BE IT REMEMBERED, That on the Twenty-third day of March, and in the Thirty-first year of the ladependence 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. ondi Arithmetic, 11. Elements of Algebra, “ IIS, Practical Arithmetic, îy. 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, Cik. Dist. of Maryland. Armsaid ? 44-45 INTRODUCTION. THE object of the two first parts has been to present to the young learner, in the most concise terms, the reasons of the various operations in Arithmetic and Algebra. The principal scope 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 science chiefly intended to exercise and cultivate the understanding Experience befides, lias thewn, 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 soon lose all the fruits of his long and painful efforts, unless he is in the way of a continua practice, and (a mischief of ftill greater magnitude) that such a method tends to damp that a&ivity of the mind the noblest prerogative of the human species above the brute creation. With an intention, therefore, of giving memory as little as possible to do, the two first parts exhibit only gere eral 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 compass, the whole system of the science. The first part contains a new method for the rule of three. The general manner in which all questions on this rule are considered, supersedes the diftin&ion of direct and inverse ; a source of difficulty for beginners, and of confusion for practitioners. Experience seemn; to have proved in favor of this method. Algebra has been reduced to such questions as are fufficient to understand application of Algebra to ge.metry, conic fece tions, fuxions, and the application of the Aluxionary calculation to some useful questions in mechanicks and hydro-dynamicks. No general method has been given for folving the equations of the third and fourth degrees; because the proceso is long and laborious, and leads to general formule extremely complicated, which are truly interesting to none but profound algebraists; fince, in practice, all particular cases can be solved by the way of trial, as it has been explained. The third part is a selection from the books generally used in schools, of the questions and examples which have appeared nost interesting All the methods of contra&tion in use 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 exainples conducive to that purpose. The fourth part contains several rules and problems of Algebra. . - Examples 90 192 Examples NUMERATION P/GE 51 Questions 226 Examples 244 98 Denomination Tables 196 Examples 233 Addition 31 Division 102 Examples 203 Examples 254 Subtraction 40 Fractions 105 Examples 206 Examples 254 Multiplication 40| Exponents 107 Eramples 207 Radical Quantities 109 Contractions 208 Examples 255 Practice 2111 Involution 111 Questions 215 Examples 256 Division 47) Evolution 118 Questions 218] Equations 121 Alligation 53 Equations of the Ist degree 123 } |