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which boys are apt to think have no application. They furnish a drill that is just as valuable to those who are not preparing for college as for those who are.

These problems are not to take the place of other geometries, but are to be used with them. And, therefore, the division into Books is made to correspond pretty closely with that of the geometries in most general use.

The use of the metric system is began at the very first, simple as that necessarily makes the problems of the first book, for the most part. No other book contains a graded set of problems on the first two books of geometry.

No apology is considered necessary for putting in quite a number of problems which presuppose some knowledge of algebra.

The order of the problems is not the same as the order of the propositions of any geometry ; neither are all the problems which illustrate an important principle placed together. The reason for this is obvious. Still, the order of the problems in the different books is approximately the same as the order of the propositions in the most popular text-books. On account of this difference in order it will be best to keep the text-book work somewhat ahead, unless one cares to select the problems beforehand to give out with the text-book lesson. Some may prefer to use the problems only with the review of the geometry.

Boys preparing for college will certainly take a lively interest in the questions, problems, and exercises selected from the college entrance papers.

The entrance papers were selected with great care, with the hope that they may prove helpfully suggestive both to teachers and pupils.

The discussion of logarithms, the explanation of their use, and the use of the table have been made as simple and clear as possible.

Only such symbols are used as are almost universally employed.

Some few proofs are put in because they are not found in all the text-books.

Notice of errors, or any suggestion, will be gratefully received.


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