Dimensions and trimming of the MS

[Jorge_Stolfi]

I include the figure here:

Maybe someone already did this plot, but anyway here it goes again:

   
The sizes are in pixels of Rene's GIF image.

It seems that the sizes cluster close to the aspect ratio heigh/width = sqrt(2) ≈ 1.414 (the straight diagonal line).  

That is the ratio of the ISO "A"-series paper sizes.  It has the property that f you divide a sheet with that aspect ratio in half, each half again has the same aspect ratio.

Moreover, there seems to be some clustering just below certain sizes.  With my superior pareidolia, I can see two series of book sizes, the blue rectangles and the green rectangles. Could these be two regional sizes?  Or maybe one is for vellum, the other for parchment?

In each series the dimensions are related by powers of sqrt(2), as if the bifolios were obtained from a standard raw sheet size, with the "A" aspect ratio, by zero or more halvings and rotations. Each book would be eventually trimmed to get even folio edges, so the final size would be a few mm less than the ideal dimension predicted by this theory.

The two series seem to be offset by a  factor close to sqrt(sqrt(2)). That is, the size of each blue rectangle is the geometric mean of the two nearest green rectangles, and vice-versa.  (I may note that computing sqrt(2) and the geometric mean of two lengths are basic exercises of Euclidean geometry.)

All the best, --stolfi

A = Med.Gr.1, ONB, Vienna
B = Voss.Lat. Q.9, Leiden
C = Graecus 1, Napoli
D = MS Grec 2179, BN Paris
E = MS Plut. 73.41, Bibl. Medicea Laurenziana, Florence
F = CLM 337, Munich
G = Ms M 652, Pierpont Morgan library
H = MS Bodley 130
J = MS Harley 1585
K = Cod. Vind. 93, ONB, Vienna
L = MS or. Arabe 4947, BN Paris
M = MS Plut. 73.16, Bibl. Medicea Laurenziana, Florence
N = Egerton 747
O = MS Lat. 6823, BN Paris
P = Ms.Canon Misc.408, Bodleian, Oxford
Q = MS 459, Bibl. Casanatense, Roma
R = MS Aldini 211, Pavia
S = Egerton 2020
T = Chigi F. VII 159, BA Vaticana
U = MS 106, Bibl. Dip. Di Botanica dell'Universita, Florence
V = MS Lat 17844, BN Paris
W = MS Hebr. 1199, BN Paris
Z = Voynich MS.