THE

TEACHER'S ASSISTANT

IN THE

COURSE OF MATHEMATICS ADAPTED TO THE METHOD OF

INSTRUCTION IN THE AMERICAN COLLEGES :"

COMPRISING

QUESTIONS, GENERAL PRINCIPLES, EXPLANATIONS

AND SOLUTIONS:

Entered according to the act of Congress, in the year 1835, by

W. WRIGHT, in the Clerk's Office of the District Court of Connecticut.

PRESS OF P. B, WHITMORE, NEW HAVEN,

Lyman 6-26-36 32.490

TO TEACHERS.

This volume is, by one of your number, dedicated to you. Whatever of value it may possess in

your estimation, you will not doubt that it has cost no small sacrifice, a necessary concomitant, as you are well aware, of writing and publishing works of this kind; a sacrifice sufficient, it is presumed, to exonerate the individual who has made it, from the charge of being mercenary. You will not, I trust, think that the

I proffering assistance in this form, supposes you incompetent to aid yourselves. Situated as most teachers are, no apology is needed for having recourse to helps in the form here presen. ted. With the charge of some thirty pupils, pursuing differ. ent branches, the labor nesessary for a clear explanation of a difficult problem, and that while the attention is distracted, cannot ordinarily fail to interrupt the order, and impair the interests of the school. It is true that our academies and higher schools should be better endowed with instruction ; but this cannot reasonably be expected from the present inadequacy of liberally educated men. To teachers situated as we have supposed, and as in fact the great body of them are, the as. sistant humbly offers its aid. And, while it is designed especially for teachers of this class, it is believed that there are portions of the work not wholly unappropriate to all teachers of mathematics,

In setting apart this treatise to you, it is of course implied that it is not intended for your pupils. Still, if judiciously

iv

used, it would not be without its value to them. It certainly could not fail to diminish some evils that are almost necessarily incident to the present system of instruction. Reference is had to the use of solutions in manuscript, which are usually accessible to the least deserving, occasioning a very unequal dis. tribution of labor among members of the same class. These helps save even the labor of transcribing; and from their great diversity, often elude detection. If there was but one version of them, the teacher would have little difficulty in dis. covering their use. This uniformity would naturally follow the use of this volume, and furnish the teacher with facilities for detection, the fear of which is always the greatest restraint upon any course considered disreputable. But there are ma. ny who have little to do with solutions readily furnished, or even with assistance directly from their instructors. The in dustry and originality of such would be encouraged by whatever should assist the teacher in adjudging to each his proper degree of merit. If therefore, your pupils make use of this book, it will, in an important sense, be an assistant to you.

So far as a plan of the work has been presented to others, I have the pleasure of knowing that their sentiments cheerful. ly coincide with mine. It is pretended to be no “ royal road to geometry,” or to any branch of mathematics ; but that it may alleviate burdens, in some instances, painfully borne, and facilitate many to the means of preparing themselves for em. inent usefulness,--especially, that it may save from neglect mathematical studies, when the walls of the institution shall have been left, and text books deserted, is the earnest desire of its

AUTHOR.