SOLUTION BOOK

CONTAINING

SYSTEMATIC SOLUTIONS OF MANY OF THE

MOST DIFFICULT PROBLEMS.

Taken from the Leading Authors on Arithmetic and Algebra, Many Prob.
lems and Solutions from Geometry, Trigonometry and Calculus,
Many Problems and Solutions from the Leading Math-
ematical Journals of the United States, and

Many Original Problems and Solutions.

WITH

NOTES AND EXPLANATIONS

BY

B. F. FINKEL, A. M., M. Sc.
Member of the London Mathematical Society, Member of the American
Mathematical Society, Editor of the American Mathematical
Monthly, and Professor of Mathematics and

Physics in Drury College.

THIRD EDITION— REVISED.

KIBLER & COMPANY, PUBLISHERS,

Springfield, Mo.

1:13 F5 1319

PREFACE.

This work is the outgrowth of eight years' experience in teaching in the Public Schools, during which time I have observed that a work presenting a systematic treatment of solutions of problems would be serviceable to both teachers and pupils.

It is not intended to serve as a key to any work on mathematics; but the object of its appearance is to present, for use in the schoolroom, such an accurate and logical method of solving problems as will best awaken the latent energies of pupils, and teach them to be original investigators in the various branches of science.

It will not be denied by any intelligent educator that the socalled “Short Cuts” and “Lightning Methods” are positively injurious to beginners in mathematics. All the "whys” are cut out by these methods and the student robbed of the very object for which he is studying mathematics; viz., the devolpment of the reasoning faculty and the power to express his thoughts in a forcible and logical manner. By pursuing these methods, mathematics is made a mere memory drill and when the memory fails, all is lost; whereas, it should be presented in such a way as to develop the memory, the imagination, and the reasoning faculty. By following out the method pursued in this book, the mind will be strengthened in these three powers, besides a taste for neatness and a love of the beautiful will be cultivated.

Any one who can write out systematic solutions of problems can resort to "Short Cuts” at pleasure; but, on the other hand, let a student who has done all his work in mathematics by formulæ, “Short Cuts,” and “Lightning Methods” attempt to write out a systematic solution - one in which the work explains itself — and he will soon convince one of his inability to express his thoughts in a logical manner. These so-called "Short Cuts" should not be used at all, in the schoolroom. After pupils and students have been drilled on the systematic method of solving problems, they will be able to solve more problems by short methods than they could by having been instructed in all the “Short Cuts” and “Lightning Methods” extant.

It can not be denied that more time is given to, and more time wasted in the study of arithmetic in the public schools than

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