Traditional academic assessments of preliminary or unconstructed mechanical engineering projects often address the authors’ intuitive approaches to this ‘paper engineering’. Estimates for machine studies, compared with detailed calculations for practical engineering projects, were often rooted in similar systematic approaches. In both cases, structural intuitions and measured calculations often extended from standard assessments of proportional geometry. Standard systematic methods helped with updates to projects, from their initial stages to advanced stages. As reflections of antique engineering methods, Renaissance engineers valued these geometric standards for their supposed structural and stylistic reliability and permenance. The present discussion will address Leonardo da Vinci’s systematic approaches to the art of engineering and the means by which he responded to similar approaches in medieval and classical antiquity. Recognized in his plans for treatises on military and mechanical engineering, this work involved research on Greek and Roman systems of proportional geometry. To address a general question with regard to his engineering drawings: for what purposes were they developed? Evidence of their development with systematic proportional methods provides part of the answer.