Begin with a square, aligned with the axes of the main temple front, and call its side length 1.000. Set its equator even with the baseline of the main lower entablature, i.e. with the top edges of the lower capitals at height .500. Its top edge will align closely with the top edge of the natural wall behind, seen at left. Draw a circle around the square, noting that its top point at height 1.207 locates the baseline of the second story entablature.
Circumscribe an octagon around the circle, and note that its facet length of .586 establishes the notional span between the axes of the main tetrastyle subtemple; the left hand column is too far to the left, for reasons to be considered below. Within the .586 facet space, step down by quadrature to find the width of the door opening (.148) and the width of the door frame (.207), though this time the alignments are better at right. More precisely, note the vertical alignments at the following heights:
.086---baseline of the central door
.207---baseline of the lateral “windows”
.354---molding on the lateral “windows”
.396---molding on the central door frame
.574---the base of the first story entablature
.646---bottom edge of the column bases in second story
.707---molding on upper statue pedestals
Following up on the octagon theme, step inward twice via octature the circle circumscribing the original unit square, and twice more from the circle of diameter .586 framed by the facets of the first octagon introduced in step Bork2. From the smaller, one finds the following heights:
.388---baseline of the main portal lintel
.750—main molding in the central tholos niche
From the larger, one finds:
.038---baseline of the central portal area
.962---moldings on the upper lateral “windows”
1.104---baseline of the second main entablature.
Note also that the vertical dropped from the diagonal at height .962 conforms closely with the edge of the “window” and the column below on the right-hand side, and that a similar relationship can be made with the next column inward, but that the relationships differ slightly on the left side, suggesting possible confusion on the builders’ part between axes and edges, or between successive steps in the octature process, or both.
To describe the upper part of the structure, step outward with octature, and then build diagonals off of that toward the apex of the composition. More specifically, if one steps out by a single octature step from the original circle seen in step Bork1, the midpoint of its upper facet will be at height 1.041, locating the tops of the column shafts in the second story. This lateral facet of this octagon corresponds closely with the right margin of the structure, and this relationship is perfect in its extension into the Doric frieze of the second entablature. Again, this is less precise on the left side, but the frieze steps inward with respect to the column below, suggesting that the builders had realized their error and were trying to fix it. The diagonal extensions of this octagon converge at height 1.500, a key point on the tholos elevation, and the raking edges of the broken pediment are defined by lines dropping from this convergence point to the points on the outer frame at height 1.153, which is where the original circle cuts its own upper octagon ray. Another horizontal level just above on the outer frame is at height 1.265, one ocature step up from the previous. The tips of the broken pediment are at height 1.367, where their slope is cut the by verticals rising from the intersections at height 1.104. There are key points on the obelisk at height 1.500 and 1.582, where diagonals from the previously described octagons converge, and its tip was probably originally at height 1.672, where an analogous structure once octature step larger would converge.
This is the so-called Monastery from Petra, Jordan. The source image comes from
Judith McKenzie, The Architecture of Petra. British Academy Monographs in Archaeology 1. Oxford: Oxford University Press, 1990, plate 139.