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PRE FACE.

THE student is recommended to go through this treatise in the following order :

First, to master the ‘Preliminary Algebra,' and not to go further until he finds that, when covering up the right-hand column and setting himself any question in the left-hand column, he can at once work out (not merely supply from memory) the required answer.

Secondly, taking the Algebraical Enunciation which stands at the top of the right-hand column in each Proposition, to learn to supply the proof which follows it. To do this, he should cover the rest of the right-hand column, and try to work out the proof for himself, with the help of the directions in the left-hand column. As every step of the work has been already done in the Preliminary Algebra,' this ought to be possible without any reference to the right-hand column: but if any difficulty should occur, there will usually be found a marginal reference to the · Preliminary Algebra,' and it will be better to turn back to the section referred to, and so refresh the memory, than to look at the right-hand column, which should only be uncovered, when the proof has been written out, as a test of the correctness of the work.

Thirdly, to practise himself in working out the same proofs, without the help of the directions in the left-hand column, from the Algebraical Enunciations only. These are given by themselves at p. 49.

Fourthly, taking the Enunciation printed in small type in each Proposition, and covering up all below it, to learn to express it algebraically, as given in the first sentence of the right-hand column.

Fifthly, taking the Enunciation printed in large type in each Proposition, and covering up all below it, to learn to repeat it with the addition of algebraical symbols for the magnitudes, as given in the small-type Enunciation.

Sixthly, to learn Euclid's Definitions and Axioms, given at p. 53.

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