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A L G E B R A.
NOTES AND OBSERVATIONS ;
DESIGNED FOR THE
USE OF SCHOOLS AND PLACES OF PUBLIC EDUCATION,
TO WHICH IS ADDED
APPLICATION OF ALGEBRA TO GEOMETRY.
BY JOHN BONNYCASTLE,
THIRD NEW-YORK, FROM THE LAST LONDON EDITION,
REVISED, CORRECTED, AND ENLARGED, WITH A VARIETY OF EXAMPLES,
AND MANY OTHER USEFUL ADDITIONS,
BY JAMES RYAN,
and Practical," &c.
Ingenuas didicisse fideliter artes
IP, E, Dean, Printer, 36 Stone Street,
Southern District of New York, ss.
BE IT REMEMBERED, That on the twenty-eightb day of December, in the forty-sixth year of the Independence of the United States of America, George Long, of the said district, hath deposited in this office the title of a book, the right whereof he claims as proprietor, in the words following, to wit:
" An Introduction to Algebra, with Notes and Observations; designed for the Use of Schools and places of Public Education. To which is added an Appendix, on the Application of Algebra to Geometry. By John Bonnycastle, Professor of Ma. thematics in the Royal Military Academy, Woolwich. Third New-York from the Last London Edition. Revised, corrected, and enlarged, with a variety of Examples, and many other useful Additions, by James Ryan, Author of an Elementary Treatise on Algebra, Theoretical and Practical, &c.
-Ingennas didicisse fideliter artes
Emollit mores, nec sinit esse feros. Coid.
THE powers of the mind, like those of the body, are increased by frequent exertion ; application and industry supply the place of genius and invention; and even the creative faculty itself may be strengthened and improved by use and perseverance. Uncultivated nature is uniformly rude and imbecile, it being by imitation alone that we at first acquire knowledge, and the means of extending its bounds. A just and perfect acquaintance with the simple elements of science, is a necessary step towards our future progress and advancement; and this, assisted by laborious investigation and habitual inquiry, will constantly lead to eminence and perfection.
Books of rudiments, therefore, concisely written, well digested, and methodically arranged, are treasures of inestimable value ; and too many attempts cannot be made to render them perfect and complete. When the tirst principles of any art or science are firmly fixed and rooted in the mind, their application soon becomes easy, pleasant, and obvious; the understanding is delighted and enlarged ; we conceive clearly, reason distinctly, and form just and satisfactory conclusions. But, on the contrary, when the mind, instead of reposing on the stability of trath and re. ceived principles, is wandering in doubt and uncertainty, our ideas will necessarily be confused and obscure; and every step we take must be attended with fresh difficulties and endless perplexity.