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"The Old Testament Trinity" of Andrey Rublyov: Geometry and PhilosophyAuthor(s): Alexander V. VoloshinovSource: Leonardo, Vol. 32, No. 2 (1999), pp. 103-112Published by: The MIT PressStable URL: http://www.jstor.org/stable/1576693.
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HISTORICAL
PERSPECTIVE
T h e l d Testament
r i n i t y
o
n d r e y
Rublyov
Geome t ry n d
hilosophy
Alexander
V Voloshinov
ANDREY
RUBLYOV AND
HIS
OLD TESTAMENTTRINITY
Andrey
Rublyov
(1360-1370-1430)
is
the
pride
and
glory
of
Russian culture. The creator of the
famous Old Testament rin-
ity
(Fig.
1)
was one of
the
three most
significant
persons
of
medieval
Russia;
the other two
being Sergius
of Radonezh
(1321-1391)
and
Dmitry
Donskoy
(1350-1389).
This Russian
trinity
left such a
deep
trace on the national
culture that all
three were canonized
by
the Russian
Orthodox
Church. If
the names of Sergius of Radonezh and Dmitry Donskoy sym-
bolize the
spiritual
and
military
renaissance of
Old
Rus and
the first
steps
towards liberation
from the
Mongol
and Tartar
yoke,
the name
of
Rublyov
is
connected not
only
with
the
flowering
of Russian art
but also with the revival
on Russian
ground
of
the
Byzantine
art
that had been ruined
in the
Osmanli
fire
[1].
Already
in
Rublyov's
lifetime
his icons
were
worth their
weight
in
gold: they
were
hunted
by
collectors,
who did not
stop
far from violence
and fraud.
Rublyov's
authority
was
so
high
that,
when
the canons
of
painting
the
Trinity
were
con-
sidered at the
Stoglavy
Sobor
in
1551
in
Moscow,
the verdict
was
unequivocal:
"To
paint
from ancient
samples
like Greek
artists
painted
and like
Andrey Rublyov painted
.
.."
[2].
It is
quite
understandable that, since the name of
Rublyov
was so
popular,
there
appeared
a
huge
number
of icons as-
cribed
to the hand of the
great
master.
The wave
of uncritical
attitude
towards the
heritage
of
Rublyov
was followed
by
a
hypercritical
one.
Nowadays
only
one
icon of
Rublyov's
circle
(excluding
the
famous frescos
from the
Cathedral
of
the
Dormition
of the
Virgin)
is an
undoubtedly genuine
work.
But
what an icon it is
It is the
masterpiece
of the
great
mas-
ter-the icon
Trinity
rom the
Trinity
Cathedral
in
the
Trinity-
St.
Sergius Monastery.
In
Sergiev
Posad
(thanks
to the
glory
of
Sergius
of
Radonezh and
Andrey Rublyov
this
small
town
not far from
Moscow
became the
capital
of
the
Russian Or-
thodox
Church).
Still the exact date
of creation
of
the icon
is
unknown-it could be either 1411 or 1425-1427 [3].
If the name
of
Rublyov
personifies
the art
of Old
Russia,
Trinity ymbolizes
the
highest peak
of
that culture.
Rublyov
and
his
Trinity
ecame
synonyms
for
the
Russian
people,
and
for a
foreigner
the whole
history
of Russian Art
is
not
infre-
quently
overshadowed
by
this
glaring peak.
What
marvels,
startles and almost scorches us
in
Rublyov's
work s not at
all the
subject,
or the numeral
"three,"
r the
cup
on the Communion able
... but the fact that
it
showed
us
truly
he Revelationbeheld
by
him.
Among
the restlesscir-
cumstances
of
the
time,
among
the
discords,
the local
wars,
the
generalsavagery
nd the
Tartar
nterventions,
among
this
lack of
peace
thathad
depravedRus,
there
opened
to the
eye
of
the soul this
infinite,
imper-
turbable,
indestructible
peace,
"the
lofty peace"
of
the celestial
world
.
. .
And this
inexplicable
world
. . .
this
incomparable sky-
blue-not the
earthly sky-blue,
but the
true
heavenly azure,
this
unspeakable
dream of
Lermontov,
who
longed
for
it,
this
ineffable
grace
of the mutual
bows,
this
peaceful
unwordliness,
this infi-
nite
submissiveness to
each
other-we consider the artistic
contents
of
the
"Trinity"
4].
ABSTRACT
The
philosophical
nd heo-
logical
ontent
of a
masterpiece
of
OldRussian
con-painting-
Andrey ublyov's
rinity-is
e-
garded
n he
light
of its
geom-
etry.
The
aspects
under
tudy
are
the
geometrical roperties
f the
rectangle
f
the
Trinity
which
en-
erate
a
sequence
of
circumfer-
ences related
by
the
goldenpro-
portion)
ndalso someof the
peculiarities
n
the
composition
f
the icon.The
roles of the
circle,
the
octagon
and nverse
perspec-
tive
n
the
Trinity
re
discussed.
Theauthor
stablishes
orrespon-
dence
between he
theological
triadRevelation-
llumination-Trans-
formation,
hichmakes
up
he
fundamentalontentofthe
Trinity,
and hemirror nddynamic ym-
metriesof the icon.
THE
CONSTRUCTION
OF
THE RECTANGLE OF THE
ICON
Let us
note
that
Old Russian icons were
necessarily painted
in
an arc. The linear
parameters
of the
margins
of the
arc
of
the
Trinity
the
height
of
the
margins h0
and its width
1)
are
pro-
portional
to
the linear
parameters
of the
arc
h,
I
and
to
the
linear
parameters
of the icon itself
H,
L:
h
=
H
-
L
(h
=
H
h,l-
1o 1 L 2 2
This fact is evident from the
similarity
of
the
triangles:
the
di-
agonals
of
the icon are
at
the same time
the
diagonals
of
the
arc. As a
result,
it
makes no difference
whether the
propor-
tions of the
composition
of
the
icon are
calculated on the in-
ner outline-the outline of the
arc-or on the
outer contour
of
the whole
icon.
According
to the
logic
of a
pictorial
com-
position,
the
proportions
of the
composition
should be
corre-
lated
with its
inner contour. But from
the
point
of
view of
per-
ceiving
the
icon
as
a
whole,
the
parameters
of
the
composition
should correlate
with
the
outer contour of the
icon.
By
keeping
the
proportion
the
same,
Rublyov
solves this
problem
[5].
But how was the rectangle itself constructed? Since
H
h
5
-..-.
