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First Principles.

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My purpose is to help the whole business of teaching, even from the very first foundation, that is to say, not only what is given in the Grammar School, and what follows afterwards, but also the elementary training which is given to infants from their first entrance, until they are thought fit to pass on to the Grammar School. In my manner of proceeding I propose to follow the precedent of those learned authors who have treated with most credit of this and similar subjects, in first laying down certain principles to which all readers will agree. By this means it is possible to pass on to the end without challenge, or if any difficulty should arise, it can always be resolved by a reference to these principles. In mathematics, which offers the best model of method to all the other sciences, before any problem or theorem is presented, there are set down certain definitions, postulates, axioms, to which general assent is asked at the outset, and on which the whole structure is built up. I am the more inclined to adopt this method, because I am to deal with a subject that must at the first be very carefully handled, till proof gives my treatment credit, whatever countenance hope may seem to lend it in the meanwhile.

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