## Book Review: Elements Of Descriptive Geometry With Their Application

Elements Of Descriptive Geometry With Their Application, by Charles Davies

I must admit that this book was not nearly as interested as I hoped it would be. To be sure, geometry can be a very interesting subject, but the approach of this author was not really as interesting as it could have been. A great deal of that relates to the approach of the author, specially since this book was a work in descriptive geometry, and that involves a lot of description and not a lot of worthwhile pictures to illustrate the point. It should be pointed out that there are some drawings here, but they are not really of the informative sort that most people will need in order to understand what the author is saying. If a picture is worth a thousand words in general, this is especially true in the field of geometry, where one is seeking to understand the relationship between lines, angles, planes, and solids. Adopting an approach to such a visually rich subject that relies in verbal description rather than illustration is putting oneself in a dangerous spot, and the result is a book that is far less enjoyable than it could have been. A great many people will find geometry a tough subject to appreciate anyway, but this book is not as enjoyable as it could have been with just a little bit of effort on the part of the author, and that is a great shame.

This book is more than 200 pages long and is divided into thirteen chapters. The author begins with the first principles of descriptive geometry (1), after which there is a chapter that deals with the projections of lines and planes in different angles (2). After that there is a discussion of lines and tangents (3). This is followed by a chapter that deals with curved surfaces and the projection of such surfaces as well as curved lines (4), and then tangents to single-curved surfaces (5) and surfaces of revolution (6). This is followed by a chapter that looks at the intersection of curved surfaces and planes, the tangent lines to these curves of intersection, and the development of surfaces on planes (7) as well as a discussion of the intersection of curved surfaces with other surfaces of their kind (8). The rest of the book is mainly focused on various practical problems related to aspects already discussed (9) as well as the construction of spherical triangles (10), fundamental principles related to spherical projections (11), as well as a chapter on orthographic projection (12) as well as stereographic projection (13), with a closing complement on warped surfaces.

It is difficult to understand why it is that a book like this on descriptive geometry would have to offer for itself anyway. Admittedly, the importance of descriptive geometry in providing encouragement on the development of projective geometry and on areas of drafting and architectural drawing is considerable. Unfortunately, those aspects of descriptive geometry that are the most relevant are those which look at the principles by which one can draw a three dimensional figure as a two dimensional figure, and in general the field is no longer an active one because of advances in contemporary computational power, by which three-dimensional figures can be drawn and manipulated and designed in three dimensions. The fact that this book is obsolete certainly does considerably detract from the pleasure of reading it, but the fact that the field of descriptive geometry is so interconnected with figures and solids and this book is remarkably deficient in figures does not make for the easiest book to appreciate, although it must be admitted that this book does offer some application to interesting fields of geometry, that can be better appreciated in better books.