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DISTRICT OF MARYLAND ;—TO WIT.

BE IT REMEMBERED, That on the Twenty-third day of March, and in the Thirty-first year of the Independence of the United States of America, L. I. M. Chevigne, of the said District, hath deposited in this office the title of a Book, the right whereof he claims as Proprietor, in the words and figures following:--to wit:-"Mathematical Manuel, for the use of Colleges and Academies. Volume First; containing four Parts, viz. ithmetic, II Elements of Algebra, "II Practical Arithmetic, IV. Practical Algebra." In conformity to the Act of the 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."

PHILIP MOORE,

Clk. Dist. of Maryland.

ཁ་་་ཐ་

34-45 INTRODUCTION.

5221;

THE object of the two firft parts has been to prefent to the young learner, in the most concife terms, the reasous of the various operations in Arithmetic and Algebra.

The principal fcope of a college education being to unfold and expand the intellectual faculties of youth, and no study being better calculated for that purpose than that of the Mathematics, it would be a great mistake to offer to the mere exertions of memory, a fcience chiefly intended to exercise and cultivate the understanding Experience, befides, has fhewn, that a system of routine requires a much longer time, and is attended with much greater labor, both for the teacher and the pupil, than that which is wholly founded upon reason.

We may add, that a youth thus taught, as it were, mechanically, will foon lofe all the fruits of his long and painful efforts, unless he is in the way of a continua practice, and (a mifchief of ftill greater magnitude) that fuch a method tends to damp that activity of the mind the nobleft prerogative of the human species above the brute creation.

With an intention, therefore, of giving memory as little as possible to do, the two firft parts exhibit only general rules, often easier to be understood than particular methods, and which being few in number, are of course more easily retained, and at once present to view, in a small compafs, the whole fyftem of the science.

The first part contains a new method for the rule of three. The general manner in which all queftions on this rule are confidered, fuperfedes the diftinction of direct and inverse; a fource of difficulty for beginners, and of confufion for practitioners. Experience feems to have proved in favor of this method.

Algebra has been reduced to fuch questions as are fuffi cient to understand application of Algebra to geometry, conic fec tions, fluxions, and the application of the fluxionary calculation` to fome ufeful questions in mechanicks and hydro-dynamicks.

No general method has been given for folving the equations of the third and fourth degrees; because the process is long and laborious, and leads to general formulæ extremely complicated, which are truly interesting to none but profound algebraifts; fince, in practice, all particular cases can be folved by the way of trial, as it has been explained.

The third part is a felection from the books generally ufed in fchools, of the questions and examples which have appeared moft interesting All the methods of contraction in ufe have been given, with an explication of their theory, in order that the learner may fully understand the reasons of all the operations they are made to perform. Such pupils as may be destined to fituations in life, which require a great practice of calculation, will find in this third part, all the methods and examples conducive to that purpose.

The fourth part contains feveral rules and problems of Algebra.

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