This textbook aims to present the mathematical sciences in clear, everyday language for apprentices, students and mechanics--willing, industrious, anxious to study at home, yet unable to give time or money for professional teaching. It is trusted that this effort to place before English-speaking students a treatise on arithmetic and algebra, freed from technicalities and expressed in simple language, will assist many who are compelled to study alone; and perhaps it may not be found unwelcome to some who wish to "brush up" their rusty mathematical information, acquired long ago under scholastic methods, and not improved by years of disuse. The writer's share in the work has been something more than that of mere translation. Many new examples have been added, and some bearing solely upon European practice have been omitted. [Adapted from the German by Henry Harrison Suplee.]