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Eclectic School Geometry.

Ray's Plane and Solid Geometry.
Ray's Geometry and Trigonometry.
Ray's Analytic Geometry.
Schuyler's Elements of Geometry.

Ray's New Elements of Astronomy.
Ray's Differential and Integral Calculus.
Schuyler's Trigonometry and Mensuration.
Schuyler's Surveying, Navigation, and Tables.







THE study of Geometry trains the eye and the hand in drawing its many figures. It calls into action the reasoning faculty in mastering the demonstrations, and especially in inventing demonstrations and solutions for the theorems and problems which are left for the exercise and development of the pupil's own skill. This work demands earnest effort and the power of continuous attention. It is, hence, an excellent stimulus to those very useful traits.

In order that pupils should receive a high degree of benefit from the study, they should be incited to self-effort. The pleasure arising from victory in an attempt at original demonstration will be a powerful stimulus.

In this book, there is much work for the student besides the memorizing of definitions and axioms, and finding the road through an argument to the conclusion, with a guide constantly leading him. Sometimes the path is blazed, and the student must find his way from one mark to the next. Sometimes he must prove himself a woodsman by determining his own direction and selecting his own mode of travel. In practical life, problems refuse to confront us in a series, graded according to difficulty; and promiscuous examples may be so carefully graded as to defeat their most important end. They should, however, be fairly based on preceding principles.

When original work is called for, if there is a general failure on the part of the class, the best plan would be to pass it for the time. Very probably they will have better success with some that follow it. Let it stand as a challenge to renewed efforts.

Pupils can not be timed in this original work. It has very little resemblance to the memorizing of a poem, the mastery of a chapter of history, or the translation of a page of Cæsar.

When a theorem is stated and its demonstration is asked of the class, the pupil who is likely to reach the end in triumph, is he who draws the figure, and, sitting, walking, or standing alone, gives it earnest thought, seeking for known principles which he may link together, and lead to the desired conclusion. If he fail at the first attempt, he comes back with double zeal after an interval of rest. In this persistent effort, he reviews much of his stock of principles, freshens them for use, and, perchance, adds to their number.

While a text-book is an almost indispensable aid to the teacher, it should not do his work for him. He should select theorems and problems from other sources, devise new illustrations of truths discussed and things defined, and constantly put his pupils to the proof.

The maximum of work by the pupil, with its supplementary minimum by the teacher, is perhaps the true maxim.

This treatise has been prepared mainly to meet the wants of teachers and pupils in high schools and normal schools.

By omitting the Exercises, a brief course can be had, but sufficient to prepare for the study of trigonometry and surveying. We would, however, urge that the Exercises be carefully studied.

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