. Should a second edition of the work be called for, the author will furnish a Section on Cask Gauging.
J. M. SCRIBNER.
Auburn, April, 1844.