Silver, Burdett and Company, 1934

**Preface**

In this text solid geometry is so presented that the student will gain (1) a knowledge of the properties of planes and lines in space; of polyhedrons, cones, cylinders, and spheres; (2) further practice in the processes of logic which were begun in plane geometry; (3) a realization that he must understand solid geometry if he wishes to comprehend nature and art and the fascinating and diversified developments of modern means of communication, transportation, construction, and fabrication; and (4) skills and attitudes that will be helpful as a part of the training essential in meeting his own personal problems of everyday living.

As examples of these attitudes the following are cited: (1) geometry is a science of necessary conclusions; (2) it wrestles with difficult problems; (3) it tolerates no guessing or jumping at conclusions; and (4) it requires strict attention to the whole problem with discriminating use of the means at hand to obtain a solution.

In this text the student's attention is directed repeatedly to the relations of solid geometry to other school subjects, such as algebra, trigonometry, geography, and physics. The functional relations of geometric quantities are emphasized, thus tying up solid geometry with modern scientific thinking. Relations of solid geometry to various phases of modern life outside the classroom are also dealt with in exercises. Attention should be directed especially to the problems which contain data of actual work of present-day steel fabrication, refractories, and public utilities.

INTRODUCTION

BOOK VI. LINES AND PLANES IN SPACE

Lines Parallel or Perpendicular to a Plane

Parallel Planes

Dihedral Angles

Locus and Projection

Polyhedral Angles

BOOK VII. POLYHEDRONS, CYLINDERS, AND CONES

Prisms

Pyramids

General Polyhedrons

Cylinders

Cones

BOOK VIII. THE SPHERE

Circles of a Sphere

Tangents

Area and Volume of a Sphere

Spherical Triangles and Polygons

Useful Reference Material

Alternative Proofs

Helpful Material for Teachers