Errata

Keys to Vézelay:

There are two errors on the last page of the "Keys of Light" chapter. A reference is made to figure 14 instead of figure 17, whereas in the text it should obviously read solstice instead of equinox.

Traced cathedrals :

On page 71, the image doesn't match the demonstration. Here's the right one:

As in the previous elevations (in the book), two equilateral triangles are mounted between the limits of the Table. This construction is completed by a ½ ratio (which forms a long square) in order to fix the starting height of the vaults. For its part, the layout of the profiles is formed by a long square, i.e. two superimposed squares, on which rises a polygon with a diagonal of 30°.

Let's check the theoretical accuracy of this construction. In the first layout, the width of the long square is equal to the half-base of the triangles. If I arbitrarily set a value of 100 units for this base, the width of the long square will be 50 units. This is the result to be obtained.

In the second plot, we need to know the sides of the squares. Since this is equal to the height of the equilateral triangles, and the latter have a base of 100 units, the side will be 86.603 units (thanks Pythagoras). Drawing a 30° angle from this base of 86.603 amounts to drawing a right-angled triangle with a height of 50 units and a hypotenuse of 100 units.

This triangle uses the same segments as the equilateral half-triangles in the first drawing. These constructions are linked by common values. Thanks to this simple demonstration, we can see that these systems have strictly identical widths. Unlike Beauvais, where the geometric construction expresses a slight theoretical discrepancy, the Amiens elevation proves to be perfect!
This masterly layout bears witness to the great science of the Amiens architect, and commands admiration.