1.25
=
-,
L
I
4
the
answer seems evident: the
proportions
of the
rectangle
of
the
Trinity
are determined
by
the ratio of
integers
5:4. The
construction
of the
rectangle
with the
help
of
a
circumfer-
ence inscribed
in
the four
squares
is
evident from
Fig.
2.
Alexander V. Voloshinov
(mathematician,
philosopher),
Saratov State Technical Univer-
sity
(SSTU),
6
Delovaya
St.,
Apt.
14,
Saratov
410040,
Russia. E-mail:
.
LEONARDO,
Vol.
32,
No.
2,
pp.
103-112,
1999 103
1999
ISAST
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Fig.
1.
AndreyRublyov,
The
Old Testament
rinity,
empera
on
wood,
142
x
114
cm,
c.1420.
The icon
from the
Trinity
Cathedral in
the
Trinity-St.
Sergius Monastery
in
Sergiev
Posad.
The
integer
ratios of the sides are
characteristic of Russian
icon-painting
in
general.
As the well-known
proportion
theorist A. Titz
[6]
established,
the inte-
ger
ratios of H:L
dominate in
Russian
icons
of
the fourteenth and
fifteenth
centuries,
namely:
4:3
(-30%);
5:4
(-30%);
3:2, 6:5,
7:5
(-12% each).
Only
approximately
4%
of these icons are
made
up by non-integer
ratios of their
linear
parameters.
From ancient times,
integer
propor-
tions
have
traditionally played
a
leading
role
in
spatial
arts,
especially
in architec-
ture,
which has been
conditioned
in
its
turn
by
the
exceptional
role
of
the inte-
ger proportions
of
consonances
in
music
discovered
by Pythagoras
[7].
According
to
Vitruvius,
the ratio of an
octave
(2:1)
[8]
is beautiful for a
temple,
and rela-
tions of a fifth
(3:2)
and a
major
sixth
(5:3)
are
suitable for an atrium
[9].
The ancient
theory
that
proportions
that are
pleasant
to
the
ear should be
also
pleasant
to the
eye
was
accepted
and
developed
in
the time of the Renais-
sance. Leon
Battista
Alberti wrote:
"There are
numbers,
with
the
help
of
which
the
harmony
of sounds fascinates
the
ear,
the
same numbers
fill the
eyes
and soul with wonderful
delight.
We
must use the
proportions,
taken from
musicians,
who
are
great
masters
in
that
kind of numbers" [10].
When
Rublyov
was
choosing
the inter-
val of
major
third
(5:4)
as the
proportion
of
the
rectangle
of the
Trinity,
he could
not have known this statement of
his
younger
contemporary,
for
Alberti's
trea-
tise Ten Books on Architecturewas
pub-
lished in
Florence
in 1485-13
years
af-
ter
Rublyov's
death. But
Rublyov
was
sure to have known
through Byzantine
architects and
icon-painters
the
idea
of
applying
musical
proportions
in
spatial
arts.
The
same
ancient masters were too
sophisticated
in
the arts and
in
math-
ematics
to confine themselves
merely
to
the
integer proportions.
On the
wooden
panel
from Hesire's
sepulcher
in
Saqqarah
(twenty-eighth
century
B.C.),
the architect Hesire is shown with
two
measuring
canes in his
hands,
the
lengths
of
which
are
related as the side
(1) and the diagonal (5 ) of the
double
square
X5
:1. There is
only
one
step
from the
diagonal
of the double
square
to the coefficient
of
the
golden
section
0
=
(
5
+
1)/2
=
1.618033989
... or its inversion
4
1/D
=
(
5
-
1)/
2
=
0.618033989 ...
That
very
step
was
made
by
Euclid in his Elements
11
].
Masterpieces
of Ancient Greece and
Rome
and Old Russian art
testify
to
the
fact
that old
masters knew the
propor-
tions based on
irrational relations such
as
(
~2:1,
F5J:1
and,
finally,
(
5
+
1)/
2:1.
The same Vitruvius recommends
the relation
42:1
[12] as well as the
musical
integer proportions
of atria.
Old
Russian
masters,
who
were
ac-
quainted
with
the
wisdom
of
Antiquity
through Byzantium,
were
sure to know
the secrets of the
golden proportion.
Such
being
the
case,
while
making up
the boards for his
Trinity,Rublyov
could
have
marked not the "musical"
rect-
angle
5:4 but the
"golden" rectangle
./j:1,
the
diagonal
of which is the
co-
efficient of
the
golden
section
(. The
geometry
of
constructing
that rect-
angle,
based on the modification
of Eu-
clidean method of two
squares,
is evi-
dent from
Fig.
3.
The
rectangles
5:4 and
-vI:I
are al-
most
indistinguishable
from each other
to the
eye (Fig.
4):
the relative differ-
ence of their
diagonals
A
=
1.05%.
But
behind
the outer
equality
of
the
two
rectangles
there are two
contrary
phi-
losophies
of art: the
philosophy
of
the
modulus-the arithmetical addition
of
the
multiple
to the modulus
magni-
tudes,
leading
to "musical"
propor-
tions,
and the
philosophy
of the
coeffi-
cient-the
geometrical
multiplication
by
the coefficient
of the
increase,
lead-
ing
to
the irrational
proportions
and,
in
particular,
to
the
golden
ones.
What
philosophy
did
Rublyov pro-
fess? We do not know the answer.
As for
the
proportions
of
the
rectangle
of the
icon,
they
are
just
between 5:4 and
4-
:1,
as
if
Rublyov
were
laughing
at fu-
ture
investigators.
As it befits
a
true
mas-
terpiece
of
art,
the
rectangle
of
the
Trin-
itykeeps
the secret of its construction.
104
Voloshinov,TheOld TestamentTrinity
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5
141
4
4
N
1
Fig. 2. The rational "musical" method of constructing the rect-
angle
of the icon with the ratio 5:4
=
1.25.
The
diagonal
of
the
rectangle
is
equal
to
41
/4
=
1.601.
THE "GOLDEN"
CHARACTERISTICS OF THE
RECTANGLE
a/:1.
No
matter how the
rectangle
of
the Trin-
ity
was
constructed,
it
possesses
the
unique "golden"
characteristics of the
rectangle
XF
1 that have not been ex-
plored
until now.
In
the
rectangle
a/ :1 let us
examine
the
succession
of
the inscribed and cir-
cumscribed circumferences and rect-
angles
(Fig.
5).
