Piero
della Francesca, *Convenerunt in unum*,
supporting David King’s interpretation (see the article „A Leap of Faith“ in
„Nature“ 29 March 2007) / © Franz Gnaedinger 1991/2007 www.seshat.ch fg(a)seshat.ch fgn(a)bluemail.ch

gia19.JPG / gia20.GIF
/ gia21.JPG / gia22.JPG

conv01.JPG / conv02.GIF / conv03.GIF / conv04.GIF / conv05.GIF / conv06.GIF / conv07.GIF / conv08.GIF / conv09.GIF / conv10.GIF / conv11.GIF / conv12.GIF / conv13.GIF / conv14.GIF / conv01.JPG

Piero della Francesca, *Baptism of Christ*, picture, geometry (square, grid 12 by 12, lower
circle of Christ, pyramid of Christ, upper circle of Holy Spirit present in a
dove), geometry applied to the picture:
gia19.JPG / gia20.GIF / gia21.JPG / gia22.JPG

Piero della Francesca, *Convenerunt in unum* (Flagellation of Christ) conv01.JPG

Frame 24 by 18 units, format 3/4, grid 20 by 14
units conv02.GIF / conv03.GIF

Braccio Fiorentino 58.36 cm; proposed unit for
Piero’s painting 1/16 braccio or 3.6475 cm; frame 65.655 by 87.54 cm or

The picture is slightly larger than the grid 14
by 20 – observe the thin strips under and above the grid: conv04.GIF

Grid applied to the picture, yellow dot: center
of perspective, red dot: center of grid, blue dot: center of small picture
within the picture: conv05.GIF

Small picture within the picture, 12 by 12
units, area 144 square units, one third of the area of the picture and frame
together (18 x 24 = 432 square units):
conv06.GIF / conv07.GIF

Diagonals of the square 12 by 12: conv08.GIF

Geometry applied to the picture: conv09.GIF

The vertical lines of Christ and cardinal Bessarion
divide the length of the picture into 7 plus 6 plus 7 units, the length of the
frame into 9 plus 6 plus 9 units or in the ratios 3/8 and 5/8 (approximating
the golden section). The diagonal connecting the bottom right corner of the
left field 14 by 7 with the top left corner of the right field 14 by7 is hold
by the Roman. Geometry applied to the picture:
conv10.GIF / conv11.GIF
/ conv12.GIF

Left square 14 by 14 plus diagonals, right
field 14 by 7 plus diagonals, applied to the picture: conv13.GIF /
conv14.GIF

The geometrical examination of Piero’s painting
confirms David King’s fine interpretation and suggests a modification as well:
Piero came first, the inscription on the astrolabium for Cardinal Bessarion
second. One may assume that Regiomontanus was a good friend and informal pupil
of Piero della Francesca, well acquainted with the picture, whereupon he
encoded not only the names but also some of the crucial numbers of the painting
into the inscription on the astrolabium honoring Cardinal Bessarion:

length
of grid 20 units –– 20 letters in the first line

height
of frame 18 units –– 18 letters in the second line

from
right side of frame to line of Christ,

from
left side of frame to line of Bessarion

15
units each –– 15 letters in the third line

height
of grid 14 units, big square 14 by 14 ––

14
signs in the last line (count as one
sign)

SUB DIVI BESSARIONIS
DE –– 20 letters

CARDINE DICTI PRASEI
–– 18 letters

DIO ROMAE SURGO
IO –– 15 letters

ANNIS OPUS **:–** 1062
–– 14 signs

For the interpretation of the couplet see David
King. Here just one addendum. The lines of Christ and Bessarion divide the
length of the picture into 7 plus 6 plus 7 units. Divide the first line
accordingly and you get

SUBDIVI BESSAR IONISDE
7+6+7 letters

*Sub divine Bessarionis* ‘under the divine Bessarion’
becomes

SUBDIVI (…) DE

subdivide, a pun by the astronomer and
mathematician Regiomontanus who transformed the painting by his presumed friend
and informal teacher Piero della Francesca
conv01.JPG
into a dedication
to Cardinal Bessarion, encoding both names and numbers of the painting.

Geometry in art,
John the Baptist (reconstructions and interpretations) gia.htm