The following study was carried out by J.P. Bourcier after reading the book Les clés de Vézelay. The intention is to verify the plausibility of the proposed layouts. Contrary to the sequence given in the book, which gives rise to the Gothic crossing from the pre-existing Romanesque nave, Mr. Bourcier carries out this construction in reverse, i.e. from the crossing to the nave. This reverses the direction of the geometric progressions, thus highlighting any discrepancies.

For those who haven't read the book, I must give an explanation, without which the following exercise would remain obscure. Vézelay's nave was built long before the transept crossing. It has 10 bays geometrically formed by equilateral triangles placed head to tail.

The crosspiece is made up of two squares joined by two equilateral triangles. In fact, in Gothic buildings, the crosspiece often takes the form of an equilateral triangle, whereas Romanesque crosspieces tend to be square. Given that these two types of architecture coexist in the basilica, it's clear that the upper part of the Table (based on triangles) was designed to govern the Gothic ensemble, while the lower part (based on squares) was tasked with taking the Romanesque nave into account.
The red segment you can see on the right-hand panel thus takes into account the proportions of the nave's bays. The length it determines is strictly identical to the sides of the bay triangles, i.e. their respective widths. Thanks to this extraordinary geometric property, the Vézelay architect was able to integrate the rhythm of the Romanesque nave into his design (see the Vézelay Tables system).

Basilica plan from Les clés de Vézelay.

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Jean Pierre Bourcier - Budapest July 5, 2019

Since the dawn of time, every design has begun in the same way. A square line must be drawn to define two reference axes. So let's assume that the square line 11 - 22 with center O is drawn. On 11 is carried on either side of O the ½ width of the span in OA and OB; the circle of radius OA is drawn, it intersects 22 in N. The intersection of two arcs of circles of radius OA and center A and N and the intersection of two arcs of circles of radius OA and center B and N define points C and D.

The intersection of two arcs of circles of radius OA with centers A and O, and the intersection of two arcs of circles of the same radius with centers O and B, define points E and F.

The table can then be drawn.

The arc with center B and radius BG is drawn, cutting 11 at G1; the segment CG1 is drawn, defining the width of the nave bay.

The arc of a circle with center C and radius CG1 is drawn, intersecting axis 22 at G3 and the extension of AC at G2.

The triangle CG3G2 is not equilateral, as the perpendicular lowered from G3 to CG2 does not pass through the midpoint M of CG2. The difference in position of the vertex for a span width of 10 m is 22 of 31mm, which is totally negligible compared to the dimensions of the building and the staking tools used.

Here, the emphasis is not on mathematical accuracy, but on simplicity of execution, as the deviation is only perceptible to the initiated.
Transferring the AH segment to AH1 and H1H2, and drawing it symmetrically with respect to 22, defines the second and third enclosures in direction 11.
Transferring the JK segment to JK1 and K1K2, and drawing it symmetrically with respect to 11, defines the second and third enclosures in direction 22.

From this layout, the nave and choir bays can be traced. Villard's routine is applied to bay n, enabling the choir to be traced completely.

This gives us the following breakdown:

All that remains is to draw the narthex, as shown in figure 5, which presents an ambiguity, as the length of the rectangle is different from the length of the rectangle in figure 6, which is the bay width; in relation to the given plan of the basilica, the narthex and nave bay widths are identical. On the other hand, it is specified that the architect at work goes to the other side of the nave aisle to make his layout. The narthex bay width is therefore slightly greater than the nave bay width, which seems to be borne out by the plan.

All these layouts are perfectly realistic, as they use simple geometric shapes - squares and triangles - that are easy to trace. The number of compass openings is three, and only two angles are used: 45° and 60° (or its complement 30°), which are easy to memorize.
We need hardly point out that, until the end of the ^19th century, many tracings were the subject of routines that were memorized and did not require knowledge of their demonstrations, so that workers could use them simply. Take, for example, the routines in the wooden carpentry butcher's booklet.
Where does the golden ratio fit into all this? The best way to find out is to send an SMS to Nicolas Flamel, with a copy to the Comte de St-Germain.