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Entered according to Act of Congress, in the year 1887,

by Richard A. Proctor, in the Office of the Librarian of Congress, at Washington.


The object I have had in view in preparing this little work (which appeared first in the pages of KNOWLEDGE) has been to remove for young students in geometry the difficulties which I remember encountering when a beginner myself. Teachers and books explained then, as now, how certain problems are to be solved, but they did not show how the student was to seek for solutions for himself. They strove to impart readiness in following demonstrations rather than facility in obtaining solutions. My method of showing here why such and such paths should be tried, even though some may have to be given up, in searching for the solution of problems, will, I believe, do more to teach the young student how to work out solutions for himself than any number of solutions given him for reading.

The notes to the first two books of Euclid and

added propositions—a knowledge of which is absolutely essential for success in solving problems—are subsidiary to the purpose of this little treatise. The similar study of later books may be commended to students more advanced than those for whom

I have written here.


ST. JOSEPH, Mo. : May 1887.

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