As
it
is
easy
to
show
from
the
similarity
of
triangles
OAB,
OCD,
OEF,
..,
the
following
equalities
are
just
ii
-1,272
for the radii of the circumferences
rk:
25
.-=1,25
1
k
4
rk
=-
,rk-rk-
=-
(k
=
1,2,3,...).
Then,
the radii
of
the circumferences
rk
and the linear
parameters
of
the rect-
angles
hk
and
1k
re related
in
golden
proportion
-
hk
-=
=
D
(k
=
1,2,3, ...)
rk+l hk+l
ik+l
Finally,
it
is
easy
to
prove
that
only
the
rectangle
:1
possesses
these
charac-
teristics.
So,
the
rectangle
of the
Trinity
natu-
rally
raises a succession of circumfer-
ences,
related to each
other
by
the
golden proportion.
Consequently,
for
any
point
inside the circle
[rk,
rk
+
],
there is a
corresponding point
inside
Fig.
3. The irrational
"golden"
method of
constructing
the
rect-
angle
of
the
icon
with the ratio
Af
:1
1.272.
The
diagonal
of
the
rectangle
is
equal
to -D 1.618.
18//
Fig.
4.
Comparison
of
the
rectangles
601
/(
:1
-
1.272
(up-
per figure)
and
5:4
=
1.25
(lower
figure).
The
diagonal
of
the
rectangle
5:4 with
the relative error A
=
1.05%is equal to the
coefficient of
the
golden
section (.
Voloshinov,
The Old Testament
Trinity
105
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presents
the
idea of God's
triplicity
as
three circles:
A
G
the
circle on the
opposite
end
of the di-
ameter
that is in
golden proportion
with
the
given
point.
As a
result,
there is an
unlimited scale of
golden
proportions
relative to the center of the
composition
of the
Trinity-the
point
of
intersection
of the
diagonals
of
the
rectangle.
The
first three
circumferences,
r,
r2,
r3,
play
the main role in the
composition
of the
Trinity:
he
smallest of
them limits
the
circle
r3,
while the other two
limit
the
corresponding rings.
Let us note
(Fig.
5)
that
AC=OE=
1O2
2
and
CE=I
3
2
i.e. the
radius of
the inner circle
(OE)
and the
width of the
outer
ring
(AC)
co-
incide,
and
the width of the
middle
ring
(CE)
s
in
golden
proportion
with
them.
Regarding
the incline
of the
diago-
nals,
since
tg
a
=
tg
ZBOA
=
aV
(Fig.
5),
then
a
=
51?50'. But
that
is
just
the
angle
of
the incline of
the
apothem
of
Cheops' Pyramid
So
AOGH,
made
up
by the diagonals of the rectangle V :1
(Fig.
5),
is
similar to the
frontal
outline
of
Cheops' Pyramid.
Abundant
empirical
material has
been
collected
testifying
to the fact
that
this
rectangle-the
rectangle
of
the
Trinity-is
the most common
among
the
formats of
pictures
in
different
epochs
and
genres
[13].
On the
other
hand,
G.
Fechner
deduced in his
experiments
that
initiated
empirical
aesthetics
[14]
Fig.
5.
The
"golden"
characteristics f the
rectangle
4:1.
h
that the format of the
golden
propor-
tion 1.618
of
rectangles
is
aesthetically
preferable.
V.
Petrov in
his work
[15]
gives
a rather
convincing
theoretical-in-
formational
explanation
of G.
Fechner's
results;
but still
the
question
as
to
why
the
format ~1.3 is
aesthetically prefer-
able remains
open. Perhaps
it is
the shift
of
the
golden
proportion
from the
outer
contour
of the
empty
rectangle
to the
inner
structure
containing
the content
of the
picture
that can
be
considered
one of
the reasons
why
the
rectangle
-4
:1
is
aesthetically preferable.
Now
let us
pass
on
from
these
general
observations to the
geometrical
and
philosophical analysis
of
Rublyov's
Trin-
ity
tself.
THEME
1. THE
THREE
CIRCLES OF THE
TRINITY
From
time immemorial
the
circle has
been considered the
most
perfect
shape,
since of all
two-dimensional
fig-
ures
only
a
circle
coincides
with itself at
any
turn round its
center,
possessing
the
highest
degree
of central
symmetry.
Because of
this,
from ancient
times
different cultures have used the circle to
symbolize
the
sky,
the
path
of
the
sun,
the
sphere
of
the
heavens-everything
lofty,
perfect,
eternal and
close to
God.
The
aesthetics of
the
circle,
with its
highest
degree
of
perfection,
led
Pythagoras
to the
hypothesis
of a circu-
lar
trajectory
of
planetary
orbits.
No
wonder,
then,
that in the
last
(thirty-
third)
song
of
the last
(third)
part
of
his
Divine
Comedy, s the last
truth,
Dante
Nella
profonda
e
chiara
sussistenza
Dell'alto lume
parvemi
tre
giri
Di
tre colori e
d'una contienza
-Paradise, XXXIII,
115
It
is no
wonder, then,
that
many
art
critics-M.
Alpatov,
V.
Lazarev,
L.
Ouspensky,
N.
Tarabukin,
N.
Demina
and others-tried
to find
circles in the
composition of the Trinity 16].
It is hard to know
whether
Rublyov
had
read Dante's
greatest
book. Most
probably
he did
not-the
distance be-
tween
medieval Russia
and the Italian
proto-Renaissance
was too
great
in
those
days.
But the
golden property
of the
rectangle
j
:1
easily helps
us to
find
Dante's
three
circles in the
composition
of the
Trinity.
It is
astonishing
how or-
ganically
the
composition
of the
Trinity
is
inscribed into
these three
circles: the
circle of the
three
faces,
the
circle of the
arms and
wings
of the
angels
on the
sides, the circle of the arms of the angel
in
the middle
and the
cup (Fig.
6).
The
majority
of
art
critics,
noting
the
circular
composition
of
the
Trinity,
did
not take the
trouble of
making
concrete
drawings.
And even if
they
pointed
to
the
circle,
as Titz
does
[17],
it was a
circle with a lowered
center,
which
was
dictated
by
the
hypothesis
of
the "musi-
cal" method
of
constructing
the rect-
angle
5:4
(see
Fig.
2),
as
opposed
to the
golden rectangle,
which
yields
circles
around the actual
center of the
icon.
These circles
form
concentric
rings
connecting the face of the left angel
with
the hand of
the
right
one,
the face
of the
angel
in the
middle with
the
cup,
etc.,
as
pointed
out
in
Fig.
