From the INTRODUCTION. How can a solid having three dimensions be exactly represented upon a surface having but two dimensions? This is the problem which Descriptive Geometry seeks to answer. As the theoretical basis of its answer it develops certain laws of relationship which connect the figure in space with its expression in a plane. These laws belong to Projective Geometry and are rigorously mathematical; when, however, actual representations of real objects are attempted, the results will be approximations of varying degrees of accuracy according to the skill of the artist. Descriptive Geometry is an art when it exercises a student in its methods; a science, when it reveals a strictly mathematical basis for its methods. To the technologist, as the architect or mechanic, it is not only necessary that the representation should be derived from the original and suggest it in a general way, but it is even more imperative that the original itself, which may have been a material object or only a creation of the imagination, may be reproduced by the skilled workman with the aid of the representation in tangible, material form, in every smallest detail of shape and measurement. Because rectangular or orthographic projection accomplishes this twofold object best, it has generally been allowed to usurp the whole domain of Descriptive Geometry, and it is not the purpose of this little book to depart greatly from the usual though inadequate interpretation of the science. For the sake of special descriptive properties easily understood, the more general science of Projective Geometry is drawn upon for a few isolated propositions.