Book excerpt: An illustrated step by step explanation of the many mathematical problems encountered in fabricating metal components for for the variety of industries where they would be needed. The book gradually progresses from the most basic principals of determining true length to the manufacture of complex transition pieces involving geometry and trigonometry, and is meant to be kept as a reference guide throughout both the apprenticeship stage and the tradesman's full career. The author has over 45 years experience in the heavy engineering industry which explains the practical, step by step approach.