NEW SYSTEM OF MATHEMATICS, WITH THE ADDITION OF A COMPLETE READY RECKONER, FOR THE USE OF FARMERS, MECHANICS, &c. NEW YORK: PRINTED BY WILLIAM H. COLYER, No. 5 HAGUE-STREET. PREFACE. THE science of numbers is universally conceded to be an important one to every class in the community. In its cultivation and attainment all are deeply interested. The merchant, the mechanic, the professional man, the manufacturer, agriculturist, and labourer also require, in a greater or less degree, an acquaintance with its principles, on a correct understanding of which depend their prosperity in the prosecution of their several pursuits. The intricacies that have entered into this branch of necessary knowledge, have detered many from undertaking its successful acquisition. The labour, the time, the study required to achieve a complete mastery over numerical science, interpose formidable objections to the system that has been so long established; which, although it commands respect for its age, yet its numberless defects furnish often almost insurmountable difficulties to its easy and rapid attainment. To reduce the science of numbers to a greater degree of simplicity and facility of acquisition; to introduce into the plan of antiquated theories an easier, a surer, and quicker method of computation, is an important desideratum, one that necessarily interest the actors in every department of business, and recommends itself to the favourable consideration of the community. Many, who have in some measure thrown off the shackles of prejudice, and have endeavoured to become reformers in this interesting field of enterprise, have failed substantially in accomplishing any very important results. They who would be improvers in oral, mental, and practical arithmetic and mathematics, have not as yet been able, with all their investigation, to present to the world a plan, by means of which these branches of science may be taught by a simplified method, and communicated with facility and precision to the understandings of the learners. To remedy these defects, and to supply the means for facilitating the acquisition of arithmetical and mathematical knowledge, has engaged much of the time and attention of the author of this work: the persevering efforts made have been crowned with complete success; and the author begs leave to tender his congratulations to the public on the important improvement thereby made to the cause of arithmetical and mathematical science, whereby its acquisition is rendered more easy and more certain, requires much less time in its practical operations than heretofore, and reduces it to so simple a system, that even the most obtuse understanding can readily comprehend its principles. The saving of time is always an important item in the calculation of business; and the more rapidly correct computative results can be arrived at, the better for those who have embarked in their transaction. This important improvement in the science of numbers, by which much time is saved and greater certainty obtained, is now about to be introduced to the public, for their approbation and acceptance. By way of exposition, it is necessary to state, that the whole of the principles of the science generally are contained and expressed in three words, viz. INCREASE. DECREASE. EQUALITY. Increase and decrease comprise addition, subtraction, multiplication, and division. Equality is the answer required, fixed by the question propounded under two different names, after which it is represented or expressed by a statement or equation, reduced by increase and decrease to the lowest term, equality, or the answer required. The science thus far concentrated, nothing remains but to simplify expressions or statements, to facilitate increase and decrease, which constitute the purport of the present publication. It is expected that the fundamental principles of the science will be taught by gradual and persevering practice; it will liberate the minds of the teachers from the imperious necessity of propounding useless and irrelevant questions, and conduct the understanding along the avenues of knowledge, until the principles in which the science is based are fully understood. A progressive and reasonable instruction will enable teachers to make pupils of every grade in society perfectly acquainted, at the age of twelve years, with the science generally, adapted completely to the attainment and prosecution of mercantile, mechanical, and mathematical knowledge. For a number of years it was the constant study of the author to bring into organic operation his simplified plan of instruction, as regulated by his fundamental principles. This method of calculation affords the power of performing calculations in whole numbers, even when the question is composed of whole fractions, or number and fractions. By an easy process in the statement the fractions are rejected, the solution or calculation is performed by the pure proportion of all variation of measure, weight, money, &c., of the whole world, entirely by whole numbers and in an uninterrupted series. It teaches to obtain, by a succession of pure proportion, an answer to any arithmetical proportional question proposed. The rule of three, or the rule of proportion, named also the "golden rule," has not this power. By this rule we are often compelled to make four, five, and more statements before we are able to obtain the answer required. These proceedings, by the common rule of calculation with fractions, render the process circumstantial and confused to the scholar, and difficult to impress on his memory; but the rule of pure proportion teaches, in an easy, agreeable, and unavoidable manner, all the rules in general, as rule of three, tare, barter, fellowship, interest, reduction, loss and gain, exchange, and others; and even in the solution and statements of these questions, wherein it is now necessary to employ |