This book examines the evolution of machine design methodology from the Renaissance to the Age of Machines in the 19th century. This premise is based in part on the work of da Vinci scholar Ladislo Reti who translated the last discovered work of Leonardo da Vinci in 1967. In the Codex Madrid, Reti found evidence that Leonardo planned to write a book on basic machine elements and compared the great artist-engineers drawings to the work of 19th C. machine theorist Franz Reuleaux of Berlin. Reuleaux is credited with classifying the basic elements of machine design and also enumerating six basic classes of mechanisms to change motion from one form to another. Moons book carries Retis thesis further and provides detailed analysis, comparing design concepts of engineers of the 15th century Renaissance and the 19th century age of machines from a workshop tradition to the rational scientific discipline used today. The design ideas of Leonardo and Reuleaux are placed in the historical, economic and social context of their times. There is also an appendix with a short description of the famous theatre of machines books of the 15th to the 18th centuries. This book makes use of the unique collection of 230 kinematic models of Reuleaux at Cornell University. Detailed comparisons of 20 basic machine mechanisms such as the slider crank and four-bar linkages in both Leonardos drawings and Reuleauxs models are made. These models illustrate the elegance and aesthetics of machine design in the 19th century pioneered by Franz Reuleaux. The book hopes to convince the reader that the development of a rational design methodology for machines that grew from the time of Leonardo to the early 20th century was as great a feat as the invention of the machines themselves.