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The present performance having passed through a number of editions since the time of its first publication, without any material alterations having been made, either with respect to its original plan, or the manner in which it was executed, I have been induced, from the flattering appro, stion it has constant ly received, to undertake an entire revision of the work; and, by availing myself of the improvements that have been subsequently made in the science, to render it still more deserving the public favour.

In its present state, it may be considered as a copious abridgement of the most practical and useful parts of my larger work, entitled, A Treatise on Algebra, in 2 vols. 8vo. published in 1813; from which, except in certain

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cases, where a different mode of proceeding appeared to be necessary, it has been chiefly compiled: great care having been taken, at the same tịme, to adapt it, as much as possible, to the wants of learners and the general purposes of instruction, agreeably to the design with which it was first written.

With this view, as well as in compliance with the wishes of several inte.

gent teachers, I have, also, been led to subjoin to it, by way of an Appendix, a small tract on the application of Algebra to the solution of Geometrical Problems; which, it is hoped, will prove acceptable to such classes of students as may not have an opportunity of consulting more voluminous and ensive works on this interesting branch of the science.

JOHN BONNYCASTLE.

Royal MILITARY ACADEMY,

WOOLWICH,
October 22, 1815.

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