THE 1857 ELEMENTS OF ALGEBRA. DESIGNED FOR THE USE OF COMMON SCHOOLS: ALSO, SERVING AS AN INTRODUCTION TO THE PRINCIPAL "TREATISE ON ALGEBRA." BY GEORGE R. PERKINS, A. M., AND PROFESSOR OF MATHEMATICS IN NEW-YORK STATE NORMAL PUBLIC LIBRARY 47937A ASTOR. LENOX AND R 1922 L Entered, according to Act of Congress, in the year 1844, by GEORGE R. PErkins, in the Clerk's Office of the Northern District of New-York. GANSEVOORT - LANSING STEREOTYPED BY C. VAN BENTHUYSEN & Co. ALBANY. N. Y. PREFACE TO THE SECOND EDITION. Our Common Schools have reached that stage of advancement which enables them to pursue a more extended course of studies than formerly. A few years ago Geographical Studies were hardly known in our Common Schools; now, every chi'd is taught, at least, the elements of Geography. In the same way, Algebra is fast finding its proper place among other branches of an elementary education. In a logical point of view, there is perhaps no science so well calculated to awaken a vigorous and rigid exercise of the reasoning powers as Mathematics. Algebra and Geometry are the two great pillars of this science. Algebra, being more nearly allied to Arithmetic, may be made to precede the study of Geometry. Indeed, Algebra is a sort of universal Arithmetic, and affords great assistance to a clear and correct comprehension of the various Arithmetical rules in frequent use. It cannot, however, be expected, at present, that our Common Schools should pursue Algebra to the same extent as pursued in our Colleges; still they may, to good advantage, acquire the more elementary portions of this branch of Mathematics. With these views before me, I have endeavored to prepare a clear and concise exposition of the Elements of this important branch of Mathematics, which should be adapted to the present wants of our Common Schools. The plan of this work is quite similar to that of my "Treatise on Algebra,” and may in some respects be regarded as an Introduction to that work. |