DISTRICT OF MARYLAND ;—To Vmt. 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 :—ta wit:— "Mathematical .Manuel, for the use of Colleges and 'S.Aq^cmiQS. .Vuhi(ne First; containing four Parts, vix. ^^(sftC^^tdwRstathm'tic, . 11. Elements of Algebra, "ll|i Practical Arithmetic, IV Practical Algebra." Ill 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. Ditl. of Maryland. r\ HE object of the two firft parts his been to prefcntto the young learner, in the moil concife terms, the reafotis 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 fludy being better calculated for that purpofe than that of the Mathematics, it would be a great miftake to offer to the mere exertions of memory, a fcienoe chiefly intended to exercife and cultivate the underftanding fcxperienctvbefid','s, has fhewn, that a fyflem of routine requires* much longer time, and is attended with much greater labor, both for th: teacher and the pupil, than that which is wholly founded upon r'afon. We may add, that a youth thus taught, as it were, mechanically, will foon lofe all the fruits of his long and painful efforts, unlefs he is in the way of a continue piaclice, and (a mifchief of ftill greater magnitude) that fuch a method tends to damp that activity of the mind the nobicft prerogative of the human fpecies 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 eafier to be underftood than particular mclfads, and which being few in number, are of courfe more ealily retained, and at onee prefent to view, in a fmall compafs, the whole fyftcra of the fciencc. The rirft part contains anew method for the rule of threeThe genera! manner in which all queftions on this rule are •onfidired, fuperfedes the diflindion of direS and inverfe; a fource of difficulty for beginners, and of confufion for practitioners- Experience feem, to have proved in favor of this method. Algebra has been reduced to fuch queftions as are fiifficient to underftand application of Algebra to ge.metry, conic fee' iiorn, fluxion, and the application of the fluxionary calculation to fome ufeful queflions in mecianicki and hydro-dynamickt. No genera! method has been given for foiling the equations of the third and fourth degrees; becaufe the procef* is long and laborious, and leads to general formula; extremely complicated, which are truly interefUng to none but profound algebraifts; fince, in practice, all particular cafes can be folved by the way of trial, as it has been explained. The third part is a (election from the books generally ufed in fciiools, of the queftions and examples which have appeared mod interefting All th ; methods of contraction in ufe have been given, with an explication of their theory, in order that the learner may fully underftand the re a fans of all the operations they are made to perform. Such pupils as may be deftined to Situations in life, which require a great practice of calculation, will find in this third part, all the methods and examples conducive to that purpofe. The fourth part contains Several rules and problems of Algebra. |