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IN WHICH THE PRINCIPLES OF OPERAT.
ING BY NUMBERS
MADE FAMILIAR BY A GREAT VARIETY OF USEFUL AND INTERESTINO
EXAMPLES, CALCULATED AT ONCE TO ENGAGE THE PUPIL IN THE
DESIGNED FOR THE USE OF
SCHOOLS AND ACADEMIES
IN THE UNITED STATES.
BY DANIEL ADAMS, M. D.
KEENE, N. H.
PUBLISHED BY J. & J. W. PRENTISS.
MORE, AND CINCINNATI, OHIO.
DISTRICT OF NEW HAMPSHIRE.
District Clerk's Office. BB IT REMEMBERED, That on the eighteenth day of September, A. D. 1827, in the fifty-second year of the Independence of the United States of America, DANIEL ADAMS, of said district, has deposited in this office the title of a book, the right whereof he claims as author, in the words following, to toit :
" ARITHMETIC, in which the Principles of operating by Numbers are ana. lytically explained, and synthetically applied ; thus combining the Advan. tages to be derived both from the inductive and synthetic Mode of instructing: the whole made familiar by a great Variety of useful and interesting Examples, calculated at once to engage the pupil in the Study, and to give him a full Knowledge of Figures in their Application to all the practical Purposes of Life. Designed for the Use of Schools and Academies in the United States. By DANIEL ADAMS, M. D., Author of the Scholar's Arithmetic, School Geography, &c."
In conforrnity to the act of Congress of the United States, entitled, “An Act for the encouragement of learning, by securing the copies of maps, charts, and books, to the authors and proprietors of such copies during the times therein mentioned;" and also to an act, entitled, “An Act supplementary to an act for the encouragement of learning, by securing the copies of maps, charts, and books, to the authors and proprietors of such copies during the times therein mentioned; and extending the benefits thereof to the arts of designing, engraving and etching historical and other prints."
CHARLES W. CUTTER,
Clerk of the District of New Hampshire. A true copy.
Attest, C. W. CUTTER, Clerk.
There are two methods of teaching,—the synthetic and the ana lytic. In the synthetic method, the púpil is first presented with a gencral view of the science he is studying, and afterwards with the particulars of which it consists. The analytic method reverses this order : the pupil is first presented with the particulars, from which he is led, by certain natural and easy gradations, to those views which are more general and comprehensive.
The Scholar's Arithmetic, published in 1801, is synthetic. If that is a fault of the work, it is a fault of the times in which it appeared. The analytic or inductive method of teaching, as now applied to elementary instruction, is among the improvements of later years. Its introduction is ascribed to PESTALOZZI, a distinguished teacher in Switzerland. It has been applied to arithmetic, with great ingenuity, by Mr. COLBURN, in our own country.
The analytic is unquestionably the best method of acquiring knowledge; the synthetic is the best method of recapitulating, or reviewing it. In a treatise designed for school education, both methods are useful. Such is the plan of the present undertaking, which the author, occupied as he is with other objects and pursuits, would willingly have forborne, but that, the demand for the Scholar's Arithmetic still
continuing, an obligation, incurred by long continued and extended patronage, did not allow him to decline the labor of a revisal, which should adapt it to the present more enlightened views of teaching this science in our schools. In doing this, how. ever, it has been necessary to make it a new work.
In the execution of this design, an analysis of each rule is first given, containing a familiar explanation of its various principles; after which follows a synthesis of these principles, with questions in form of a supplement. Nothing is taughi dogmatically; no technical term is used till it has been first defined, nor any principle inculcated without a previous development of its truth; and the pupil is made to understand the reason of each process as he proceeds.
The examples under each rule are mostly of a practical nature, beginning with those that are very easy, and gradually advancing to those more difficult, till one is introduced containing larger numbers, and which is not easily solved in the mind; then, in a plain, familiar manner, the pupil is shown how the solution may be facilitated by figures. In this way he is made to see at once their use and their application.
At the close of the fundamental rules, it has been thought advisable to collect into one clear view the distinguishing properties of those rules, and to give a number of examples involving one or more of them. These exercises will prepare the pupil more readily to understand the application of these to the succeeding rules ; and