The experienced teacher will observe:

(a) The economy of arrangement.

Many of the smaller figures are placed at the side of the

page rather than at the center.

The individual numbers of

theorems are omitted.

(b) The superior character of the diagrams.

(c) The omission of the words "since" and "for."

The advance statement is made and the reason asked for and usually cited. The inquiring mind fails to understand the force of preceding and following some statements with the same reason.

(d) Originals that are carefully classified, graded, and placed after the natural subdivisions of the subject-matter. (e) The independence of these originals.

Every exercise can be solved or demonstrated without the use of any other exercise. Only the truths in the numbered paragraphs are necessary in working originals.

(f) The setting of every theorem, corollary, and problem of the text proper in fullface type.

(g) The consistent use of such terms as "vertical angles," "vertex-angle," "adjacent angles," "angles adjoining a side," and others.

(h) The full treatment of measurement and the illustrations of the terms employed.

(i) The summaries that precede earlier collections of original exercises.

(j) The emphasis given to the discussion of original constructions.

As in all subjects that are new to a class, the successful teacher will be content with short lessons at the beginning, and will progress slowly until the class is thoroughly familiar with the language and the general method and purpose of the new science.

The author sincerely desires to extend his thanks to those friends who, by suggestion and encouragement, have inspired him in the preparation of these pages.

THE WILLIAM PENN CHARTER SCHOOL,

PHILADELPHIA.

EDWARD R. ROBBINS.

PLANE GEOMETRY

INTRODUCTION

1. Geometry is a science which treats of the measurement of magnitudes.

2. A definition is a statement explaining the significance of a word or a phrase.

Every definition should be clear, simple, descriptive, and correct; that is, it should contain the essential qualities or exclude all others, or both.

3. A point is that which has position but not magnitude. 4. A line is that which has length but no other magnitude.

5. A straight line is a line which is determined (fixed in position) by any two of its points. That is, two lines that coincide entirely, if they coincide at any two points, are straight lines.

6. A rectilinear figure is a figure containing straight lines and no others.

7. A surface is that which has length and breadth but no other magnitude.

8. A plane is a surface in which if any two points are taken, the straight line connecting them lies wholly in that surface.

9. Plane Geometry is a science which treats of the properties of magnitudes in a plane.

10. A solid is that which has length, breadth, and thickA solid is that which occupies space.

ness.