Pattern cutting as applied to sheet-metal work. by its very nature, involves the application of geo-metrical principles. Any treatise on descriptive geometry presents in a general way all the principles that enter into the science of pattern cutting. To those who have had the advantages of a mathematical education these principles are well known and by such their application is easily made. For the benefit of those, however, who have not had such advantages, this work purposes to make specific application of those principles in a way to be readily understood by the mechanic. While throughout the work the use of an unnecessary number of technical terms and words not in common use among mechanics will be carefully avoided, it must he here noted that precise language in describing all geometrical figures and operations becomes a necessity, and therefore compels the employment of some terms not in the every day vocabulary of the workshop, which it is proper to define and explain at the outset. As the language of the workshop is usually far from accurate and varies with the locality, every student of this book will find it greatly to his advantage to give careful attention to this and the other introductory chapters for the purpose of increasing and improving his vocabulary, and of enabling him to more readily comprehend the demonstrations in the pages following. The list of terms herein defined has not been restricted to the barest requirements of the hook, hut has been made to include nearly all the terms belonging to plain geometry, and such architectural terms as are usually met with in problems relating to cornice work. The terms are arranged first logically, in classes, after which follows an alphabetical list by which any definition can be readily found.

1. Geometry is that branch of mathematics which treats of the relations, properties and measurements of lines, angles, surfaces and solids.

2. Sheet-Metal Pattern Cutting is founded upon those principles of geometry which relate to the surfaces of solids, and may be more accurately described as the development of surfaces, under which name its principles are now being taught to a great extent in schools of practical instruction. Articles made from sheet metal are hollow, being only shells, and must, therefore, be considered in the process of pattern cutting as though they were the coverings or casings stripped from solids of the same shape.

3. A Point is that which has place or position without magnitude, as the intersection of two lines or the center of a circle; it is usually represented to the eye by a small dot.