## Kes an easy roadto the laws o.

E 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 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 t.

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 itsmost interesting applications before he faces the difficulties ofnegative numbers.The third chapter contains a simple explanation of negativenumbers. The recognition of the facts that the real nature ofiiiPREFACE. ivsubtraction is counting backwards, and that the real nature ofmultiplication is forming the product from the multiplicand precisely as the multiplier is formed from unity, makes an easy roadto the laws of addition and subtraction of algebraic numbers, andto the law of signs in multiplication and division. All the principles and rules of this chapter are illustrated and enforced bynumerous examples involv.

Number. In thefirst two chapters only positive numbers are involved, and thelearner is led to see the practical advantages of Algebra in itsmost interesting applications before he faces the difficulties ofnegative numbers.The third chapter contains a simple explanation of negativenumbers. The recognition of the facts that the real nature ofi.