6.
Rublyov
puts
the two central
elements
con-
nected
by
the
golden
proportion-the
face of the
angel
in the
middle and the
cup-on
the same axis
and,
at
the same
time,
slightly
shifts their
axis from
the
vertical. So there
appears
an
extraordi-
nary expression
and
magnetic
unity
in
perceiving
the two
most
important
ele-
ments of the
icon.
As to the
philosophical
content of
the
geometry of the circle, I should say that
it
corresponds
in the best
possible way
to
the
ecclesiastical
dogmata
of
Triunity,
Homoousios,
Non-Amalgamation,
and
Inseparability:
the
Triunity
of the
angels
in
the one
circle,
and the
Homoousios
(or
consubstantiality)of
the
algorithm
of
constructing
the
circle,
which is
uniform
for
all
points
of the circle.
The
Non-
Amalgamation
is the
qualitative
distinc-
tion of
every
new
point
of
the circle.
106
Voloshinov,TheOld TestamentTrinity
B
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The
Inseparability
is
the unlimited
self-
similarity
of
circular motion. In
the icon
the
middle
angel, although
higher
than
the
others,
is
equal
to
them
in
the
circle;
he
neither
suppresses
nor dominates
the others. Thus
the circular
composi-
tion of the
Trinity
s much
richer
philo-
sophically
and
geometrically
than
any
of
the known
linear
compositions
(for
ex-
ample,
the
Pscovian icon of the six-
teenth
century:
Old
Testament
Trinity).
The question "Whois who in the Trin-
ity?"
parked many
a
heated
argument;
Czar
Ivan IV the Terrible
posed
the
ques-
tion to
the
Stoglavy
Sobor
in
1551. The
answer of
the Sobor was:
"Christ is the
angel
in the
middle,
the one
higher
than
the
others."
Thus,
in
the
Orthodox
church,
God the Son was
put higher
than
God the
Father,
while in the Catholic
church
they
are
equal.
As
evinced
by
the
geometry
of the
Trinity,Rublyov
cannot
be
reproached
for
inspiring
the
Sobor
with their decision. For
Rublyov
all the
three
hypostases
are
equal
in
the
circle.
Four hundred years later the Sobor's
decision was
supported by
distinguished
art critics
M.
Alpatov
and V.
Lazarev
[18],
while
theologians
N.
Golubtsov
and
A.
Veletev
[19]
were of
another
opinion.
The latter
noticed a
"Majestic
element" in
the
angel
in
the middle that
corresponds
more to the first
hypostasis
of
the
Trinity,
i.e. God the
Father. Ac-
cording
to
A.
Veletev,
the
angel
in the
middle-God the
Father-is
inclining
the Son
(the
left
Angel)
toward self-sac-
rifice for the
redemption
of
sin,
as
evi-
denced
by
the
expressive
bent of His
head towards the Son. The right angel-
the
Holy
Ghost-is bent
over the
Com-
munion table
more than the others and
is most
sorrowfully pensive.
But the wisest
opinion
in
this
matter
seems to be that
of G.
Pomerantz,
a
modern
philosopher
and
culturologist:
The man
who
really
feels
Rublyov's
Trinity
s
sure to feel
that the
question
"Who is
who?"
is
idle and
digressing
from the
main
point,
that
Non-Amal-
gamation
and
Inseparability
of the an-
gels
is
the
very
essence of the
matter;
and if
we
try
to
see
a
difference be-
tween them
we are sure
to turn
the
Trinity
into "three
goats,"
as Maister
Ekkehard said
[20].
THEME
2.
THE
THREE
OCTAGONS OF
THE
TRINITY
The
theme of the
octagons
is the
logical
continuation of the
theme of the
circle.
The number
8 was
associated with
eter-
nal
life
in
the
medieval Christian
cul-
Fig.
6.
Theme
1.
Three
"golden
circles" of
the
Trinity.Centrally symmetrical golden pro-
portions of the most important symbolic elements of the Trinity.
ture. We can also remember
Leonardo
da Vinci's
plan
of
a
cathedral
[21],
the
foundation
of
which is a
rectilinear octa-
gon
and a
"not musical" scale of
propor-
tion
'2:1.
Just
like the
circle,
the
octagon
in the
composition
of the
Trinity
was noticed
by
M.
Svechev
[22],
D.
Likhachyov
[23]
and
others,
but
no
one had
pointed
out its
concrete
position
in
the icon.
If
we con-
struct a
circumference,
touching
not the
vertical but the horizontal sides of the
arc of
the
icon
(Fig.
7),
and
also
do
the
constructions shown in
Fig.
7,
we can
easily
find
not
one,
but three
octagons.
The first
(the
largest)
of them em-
braces all the
elements
of
the
composi-
tion with
mathematical
precision.
As il-
lustrated
in
Fig.
7,
the four
inclined
sides of
the
octagon
mirror the
slopes
of
the thrones
and
pedestals
of the
angels,
the
axonometrical
axis
of the left build-
ing
(either
Abraham's house
or
a
temple)
and even the
tangent
to
the
right
mountain. The second
octagon,
with the
same mathematical
precision,
involves the main elements of the
com-
position-the angels
and the sacrificial
cup.
And
finally
the third
octagon-the
smallest-includes the focal
point
of
the
composition-the cup
and the
arms
stretched
out towards it.
Besides
its
symbolic
link to eternal
life, the main octagon also has a certain
compositional meaning. Opposed
to the
smooth,
gentle
arcs of the circular com-
position
(see
Fig.
6),
which would have
been too
amorphous,
Rublyov
instead
outlines
with
the
sharp,
hard borders of
the
octagon.
Thus the celestial circle of
angels
is confined within the
octagonal
frame
of
earthly
elements: the
tree,
the
mountain,
the
temple
and the
pedestals,
which
symbolize
correspondingly
the
Voloshinov,7he Old TestamentTrinity
107
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world
of
animate
nature,
the
world of
inanimate
nature,
the
world of eternal
culture and the
world
of
everyday
life.
THEME 3.
THE
INVERSE
PERSPECTIVE OF THE TRINITY
If there is
mathematical strictness
in ar-
ranging
elements in the
plane
of an
icon,
then there is absolute chaos
in
conveying
space
within the
plane.
This
fact has been noticed not only in
Rublyov's
works,
but in all Russian icon-
painting;
that
is
why
Russian
icon-paint-
ers have
long
been accused of
"naivete,"
"incorrectness"
and
even
"primitiveness"
in their
geometry.
