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of numerical equations of all degrees. The whole subject is here presented, however, in a condensed form, the student being conducted, in & manner direct as possible, from the theoretical to the practical. The section on the Properties of Equations, it is proper to say, owes its improved character to the able hand of Prof. I. F. QUINBY, of the University of Rochester, whose services in perfecting other books of this Series deserves especial mention.

The effort which has been made in this treatise, to combine the best practical with the highest theoretical character, is specially commended to the notice of the true educator. Great care has been taken everywhere to set forth in distinct form the principles of the science, their exact logical relations being noted by proper references; while due prominence has been given to those numerous precepts and expedients which are so necessary to the constitution of an expert Algebraist.

The design throughout has been, not to conceal, but fully to reveal the difficulties of the science, and to encourage the learner, not to avoid, but to grapple with, and overcome them; since, to the student of Mathematics, labor rightly directed, is discipline,and discipline, after all, is the true end of education.

It is but just to state, that J. C. PORTER, A. M., has had the constant care and supervision of the present work, having also rendered important assistance in the preparation of some other works of the Series,-a fact which, considering his long and distinguished success as a teacher of Mathematics, and his acknowledged ability as a mathematical scholar, ought to afford a sufficient guarantee for the utmost accuracy and classroom fitness on every page.

Thus distinguished for fullness of matter; for scientific arrangement; for ample discussion and rigid demonstration; for clear statement and close definition; for rules brief and of easy application ; for examples numerous, apt and strictly practical; for the nicest adaptation to the purposes of teaching; for the finest mechanical execution; for whatever, in short, care, skill, science and taste can accomplish ;-the New University Algebra is submitted to the public.

July, 1862.

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