THEORETICAL AND PRACTICAL ARITHMETIC: IN WHICH THE PRINCIPLES OF THAT SCIENCE ARE CLEARLY AND FULLY EXPLAINED; BEING INTENDED AS AN INTRODUCTION TO THE Wigher Branches of Mathematics. BY BEZOUT. ENLARGED, AND ADAPTED TO THE USE OF YOUNG TRADERS,* BY F. PEYRARD, EX-PROFESSOR OF MATHEMATICS AND ASTRONOMY OF THE ROYAL TRANSLATED FROM THE FRENCH, IMPROVED AND ADAPTED BY NOBLE HEATH. NEW-YORK : PUBLISHED BY SAMUEL WOOD & SONS, 261 PEARL-STREET, AND Southern District of New-York, ss. IT REMEMBERED, That on the tenth day of August, A.D. 1825, NOBLE HEATH, of the said district, hath deposited in this office the title of a book, the right whereof he claims as Proprietor, in the words following, to wit Bin the fiftieth year of the Independence of the United States of America, "A Theoretical and Practical Arithmetic: in which the Principles of that Science are clearly and fully explained; being intended as an Introduction to the Higher Branches of Mathematics, By Bezout. Enlarged, and adapted to the use of young Traders, Bankers, &c. &c. By F. Peyrard, Ex-Professor of Mathematics and Astronomy of the Royal Bourbon College, &c. &c. Translated from the French; improved, and adapted to the Currency of the U. S. By Noble Heath." 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," and also to an Act, entitled "An Act, supplementary to an Act, 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 extending the benefits thereof to the arts of designing, engraving, and etching historical and other Prints." JAMES DILL, Clerk of the Southern District of New-York. PREFACE. MATHEMATICAL Sciences, above all others, delight us by the ease and certainty with which they attain their object. He who habituates himself to a close examination of their fundamental principles, and of the mutual dependence and connexion of these principles, acquires a justness of conception, a conciseness of reasoning, and a strength of judgment, scarcely attainable by any other means. As Arithmetic may justly be considered the basis of mathematical science, the knowledge of its principles is an acquisition of great importance, and books in which those principles are clearly and fully developed, form a desideratum the want of which has long subjected both teachers and students to much inconvenience;-the arithmetics in common use being generally an assemblage of rules and examples without demonstration. The study of such rules is uninteresting and wearisome; and the scholar, after having committed them to memory, and learned by their means, to perform arithmetical calculations, as it were, mechanically, quits the study entirely ignorant of the principles upon which they subsist; and if, as is often the case, he forgets these dogmas, he loses with them all the fruits of his labour. On perusing the present work in the original, I was struck with the ease and perspicuity of the style, in which Bezout has developed the principles and demonstrated the different operations of arithmetic; and from a full persuasion that it would be a great relief to teachers, and amply reward the investigation of the industrious student, I determined upon its translation. In the execution of my design, I have ́endeavoured to keep as near to the original, as the genius of our language, and the adaptation of the work to the commerce of this country, would permit. The explanation of the signs made use of in the work, the elucidation of duodecimals, some practical examples, and the insertion of the table of logarithms from one to ten thousand, instead of a small table from one to two hundred, are the principal augmentations which I have thought proper to make. The text of Bezout is numbered according to the order which he established; and the parts marked with an asterisk, are the augmentations made by F. Peyrard, which form a very valuable addition to the elegant original. New-York, 1825. THE TRANSLATOR. |