Errata  

The Keys to Vézelay:

There are two errors on the last page of the chapter “The Keys to Light.” A reference is made to Figure 14 instead of Figure 17, while in the text, “solstice” should obviously be read instead of “equinox.”

Les cathédrales retracées :

On page 71, the image does not correspond to the illustration. Here is the correct one:

As in the previous elevations (in the book), two equilateral triangles are positioned within the boundaries of the Table. This construction is supplemented by a ratio of ½ (forming a long square) to establish the starting height of the vaults. For its part, the profile layout consists of a long square—that is, two superimposed squares—on which rises a polygon with a diagonal of 30°.

Let’s verify the theoretical accuracy of this construction. In the first layout, the width of the long square is equal to half the base of the triangles. If I arbitrarily set this base to 100 units, the width of the long square will be 50 units. This is the result we are seeking. 

In the second diagram, we need to know the side length of the squares. Since this is equal to the height of the equilateral triangles, and since those triangles have a base of 100 units, this side will be 86.603 units (thanks, Pythagoras). Drawing a 30° angle from this base of 86.603 is equivalent to drawing a right triangle with a height of 50 units and a hypotenuse of 100 units.

We can thus see that this triangle uses the same segments as the equilateral half-triangles from the first construction. These constructions are linked by common values. Thanks to this simple demonstration, we can see that these systems have exactly the same width. Unlike in Beauvais, where the geometric construction reveals a slight theoretical discrepancy, the elevation of Amiens proves to be perfect!
This masterful design attests to the great skill of Amiens’ architect and commands admiration.