Excerpt from Solid Geometry
The Solid Geometry is prepared for the same purpose and with the same general features as is the Plane Geometry. In both books the two main characteristics are analysis and emphasis.
One of the great objectives in education is to train young people to attack difficulties through an analysis of the problems presented. It is because of this fact that both the Plane and the Solid Geometry are prepared as suggestive method texts with the suggestions in the form of a logical analysis.
Moreover, if the mind is to retain any lasting impression of the work covered, distinctions in emphasis are necessary. The material presented in both the Plane and the Solid Geometry has been arranged with this fact in mind. Attention is called particularly to chapters ii, iv, and v. Chapter ii discusses the nature and properties of the various surfaces and solids ordinarily studied in solid geometry with the exception of the sphere, which is studied in chapter iii. All areas and volumes are considered in chapter iv. Similarity is considered in chapter v.
There are several advantages gained from this arrangement. It enables the pupil to take up the study of areas and volumes with a clear idea of the solids considered. It makes possible a more logical arrangement of material. Cylinders are compared with prisms and cones with pyramids when the properties of these solids are studied; but as the volume of the pyramid is obtained from that of the prism, a different order is used when volumes are studied. Moreover, the theorems concerning areas and volumes may be worked into a logical whole when considered together, which is not possible in the traditional arrangement.
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This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works. Это и многое другое вы найдете в книге Solid Geometry (Classic Reprint) (Mabel Sykes)