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The Reader is now presented with the Third Volume of our SCIENTIFICAL LIBRARY, containing four brief Treatises on LOGARITHMS, APPLICATION of ALGEBRA to GEOMETRY, PLANE and SPHERICAL TRIGONOMETRY. A slight knowledge of these sciences is indispensable to the student, but a very slight knowledge is sufficient. Their elementary principles, and enough of practice to confirm those principles in his mind, are all that is necessary to be given : it would be totally inconsistent with the plan of our Library, which professes to give all that is essential, but nothing more, to swell out our volume with formulæ which are only to be met with in profound investigations far beyond the aim of the general reader. In Spherical Trigonometry, especially, we have limited our Treatise to the exhibition of those formulæ alone which frequently occur in Astronomy and the Elementary Sciences: by which means we have been able to reduce this intricate branch of mathematical knowledge to a very simple form and very trifling dimensions. On the same principle, we have excluded from our Plane Trigonometry everything which was not absolutely necessary to the student, retaining, we hope, everything which will be found at all useful, In our second Treatise the Cartesian method of Algebraic Geometry has been omitted, as being much more remarkable for its elegance than utility. Of Logarithmic and Trigonometric Tables we have given just what may serve as examples of their use and construction: a complete set would occupy many such volumes as ours, and after all be of little use except to one class of readers.

We may add, that the same plan is followed in this as in our preceding Treatises, namely: that of subjoining, under DOUBLE RULES, such principles of each science, as, though not indispensable, might be found of advantage. These may or may not be read, according to the Student's fancy.

Of the above-mentioned four Sciences the various uses and applications will be evident to him who proceeds but a little way in the road to mathematical and physical knowledge. Even in the commonest affairs of life-in accompts, measurements, &c. their utility is scarcely imaginable. They enter, one and all, into every numerical investigation of any magnitude, and are latent in almost every mechanical invention. LAPLACE could not have written his MECANIQUE CELESTE without their help; nor the simplest artificer pursue his trade without, at least, a practical acquaintance with their principles. No more, we apprehend, need be said to gain for these Sciences the notice of every Reader who is desirous to improve his mind or worldly condition.

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