Can we appreciate the work of the military engineer Sébastien Le Prestre de Vauban as art? Is there a point at which we can see that this mixture of landscape and architecture transcends its utility as military engineering and becomes an object of aesthetic speculation? Could Vauban himself have regarded his work, at the point when the engineering requirements had been satisfied, as being art? Vincent Scully suggests as much:

It's unlikely that Vauban considered his work as aesthetic in any sense. The concept of sweeps of space was undoubtedly linked, however, to the work of the architects Louis Le Vaux and André Le Nôtre at Vaux-le-Vicomte. Theirs was an reinterpretation of the sweeps of celestial space of Kepler's Three Laws of Planetary Motion as sweeps of terrestrial space, as I describe in my article Vaux-le-Vicomte: Architecture and Astronomy.

Some of my favourite artists use architectural ideas to structure landscape: Richard Serra and Donald Judd, and especially Maya Lin: her Wave Field consists of shapes in the landscape generated by a "naturally occurring repetitive water wave". It is an approach to understanding architecture and landscape that I used fruitfully at the University of East London, Universität Liechtenstein and, most recently, at the University of Dundee, where I ran my Year 4 Design Research Unit: Landscape:Architecture. The reinterpretation of objects not originally conceived as art, such as grain elevators, has acknowledged the - intended or not - aesthetics of engineering. The composer, engineer and architect Iannis Xenakis was captivated by the stochastic trajectories of gunfire during the Second World War.

The development of baroque architecture is often seen as a matter of style or connoisseurship, and dismissed as decorative. Baroque domestic and military architecture was developed by architectural theoreticians and practitioners who not only were familiar with contemporary treatises in mathematics and astronomy but were aware of their practical applications. The shift from renaissance to baroque was fundamentally a shift in knowledge. This is a theme I developed in two articles on Architecture and Astronomy: Vaux-le-Vicomte and The Temple of Apollo at Stourhead.

In the mid-sixteenth century in France a number of factors, interconnected and acting simultaneously, formed an epistemological break or paradigmatic shift in the understanding of space, whether geometrical, astronomical, architectural or topographical: first, the conceptual leap in astronomy of space as infinite with planets in elliptical orbits around the sun, by the German astronomer Johannes Kepler; second, the rediscovery of conic sections - ellipses, parabolas and hyperbolas - in mathematics, in projective and descriptive geometry, by the French mathematician and architect Girard Desargues; third, the practical application of projective and descriptive geometry in architecture and landscape, both in design and construction, by architects such as Louis Le Vaux and André Le Nôtre, and fourth, the application of projective geometry as both a symbolic representation and practical embodiment of the French State in the person of Louis XIV, the Sun-King. Some at least of these factors applied to England, as described by Stephen Johnston and Anthony Gerbino in Compass and Rule: Architecture as Mathematical Practice in England 1500-1750.

The mathematics of conic sections supported a new science of optics. Among the new optical tools were the theodolite and level, made more accurate by the use of the telescope for sighting long distances and microscope for reading vernier scales. The astronomer Jean Picard of the Académie Royale des Sciences, famous at the time for accurately measuring the diameter of the Earth, made a telescopic level for setting out the gardens at Versailles, necessary because of the large basins of water and poor water supply. The sector or military compass could be used used both for surveying and gunnery; Galileo is credited as one of its inventors, published in Le Operazione del compasso geometrico e militare in 1606. The architect Pierre Bullet made a plane table, called a pantomètre, for his pioneering map of Paris; he published Traité de l'usage du pantomètre in 1675, and Traité du nivellement in 1688 as well as Architecture pratique in 1691. Of course, the instruments used for surveying (reproducing the landscape on a small scale on paper) could also be used for setting out designs from drawings at a large scale onto the landscape. We know that Vauban used these surveying techniques because scale models of his fortifications (and many others) are exhibited in the Musée des Plans-Reliefs in Paris, founded for him in 1668.

Military architecture in Europe developed from Italian Renaissance models; bastions had been developed by Giuliano da Sangallo at Poggio Imperiale in 1487 and Antonio da Sangallo the Elder at Civita Castellana in 1494. Antonio da Sangallo the Younger used bastions at an urban scale for the walls of Rome in 1534; by the end of the century a coherent system of fortification called trace italienne had developed. The French soon had their own treatises, such as Jacques Perret: Architectura et perspectiva: des fortifications & artifices [Architecture and Perspective: Fortifications and Fireworks] published in 1601, and Bernard Forest de Belidor. Baroque military engineering did not overturn these designs: it extended them into the landscape.

Conic sections and projective geometry had a practical as well as a conceptual application in architecture. The fabulous precision and inventiveness of French stéréotomie - the geometry of stone cutting - was available for all to see not only in medieval churches, where it was the preserve of maçons [masons], but in renaissance domestic architecture: spiral staircases often appeared as chef d'oeuvres, such as the double spiral at the Château de Chambord (1519-), the tower at the Château de Blois (1515-19), and in innumerable lesser ones. The application of stéréotomie for architects was the design of complex shapes, but it had a practical purpose for masons: stone needed to be cut swiftly and accurately in yards on the ground and then hoisted into position on the work site. This could mean, in domestic architecture, the intersection of a window - trapezoidal in plan and with a vaulted head - in an oval room, and in military architecture an embrasure - trapezoidal in plan, perhaps falling to the exterior in section and with a vaulted head - in an irregular bastion, and in fact just this type of design problem appeared in Frézier's La Théorie et la Pratique de la Coupe des Pierres [The Theory and Practice of Stone Cutting] of 1737.

Thomas Deckker
London 2022