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THE USE OF THE ROYAL MILITARY ACADEMY.
CHARLES HUTTON, LL.D. F.R.S.
LATE PROFESSOR OF MATHEMATICS IN THAT INSTITUTION.
A new and carefully corrected Edition,
AND ADAPTED TO THE COURSE OF INSTRUCTION NOW PURSUED IN THE
ROYAL MILITARY ACADEMY.
BY WILLIAM RUTHERFORD, F.R.A.S.
ROYAL MILITARY ACADEMY, WOOLWICH.
PRINTED FOR THOMAS TEGG, No. 73, CHEAPSIDE,
THE various works of Dr. Hutton have ever been held in high estimation by a numerous class of instructors, and the intrinsic excellence of his Course of Mathematics has been universally acknowledged.
During the lapse of the last twenty or thirty years, the achievements in science have been varied and extensive. In the higher branches of Mathematics, several elegant and useful theoretical researches have added considerably to the previous stock of knowledge; while in the elementary branches many new and valuable arithmetical processes have been discovered, affording additional facilities to the practical computist. Were proof of this necessary, we have only to refer to the valuable discovery of M. Sturm for the separation of the real and imaginary roots of equations of all degrees—a subject on which energies of every order have been hitherto unavailingly exerted, but which has now yielded to the talents and industry of this ingenious and distinguished continental mathematician. Not less valuable and important have been the results of the researches of our countryman, the late W. G. Horner, of Bath, especially his beautiful, simple, and effective process for the evolution of the roots of numerical equations; which, combined with the theorem of Sturm, furnishes the student with ample means for the complete resolution of any numerical equation whatever.
The Editor of this edition of Hutton's Course has availed himself of these valuable discoveries; and, thinking that a work on elementary mathematics would now be considered incomplete without them, he has not scrupled to devote a sheet or two of this work to the important subject of Equations.