For
example,
it
is
easy
to
notice
the
super-
position
of at least three
points
of
view
in the
Trinity:
the left
angel
is shown
from the
right,
the
right
one from the
left and
the
angel
in the middle from
the
front.
Furthermore,
the
pedestal
of
the left
angel
is
depicted
in
slight
in-
verse
perspective,
while the
pedestal
of
the
right
one is
depicted
axono-
metrically.
The
temple
on the left
is
also
depicted axonometrically,
but its
spatial
axis is directed
opposite
the
axis
of
the
right pedestal (Fig.
8).
It is
easy
to
imagine
the
edges
of the Commun-
ion
table,
which is
covered
by
the
an-
gels'
knees:
following
the
logic
of con-
structing
the left and
right parts
of the
icon they can only diverge (Fig. 8).
As a matter
of
fact,
the
problem
of
conveying
the
depth
of
space
in
the
two-dimensional
plane
of an
icon
was
not a scientific one for Russian icon-
painters
as
it
was for
European
Renais-
sance artists. Not the
geometry
of
space,
but the
geometry
of
symbol
in-
spired
the
Russian
icon-painter.
He did
not
copy
the real world
according
to
the laws of
perspective,
but
created his
own irrational world of the
space
of the
Fig.
7.
Theme
2.
Three
octagons
of
the
Trinity:
he
all-embracing octagon,
the
octagon
of
the
angels,
the
octagon
of the hands and the
cup.
icon.
That
is
why
P.
Florensky,
compar-
ing
the
straight
and inverse
perspec-
tives,
called the first one
"rapaciously
mechanistic" and the second
one
"meditatively
creative"
[24].
Since the triune God
exists for the sake
of
man,
Rublyov
turns his
Trinity
owards
the
audience. This is
possible
to achieve
either
by putting
the three
angels
in
one
row
(such
compositions
of the
Trinity
are
known,
but
they
are too
primitive
and too
"non-triune"), or by presenting the an-
gels
on
the
sides
from
opposite points
of
view,
ust
as
Rublyov
does.
But the
superposition
of the two
op-
posite points
of view leads to a
strong
in-
verse
perspective
of the Communion
table
(see
Fig.
8),
which is
flagrantly
in-
adequate
to the
perceived space.
Under-
standing
that,
Rublyov
conceals the
sides of the Communion table behind
the
knees
of the
angels.
Now
the
oppo-
site
angels
sit
a
little too
close,
leaning
upon
the
table,
but
they
hide the too-
obvious contradiction within the icon.
Note that, following the logic of inverse
perspective,
the
fact that the
image
of
the
angel
in
the
middle
(the
distant
one)
is
higher
than the
images
of the
other
two
(the
near
ones)
is
quite
justi-
fied.
It
corresponds
to the
equal posi-
tion of the
angels
in the
real
space.
We shall not
regard
here
the
geo-
metrical,
physiological
and
composi-
tional reasons
for
using
inverse
perspec-
tive in Russian
icon-painting
that were
reviewed in detail in Rauschenbach's
work
[25]. Rather,
we shall
stop
at
its
philosophy,
for the roots of
any
world
outlook,
reflected
in
art,
are to
be
searched
in its
philosophy.
It is not the Western
way
(i.e.
the
logi-
cal
cognition
of
the
particular)
but
the
Eastern
way
(i.e.
the
extralogical
con-
templation
of the
whole)
that is closer to
the
way
of the Russian
icon-painters.
Not
so much the factual
as the
elevated
meaning inspired
them. The
"un-
earthly"
geometry
of inverse
perspective
and the
geometrical
liberties
of
Russian
icon-painting
on the whole are dictated
by
the
philosophy
of
the
heavenly
world,
the celestial town, which is higher than
any geometrical
or
logical
details. Not
the
physical
side of the
picture,
but its
spiritual meaning;
not the
reviewing
of
earthly things,
but the ascension towards
Heaven-these were the
philosophy
of
the Old Russian
icon-painters.
The
versatility
and reticence
of the
philosophy
of
Rublyov's
Trinity
alled for
a similar
approach
in
the
geometry
of
the icon. That is
the
reason
for
the
com-
bination of different axonometries
in
108
Voloshinov,
The
Old Testament
Trinity
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the
Trinity
and the
uncertainty
of the
outline of the Communion
table. True
art
says
much,
but
it
holds back
more.
The
power
and charm of
Rublyov's
Trin-
ity
s
in
its reticence.
THEME 4. REVELATION:
MIRROR SYMMETRY
Symmetryimplies
ideas
of
homogeneity,
invariance and
equilibrium.
Mirror
sym-
metry
has also a
tinge
of calm.
The
verti-
cal axis or the
plane
of
symmetry
(bilat-
eral
symmetry)
in
nature characterizes
the
stability
and
equilibrium
of an
object
(mirror
symmetry
of the
right
and the
left).
Snow-covered mountains are re-
flected
in
the frozen water
of a
highland
lake
(mirror
symmetry
of the
top
and
the
bottom).
The first
type
of
mirror
symmetry
is realized in the
Trinity.
As
seen in
Fig.
9,
the left and
right
sides
of the
Trinity
are
mirror-symmetri-
cal.
The outlines of the backs of the
left
and
right angels
coincide
exactly,
and
the centers of the faces also coincide ex-
actly, although
the
faces themselves and
the halos are shifted
slightly.
The
posi-
tions
of
the feet
and the
pedestals
are
shifted
slightly,
and the
temple
is
mir-
ror-symmetrical
to the mountain.
Mirror
symmetry
is broken
principally
only
in the outline
of
the central
angel:
the turn of his
body
and hands is
asym-
metrical,
his head is bent toward the
viewer's
left,
while the
cup,
at
which
he
points,
is shifted to the
right.
Finally,
the
whole
asymmetry
of the center is under-
lined
by
the Mamrean Oak-the
only
principally asymmetrical
element
of the
composition,
devoid as
it
is
of
a
mirror-
symmetrical
match.
It
is
the central
asymmetrical
angel
who
is the source of movement and
energy.
It
is from
him
that
the
Revelation
issues to
the
two
angels
on
the
sides,
who listen to
him immovable
in
mirror-symmetrical
equilibrium.
The Revelation found and
the calm of the truth found
following
it-
the
asymmetry
of the center
exploded
in
the center and calmed down
in the mirror
symmetry
of the
right
and left
sides-are,
in my opinion, the philosophical content
of mirror
symmetry
of the
Trinity.
