Lines Of Development traces the history of ruled surface geometries and their relationship to architectural design and practice. Much attention has been paid to developable surfaces in building technology recently, especially in the area of digital geometric consultancy. The advent of complex forms in contemporary architecture has necessitated the use of developable surfaces to post-rationalize geometries of double curvature for economy and constructability. In lieu of such remedial measures, these forms might serve as the a priori buildings blocks of a new spatial and tectonic language. These surfaces require specific knowledge of their curvature and isometry for successful deployment. They offer productive resistance in terms of how they permute, generating geometric grammars and legible syntaxes—attributes necessary to bring their virtues into a discursive frame. Lines Of Development traces the history of ruled surface geometries and their relationship to architectural design and practice. Theoretical writings describe the intractable presence and mathematical significance of ruled surfaces throughout the history of architecture leading up to contemporary practice. A collection of case studies with analytical drawings and descriptions show how ruled surfaces are used in historical and current precedents. A geometric primer exhibits various combinatory techniques used to produce formal architectural idioms. Finally, a collection of architectural projects exhibits these geometric design techniques.