Geometry of bastion fortifications magistral line: influences and development

Abstract

In the middle of the 15th century, the fortification system of medieval European cities underwent a transformation into a bastion fortification system. This system will dominate until the mid-19th century, experiencing its zenith by the late 17th century with the improvements of the French military engineer Vauban. A defining feature of this system is the distinct contour of the magistral line in the ground plan, with its geometry progressing from simplicity in the early stages, to comprehensive solutions that addresses dimensions of all elements within bastion fortifications, in the final ones. Our research encompasses the geometric principles used by four selected military engineers from this period (Marolois, de Ville, Pagan, Vauban) with the aim to identify the development of geometric procedures in the design of the magistral line. We explore the specifics and differences in their approaches and methodologies. Conducting a comparative analysis of the geometric principles employed by different builders, using the example of star fortresses, we follow the progression of theoretical framework and design aspirations underlying the key elements of the magistral line. We consequently consider whether the “Vauban style” is a spontaneous creation of a single genius, or an outcome that emerged from the collective contributions of numerous predecessors across Europe. This paper spotlights the principles of bastion fortress design based on geometry, offering a way to identify markers of influence in observed examples, and also to complement non-invasive methods of cultural heritage preservation with adapted 17th-century geometric procedures, making them more compatible with modern approaches.

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