In
this
light,
the
geometry
of the Trin-
ity
seems
to
favor not the
Stoglavy
Sobor's
decision,
but that of
theologians
N.
Golubtsov and A. Vetelev: the
angel
in
the middle is the first
hypostasis
of the
Trinity,
God the
Father,
appealing
for the
THEME 5.
ILLUMINATION:
THE THREE
CUPS OF THE
TRINITY
The
calm of the
Revelation cannot last
forever.
Having
entered the listener's
soul,
the Revelation is
inevitably replaced
by
the Illumination:
by
the
splash
of
the
listener's
thought;
the
passive perception
is
replaced by
the active creation.
What
thought
illumines
and
unites
the
Trinity?
It is the
thought
of the
cup.
The
cup
is the center of the
composi-
tion of
the
Trinity,
he main
guarantor
of
Inseparability
and
Homoousios
(consubstantiality?)
of the
Trinity.
The
movement of all
three
angels'
right
hands is
directed toward the
cup,
which
seems to
keep
the
centripetal
forces of
the
Trinity
in their eternal
circular mo-
tion. The
cup
itself,
placed
on the altar-
like
Communion
table,
expresses
the
idea of sacrifice. ". . . the
cup
which
my
Father hath
given
me,
shall I not drink
it?" (John 18:11).
But in the
composition
of
the
Trinity
Fig.
8.
Theme
3.
The inverse
perspective
of
the
Trinity.
A
combination of the two differ-
ently
directed axonometries
in
the
Trinity
s the reason for the
strong
inverse
perspective
of the Communion table.
.
necessity
of
offering
his
Son for the re-
demption
of sin.
For,
"Greater ove hath
no man
than
this,
that
a
man
lay
down
his
life for his friends"
(John
15:13).
Voloshinov,
The Old Testament
Trinity
109
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Fig.
9.
Theme
4.
The
Revelation:
mirror
symmetry.
The
mirror
Fig.
10. Theme
5. The
Illumination:
three
cups
of the
Trinity.
The
symmetry
of
the left and
right
parts
of the icon
and the
asymmetry
three
cups
are the three
symbols
of sacrifice for
Faith,
Love and
of the central
part.
Hope.
we can
easily
see not
one
but three
cups:
the
cup
on the Communion
table,
the
cup
made
up by
the inner outlines
of
the
angels
and the
cup
made
up by
the
outer contours
of the
angels
and
thrones
(Fig.
10).
What
cups
are these?
I wish to offer the
following interpre-
tation of
the three
cups
of the
Trinity.
The
first
(inner)
cup
is Abraham's
sac-
rifice
for
Faith.
As the Old Testament
tradition
says,
Abraham
and his wife Sa-
rah met three
angels
under
the shade
of the Mamrean Oak
very
amiably.
Abraham
told Sarah
to knead "three
measures
of fine meal" and
to
"dress
a
calf tender
and
good,"
and
they
treated
the
angels.
They
surmised
that it was
God in their house and
expressed
their
Faith
in Him and their belief
in His
prophecy
that Sarah
would
have
a
son
(Genesis, 18:1-16).
The
second
cup represents
God
the
Father's
sacrifice
for the Love
of
Hu-
manity. According
to
the Father's
will,
the Son was
chosen to
be
the
Savior of
the
world and Man.
The
Son
goes
to
earth to atone
for human sins with
his
own
sufferings.
Father sacrifices
Son and
Son sacrifices himself
for the love
of hu-
manity.
That
is
the
symbolism
of
the sec-
ond
cup, greater
in
meaning
than
the
one
placed
on
the
Communion
table.
But
if
the
first
cup
contains the head
of
the sacrificial
calf,
the second
cup
can
contain
only
Our Savior-in which
case,
is the
angel
in
the middle Christ?
Maybe
this
exchange
of
roles
took
place
while
the
Revelation
was
changed by
the Illu-
mination,
for the
Trinity
itself
is
homoousian,
non-amalgamative
and in-
separable.
Finally,
the third
(outer)
cup
repre-
sents the
Trinity's
sacrifice
for the
Hope
of
Salvation.
The
third
cup
is made
up
by
the
Trinity
and contains
the whole
Trinity.
God the Father and the
Holy
Ghost
cannot leave God
the
Son alone
in the second sacrificial
cup,
for the
Trinity
is
inseparable: they
make
up
the
third and
greatest
sacrificial
cup
which
includes themselves.
They
believe
that
the sacrifice for
Love will
not
be
in
vain,
and the whole Trinitysacrifices itself for
the
Hope
of Salvation.
So,
we
have
two
contrarily
directed
movements
in
comprehending
the
meanings
of the
Trinity.
The outer
circle
of the
angels
and the
outer octa-
gon
of the
composition
lead us to the
most
sacred
place
of the
icon-the
cup
and the
angel's
hand
pointing
at
it,
which are
confined in
the
inner circle
and
octagon.
The
contrary
movement
issues from the
cup
on the Communion
table to
its
latent
semantic
generaliza-
tions in the inner and outer contours
of
the
angels.
The
idea of sacrifice could not
help
being
the cornerstone
of
Rublyov'sgreat-
est work:
it touched
every
Russian heart
in
Andrey
Rublyov's
day, especially
since
Rus itself turned
out to be
sacrificed
to
the Tartar
nterventionists
in the name
of
the salvation
of
European
culture.
THEME
6.
TRANSFIGURATION:
DYNAMICSYMMETRY
The
outburst
of
Illumination is inevita-
bly
followed
by
the
Transfiguration-the
rise of a lucid soul to the new
peaks
of
thought
and sense.
Transfiguration
is
dynamism,
the
vertical
rise,
the realiza-
tion of the truth born by the Illumina-
tion. If the
geometry
of
the
Revelation is
calm,
static and horizontal
(horizontal
mirror
symmetry),
the
geometry
of the
Transfiguration
must
be
impetuous,
dy-
namic,
vertical.
A whole
gamut
of verti-
cal
proportions
of the
golden
section in
the
Trinity orresponds
to that idea.
If
the
height
of the icon is
H
=
1,
we
can see that the line
of
the
main
golden
section
4)
let
us call
it
the line
of
the
compositional
center
1)
passes exactly
110
Voloshinov,
The Old Testament
Trinity
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Fig
11.
Theme 6.
The
Transfigura-
tion:
dynamic
ym-
metry.
The series
of
the
golden
section
1,
0,
2,
03,
,4,
4,5, ,6,
47
in the
vertical
proportions
of
the
Trinity.
I _
-~
through
the
center of
the
cup
(Fig.
