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The work on A bra of which this volume forms the first part, is 80 far elementary that it biua at the beginning of the subject. It is not, however, intended for the use of absolute beginners. The teaching of Algebra in the earlier stfes ought to consist in a gradual generalisation of A rithmetic; in other words, Algebra ought, in the first instance, to be taught as A rithmetica Universalia in the strictest sense. I suppose that the student has gone in this way the length of, say, the solution of problems by means of simple or perhaps even quadratic equations, and that he is more or less familiar with the construction of literal formula, such, for example, as that for the amount of a sum of money during a given term at simple interest Thi it becomes necessary, if Algebra is to be anything more than a mere bundle of unconnected rules, to lay down generally the three fundamental laws of the subject, and to proceed deductively -in short, to introduce the idea of A lgdn-aic Form, which is the foundation of all the modem developments of Algebra and the secret of analytical geometry, the most beautiful of all its applications. Such is the course followed from the beginning in this work. QS OS i ,,,.
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