640px Stonehenge renderSarsen Circle (blue) within the preexisting outer circle of Stonehenge

It is important to see the practical problems faced by the builders of megalithic monuments.  By 3000 BC, Stonehenge was the ring now called the the Aubrey Circle, a set of postholes now thought sockets for bluestones brought from the Preseli hills in Wales. Other rings of postholes were dug in the centuries following, the Z and Y-rings, these perhaps containing 30 and 29 sockets for bluestones but not properly concentric with the Aubrey Circle or evenly spaced. Around 2500 BC, a new and complex design was carefully and concentrically placed within the area within the Y-ring. It has been suggested its design was influenced by the dynastic cultures of Egypt which had their own megalithism of pyramids and obelisks, employing faced masonry and stone joints but now in the British idiom of stone circles natural to higher latitudes. The Aubrey Circle came to be just as dynastic Egypt began whilst the Sarsen Circle was built in the middle of the second dynasty (Old Kingdom) (2625-2510). 

An interesting way to have placed the new Sarsen Circle was proposed by Rory Fonseca in 1995 [ref 1], and we can compare this with other suggestions and suppositions. Fanseca proposed a technique familiar to the Gothic architects, called Ad Quadratum. Ad Quadratum uses the properties of a square to form a module of expansion or contraction in size through the step and repeat process of drawing alternate squares and squares tilted 45 degrees to them, in which: the corners of the lesser square touches the center points of the sides of the greater square. This technique is easily applicable to concentric circular structures because the four central points, of the sides of each square, defines where an inscribed circle with a diameter equal to the side length of the square touches that square. 

We will not go further in this article than to show what happens if one applies a decreasing ad quadratum sequence within the Aubrey Circle, using the best traditional survey made by Alexander Thom (with Richard Atkinson) in 1972-3. 

Thom Stonehenge Quadratum

Figure 2 Using Ad Quadratum three times to establish the location of the Sarsen Ring of Stonehenge

In figure 2 the larger red circle runs through the Aubrey Circle whilst the smaller red circle runs around the inside of the (remaining stones of) the Sarsen Circle. One can see from visual inspection that the hypothesis works well. I also include the blue lines, with the caveat that geometries laid over a site plan can lead to many coincidences not always intended by the actual builders. The outer circle appears to enclose the reverse-henge order at Stonehenge of its outer bank then ditch ("Although having given its name to the word henge, Stonehenge is an atypical henge in that the ditch is outside the main earthwork bank." Wikipedia).

In his article, Fanseca analyses the other concentric features inside the Sarsens using the method of geometric means found in ad quadratum, then comparing with Thom's own methods [ref 2]. His style is clear and he appears to throw light on how the inner monument we call Stonehenge, might have been designed based on the knowledge of the properties of square numbers and geometries found in 1800 BC in Old Babylonia viz. YBC 7289 [pdf] and deducible in the megalithic from their familiarity with measured geometries. Many people see geometrical relationships as a static and out-of-time relatedness whilst the monument builder is actively generating solutions to their overall plan. An alternative to the above was provided by Robin Heath in Sun, Moon and Stonehenge who saw two geometric procedures, based upon the heptagon (7) and the octagon (8), as implied between the circles (see figure 3).

Heath Robin SMS fig9.7

Figure 3 Robin Heath's solution to the location of the Sarsen Circle in Sun, Moon and Stonehenge. The outer circle is Aubrey and inner the Sarsen.

Robin Heath's proposal of both seven and eight fold geometries reminds us there are 56 Aubrey holes in its Circle. However, the octagon model is in conflict with the sides of the station stone rectangle being 12 long and 5 wide since the inner angle is 22.6 degrees whilst division by 16 leaves 360 degrees split into 22.5 degree sectors. The virtue of the heptagon design is that the Sarsen's radius can be seen as in the ratio 12 units to the Aubrey's 19 units, and the key numbers of time between the sun and moon are the 12 month lunar year, 12 7/19 month solar year thence a 19 solar year Metonic of 235 months, the megalithic yard being 19/7 feet, the Egyptian cubit 12/7 feet and so very on... in an implex of meaning that surrounds the monument as the expression of a mature numerical tradition. 

References

1. Fonseca, Rory. "STONEHENGE: ASPECTS OF AD QUADRATUM GEOMETRY." Journal of Architectural and Planning Research 12, no. 4 (1995): 357-65. http://www.jstor.org/stable/43029177.

2. Thom, Alexander. "Megalithic Remains in Britain and Brittany.", Oxford: Clarendon: 1978. chapter 11. Try: https://smile.amazon.co.uk/Megalithic-Remains-Britain-Brittany-Thom/dp/0198581564/

3. Heath, Robin. "Sun, Moon and Stonehenge: Proof of High Culture in Ancient Britain". Cardigan: Bluestone Press 1998. Try: https://smile.amazon.co.uk/gp/offer-listing/0952615177