11).
Measuring off
4,2
upwards and O3down-
wards
from
11,
we
get
correspondingly
the
upper
line of
the
compositional
cen-
ter
l2
(this
is
the
line of
the
angel
in
the
middle)
and
the lower
line of
the
com-
positional
center
13
(this
is the
line of
the
angels'
bent
legs).
Finally,
measuring
off
,)4
upwards
and
45
downwards
from
11,
we
get
correspondingly
the
upper
mean
line
of
the
compositional
center
14
(this
is
the line
of the
halo
and
shoulders of
the
angels
on
the
sides)
and the
lower
mean
line of
the
compositional
center
15
(this
is the
line of
the
front
edge
of the
Communion table). The smaller vertical
articulations of
the
Trinity
n
golden
pro-
portion
are
also shown in
Fig.
11.
So,
the
vertical
construction of
the
composition
of
the
Trinity
s
defined
by
at
least
eight
members of
the
golden
sec-
tion series
1,
4,
02,
43,
04, 05,4
6,
47.
We
can
also
determine a
series
of
golden
proportions
that
are not
con-
nected
with
the
compositional
center
11.For
example,
the
height
of
the an-
gels on the sides from the top of their
heads
to
their feet
are
exactly
equal
to
4,
and the visible
height
of
the
angel
in
the middle
from
the
top
of
the head
to
the
Communion
table
is
42,
i.e.
the
heights
of
the
icon,
the
angels
on
the
sides,
and
the
angel
in
the
middle are
related in
the
golden
proportion.
The
vertical
dimensions
of
the
angels'
heads
without
the
halos
are
45,
and
with
the halos
they
are
(4
(in
order
not
to
complicate
Fig.
11
these
proportions
are
not
shown).
And so
on
upwards
and
downwards
on
a
vertical the
quietly
noble "rye" gold of Rublyov's colors
turns
into
the
proudly glorious
"gold"
of
its
proportions.
As if in
a
temple,
the
mighty
chords
of
golden
proportions
of
the
Trinity
rise
vertically
in
it.
The
dynamic
symmetry
of
life,
the
harmony
of
the
truth
find
sound
in
these chords.
The
rise
to the
new
Truth-is
this
not
the
Transfigura-
tion
that
we
know
from the
New
Testa-
ment:
". . .
and
bring
them
up
into
an
high
mountain
apart,
and was
transfig-
ured
before
them:
and
his
face did
shine
as the sun, and his raiment did shine as
the
light"
(Matthew,
17:1,2).
CONCLUSION
This
investigation
of
the
geometrical
and
philosophical
aspects
of
Rublyov's
Trinity
n no
way
has
a
claim on
comple-
tion;
as
with
most
dissertations on
differ-
ent
masterpieces,
this
one
has
barely
be-
gun
to
scratch the
surface.
Stendhal
once
said:
"The
point
is
not
to
learn
to
draw,
but
to learn to
think."
Earlier,
Plato
voiced
a
similar
thought
with the motto over the entrance to his
Academy:
"Do
not enter if
not a
geom-
eter."
In
my
opinion
the
true
artist
must
be a
philosopher
and
a
geometer.
Russian
saint
Andrey
Rublyov
surely
was
both.
The
urge
to
analysis
and
discourse
is
a
human
characteristic,
especially
for
those
of us
influenced
by
a
history
of
Western
logic
and
thought.
But
maybe
it
would
be
wiser to
stop
these
efforts to
comprehend
the
incomprehensible
and
to
admit
the
divine
inspiration
Voloshinov,
The Old
Testament
Trinity
111
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present
in
the
great
work
of
the
humble monk
Andrey Rublyov.
References
and Notes
1. The
number
of
writings
about
these three men
of
Old R ussia is
really
incalculable,
so
I
will mention
a
few of the most
significant:
V.
Kluchevsky,
"The
Sig-
nificance
of
Reverend
Sergius
for
the Russian
People
and
State,"
Bogoslovsky
Vestnik, November
1892)
pp.
190-204
(in Russian).
D.
Likhachyov,
The
Culture
of
Rus
in
the Time
of
Andrey Rublyov
and
Epiphanius
the
Wise
late
fourteenth-early
fifteenth
centuries)
(Moscow-Leningrad:
The
Printing-House
of the Academy of Science of the USSR, 1962) (in
Russian).
M.
Alpatov,
"On the Global
Significance
of
Andrey Rublyov's
Art,"
Khudozhnik
2
(1980)
pp.
48-57
(in
Russian).
V.
Plugin, "Sergius
of
Radonezh-Dmitry Donskoy-Andrey Rublyov,"
The
History
of
the
USSR,
No.
4,
(1989)
pp.
71-88
(in
Russian).
M.
Alpatov,
"La valeur
classique
de
Rublev,"
Commentari
(1958)
pp.
25-37.
V.
Lazarev,
Andrej
Rublev
Milan,
1966).
2.
Stoglav
(St.
Petersburg:
The
Printing-House
of
His
Majesty's
Academy
of
Science,
1863)
p.
128
(in
Russian).
3. N.
Demina,
Andrey
Rublyov
and the Artists
of
His
Circle
Moscow:
Nauka,
1972) (in Russian).
4. P.
Florensky,
"The
Trinity-St.
Sergius Monastery
and
Russia,"
in
The
Trinity-St. Sergius Monastery
(Sergiyev
Posad:
1919)
pp.
19-20
(in Russian).
5. Far from
all
ancient
icon-painters
paid
attention
to such
a "trifle."
It
is
also
disregarded
in
easel
painting,
for
the frame of a
picture,
manufactured
from
molding
of
equal
width,
changes
the
propor-
tions of
the
picture
and the frame as
a
whole.
6.
A.
Titz,
"Some General Features of the
Composi-
tions
of
the Icons of
Rublyov
and
His
School,"
in
AncientRussian Art
of
the
Fifteenth
nd
Early
Sixteenth
Centuries
(Moscow:
The
Printing-House
of the
Academy
of Science of the
USSR,
1963)
pp.
22-53.
7. As historical records
unanimously
state,
Pythagoras
discovered
the ratios for the
three most
harmonious musical
intervals called
perfect
(main)
consonances:
octave-2:1;
quint-3:2;
fourth-4:3.
The fact that the
proportions
of
perfect
conso-
nances were described with the
help
of
four natural
ntimbers, which total the sacred number
10
(1
+
2
+
3
+ 4
=
10),
drove
the
Pythagoreans
to
mystical
entrance.
