The Ellipse and the Oval in the Design of Spanish Military Defence in the Eighteenth Century

The Spanish military engineers built several U-shaped strongholds during the eighteenth century, using the geometrical constructions of the ellipsis et ovum . In the project on paper, engineers used the oval because of its ease of layout, but they could use either of the two figures in the staking of the fortifications. In 1704 Vicente Tosca published a methodology for building infinite ovals from its main axes. The assessment of the staking of the artillery platform of San Jorge reveals that the trace can be based both on the ellipse as the oval shape, since they have negligible difference on the scale of construction. The ellipsis et ovum discussion had a linguistic aspect from the perspective of applied mathematics, since different geometrical approximations for these artillery platforms may converge.