## Use this book will learn how.

Le questions of arithmetical progression and of geometricalprogression are so interesting in themselves, and show so clearlythe power of Algebra, that it will be a great loss not to take theshort chapters on these series.The last chapter is on square and cube roots. It is expectedthat pupils who use this book will learn how to extract thesquare and cube roots by the simple formulas of Algebra, andbe spared the necessity of committing to memory the long andtedious rules given in Arithmetic, rules that are generally forgotten in less time than they are learned.Any corrections or suggestions will be thankfully received bythe author.A.

In each of these three chaptersa considerable number of problems is given to state and solve.By this means the learner is led to exercise his reasoning faculty,and to realize that the methods of Algebra require a strictly logical process. These problems, however, are divided into classes,and a model solution of an example of each class is given as aguide to the solution of other examples of that class.The course may end with the chapter on quadratics, but thePREFACE. vsimple questions of.

Mplicity, great care has been givento the explanations of the fundamental operations and rules, thearrangement of topics, the model solutions of examples, and themaking of easy examples for the pupils to solve.Nearly all the examples throughout the book are new, andmade expressly for beginners.The first chapter clears the way for quite a full treatmentof simple integral equations with one unknown number. In thefirst two chapters only positive numbers are involved, and thelearner is led to see the practical advantages of Algebra in its.

Ations with two unknownnumbers, and a chapter on quadratics follow in order. Only onemethod of elimination is given in simultaneous equations andone method of completing the square in quadratics. Moreover,the solution of the examples in quadratics requires the squareroots of only small numbers such as every pupil knows who haslearned the multiplication table. In each of these three chaptersa considerable number of problems is given to state and solve.By this means the learner is led to exercise his reasoning faculty,and to realize that the methods of Algebra require a strictly logical process. These problems, however, are divided into classes,and a model solution of an example of each class is given as aguide to the solution of other examples of that class.The course may end wi.

Model solution of an example of each class is given as aguide to the solution of other examples of that class.The course may end with the chapter on quadratics, but thePREFACE. vsimple questions of arithmetical progression and of geometricalprogression are so interesting in themselves, and show so clearlythe power of Algebra, that it will be a great loss not to take theshort chapters on these series.The last chapter is on square and cube roots. It is expectedthat pupils who use this book will learn how to extract thesquare and cube r.

On square and cube roots. It is expectedthat pupils who use this book will learn how to extract thesquare and cube roots by the simple formulas of Algebra, andbe spared the necessity of committing to memory the long andtedious rules given in Arithmetic, rules that are generally forgotten in less time than they are learned.Any corrections or suggestions will be thankfully received bythe author.A teachersâ€™ edition is in press, containing solutions of examples, and such sugges.