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THE design, in making this Compilation, is to collect suitable exercises to be performed by the Classes at the private Lectures on Mathematics, given in the University. The view, which the CORPORATION had of the great advantages, that the Students might derive from a judicious work of the kind, produced this attempt to promote their improvement. The parts of the most approved writings, selected for the purpose, are copied, with only such alterations, as appeared to be useful. The Authors of the principal part of most of the branches are Dr. Hutton and Mr. BONNYCASTLE; the Navigation is principally from that of Mr. Nicholson; and much use has been made of a Manuscript, containing certain mathematical exercises to be performed by the Students, Mole's Algebra, the Works of Emerson, CRAKELT's translation of Mauduit's Treatise on Spheric Trigonomety, and Kelly's Spherics. IN ISOf

1808

3-7809

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Respecting the Second Edition.

In compiling this work, when I was Hollis Professor of Mathematics and Natural Philosophy, such parts of the most approved writings on the several branches of Mathematics, contained in it, as seemed best adapted to the purpose, were selected; and such alterations and additions made, as appeared to be useful, or conducive to the accomplishment of the proposed object. Some variations from the first are to be found in this edition, which, having occurred to observation in using and reviewing the work, were deemed to be advantageous. To diminish the difference of the two volumes in bulk, the first is extended to the end of Mensuration of Superficies. Beside this the most material alterations in the first volume are reduce tion, in a few arithmetical articles, of matter merely practical, and unnecessary for the purpose of illustrating the principles ; and the addition of Notes to most of the Geometrical Problems, containing the prin ples, on which their solutions respectively depend. Notice of the principal alterations in the second vol, ume is prefixed to it.

S. W. Cambridge, April 18, 1808.

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