Serapeum of Hadrian’s Villa

Here is the plan of the so-called Serapeum of Hadrian’s Villa, following Favro. The following slides will describe the unfolding of its geometry.

Begin with a large circle, with diameter 31.40m; this is the same as the interaxial width of the Pantheon porch. At the Serapeum, the tangents to this circle align with the inboard faces of the small apses flanking the squarish pool. Within the large circle, construct a smaller one by quadrature, whose diamter will thus be 22.20m, or 75 Roman feet. This smaller circle locates the back surfaces of the niches in the main apse.

The back wall of the main apse behind the niches fits into an orange circle one octature step larger than the smaller red one. The orange circle thus has diameter of 22.20m/cos22.5 = 24.03m. The lower horizontal tangent to this circle locates the front edge of the wall from which the two small apses protrude. The red diagonals tangent to the smaller red circle intersect the red verticals tangent to this same circle in points 26.75m back from the center point of the circular composition, thus locating the approximate midline of the rear wall.

Next, a yellow octagon can be constructed such that its diagonal facets touch the corners of the orange box around the orange circle. Then, a yellow circle can be constructed around the octagon. The octagon will thus have facial diameter of 31.40m/cos22.5 = 33.99m, and the yellow circle will have diameter of 33.99m/cos22.5 = 36.79m. Note that the bottom point on the yellow circle locates the front edge of the squarish pool, and that the left point of the circle locates the middle of the wall between the two narrow halls. The top facet of the octagon, meanwhile, locates the wall to the left of the axial cryptoporticus.

Here the box around the yellow circle appears explicitly to make some of those alignments more visible. Note, for instance, that the bottom green line aligns with the front right wall by the stairs. Meanwhile, in the large central niche of the main apse, diagonals have been drawn from the top of the small red circle down to the yellow rays to the octagon corners. Green verticals rising through these intersection points are 6.47m apart, falling within the walls flanking the axial cryptoporticus. These green verticals intersect the yellow extensions of the octagon facets in points 27.27m beyond the center of the circular composition, thus locating the exterior face of the back wall.

Here we see many new details within this framework. The unfolding arc in the lower right sets the interior wall surface 26.01m from the circle center. (The exterior surface closely matches the intersection of the blue diagonals from the corner of the green box and the midpoint of the yellow octagon, although this mixture seems unappealing). The arc cuts the orange horizontal near the ends of the walls framing the laterial niches. The entrances into the small apses have outer door surfaces aligned with the intersection between the yellow rays and the large red circle. Now, working inward, let us consider the main apse…

The apse diameter measured to the interior wall surface between the niches is 16.99m, i.e. a quadrature factor less than the 24.03m to the outside of the drum. The outer diameter of the outer ring channels is one octature step smaller, measuring 15.70m, and the inside in another such step smaller, at 14.50m, aligning with the columns and frame around the squarish pool. The inner lip of the inner channel is half as large, with a diameter of 7.25m. An octagon whose facial radius is one quadrature factor larger has a facial diameter of 10.26m and a facet length of 4.25m; this latter dimension becomes with width between the walls of the axial cryptoporticus.