The
discovery
of the
law
of consonances
uirged
on
the
Pythagoreans
to the famous motto
"all is number" and to
searching
musical
propor-
tions in the whole universe
(the
theory
of the har-
mony
of
spheres).
One hundred
fifty years
after
Pythagoras,
the
Pythagorean
scholar
Archytas
added
to
the
three
perfect
consonances two
imper-
fect
ones:
major
third-5:4;
minor third-6:5.
8.
Vitruvius,
Ten Books on Architecture
NY:
Dover,
1960).
(Book
IV,
Ch.
4,
Para.
1).
9. Vitruvius
[8]
(Book.
VI,
Ch.
3,
Para.
3).
10. L.B.
Alberti,
7Ten ookson Architecture
London:
Tiranti,
1955).
11.
Let us remember that the
golden
section
(Leonardo da Vinci's term) or the divine propor-
tion
(Johannes
Kepler's
term)
is
the
geometrical
proportion
that divides the whole a into a
larger
part
x and
smaller
part
a
-
x
so that:
a
x
x a
-
x
where
/5+1
x =a
O4,
)
= =
1.618033989 ..
2
with
4D s
the coefficient of the
golden
section.
Regarding
the inverse ratio
a
-
x : x
=
x:
a,
there is
the inversion of the coefficient of the
golden
section
1
/5-1
=-=
=
0.618033989...
q
2
Each of the
"golden" parts
of
the whole can be fur-
ther divided
in
golden proportion
and so
on,
infi-
nitely.
Therefore,
where the
golden proportion
is
implemented,
there
appears
a whole
gamut
of
golden proportions,
so
it would be more correct to
speak
of a
golden
section series
1,
?,
?2,
?
,
...
possessing
the additive characteristics
+
=
1
,2
+
?4
=
?,
?,
+
04
=
?.2
The
rational
approximations
of the
golden
section
coefficient
are defined
by
the ratio of the two
neighboring
numbers
of Fibonacci:
{u
}
=
1,1,2,3,5,8,13,21,..
. (u
=
u + u
,,n
>
1)
so
i-oo
U
The geometrical method of constructing the
golden
section with the
help
of the
diagonal
of the
double
square
is
described in Euclid's Elements
(Book
II,
Proposition
11).
The division in the ex-
treme and
medium ratios is written of in Plato's
Timea,
but
Pythagoreans
seem to
have known about
the
golden
section,
too.
The
pentagram-their
se-
cret identification
mark and a
symbol
of health-
testifies to
it,
since
it
contains an
infinite
golden
section series.
12.
Euclid
[11]
(Book
VI,
Ch.
3,
Para.
3).
13. V. Petrov
and
N.
Pryanishnicov,
"The Formulas
of
Beautiful
Proportions,"
Number nd
Thought,
No.
2
(Moscow:
Znaniye,
1979)
pp.
72-92
(in Russian).
14. G.
Fechner,
Vorschule der Asthetik
(Leipzig:
Breitkopf
&
Harlet,
1876).
15. See Petrov and
Pryanishnicov
[13].
16. The
Trinity of
Andrey
Rublyov.
Anthology,
G.
Vzdornov,
ed.
(Moscow:
Iskusstvo,
1989) (in Russian).
17. See Titz
[6].
18. See
Alpatov
and Lazarev
in
Anthology
16].
19. See Golubtsov and
Vetelev
in
Anthology
16].
20.
G.
Pomerantz,
"Rublyov's
Trinity
and
Trinitary
Mentality"
in The
Way
Out
of
a Trance
(Moscow:
Yurist,
1995)
pp.
316-337
(in Russian).
21.
See D.
Pedoe,
Geometry
and the Liberal Arts
(Harmondsworth:
Penguin
Books
Ltd.,
1976).
22.
See Svechev in
Anthology
16].
23. See Likhachyov [1].
24.
P.
Florensky,
"The Inverse
Perspective,"
in
The
Philosophyof
Russian
Religious
Art
of
the Sixteenth o
7Twentieth enturies.
Anthology
(Moscow:
Progress-
Culture,
1993)
p.
247-264.
25.
B.
Rauschenbach,
Spatial
Constructionsn the
Old
Russian
Painting
(Moscow:
Nauka,
1975).
Glossary
axonometry (parallel perspective)-historically
the
first
artistic method of
depicting space
on
the
plane,
in which the third coordinate
(depth)
was
given along
some inclined axis. lines
paiallel
ill
the
depth
of
space
remain
parallel
in
axonometry
(thus
it
is also called
parallel perspective).
Homoousios
(consubstantiality)-(from
the Greek
"homoousios,"
meaning
"of one
substance")
one of
the main
dogmata
of the
Trinity, asserting
that all
three of its
hypostases
have the same substance. In
the "strict"
ormulation,
the
dogma
of Homoousios
affirms that the one and
only
God consists
of
three
hypostases,
each of
which
is
God
(possesses
divine
substance).
hypostasis-in
Christian
ideology, any
of the three
persons
of the
Trinity. According
to the
dogma
of
Triunity,
God is
presented by
three
hypostases:
God
the
Father,
God the
Son,
and God the
Holy
Ghost.
Inseparability-one
of
the main
dogmata
of the
triplicity, asserting
that all three
hypostases
of the
Trinity always
exist and
act
together.
The
dogma
of
Inseparability absolutely
excludes the
acting
of
one
hypostasis
of the
Trinity
independent
from
the others.
inverse
perspective-an
artistic
method
of
repre-
senting
space
on the
plane,
in
which remote ob-
jects
are shown
larger
than close ones. Lines
paral-
lel
in
the
depth
of
space
are
presented
as
divergent.
linear
(straight
or
Renaissance)
perspective-a
sci-
entific and
artistic method of
representing space
on the
plane,
in
which remote
objects
are
shown
smaller than
close ones. Lines
parallel
in
the
depth
of
space
are
presented
as
meeting
in
some
center-
the central
point
of
the
picture.
Non-Amalgamation-one
of the main
dogmata
of
the
triplicity, asserting
that all
three
hypostases
of
the
Trinity
exist
simultaneously
and
eternally,
that
they
are different
in
quality
and cannot stand
for
each other or
be
brought together.
Old
Russian
icon-painting-a unique
form of
art
in
Old R ussia that
always
had
a
religious subject
and was
destined for
religious worship.
Old
Rtissian cons are
pictorial
compositions
made as a rule on wooden
boards and
mostly
in
the
technique
of
tempera.
Rus-the initial name of
Russia,
taken from the
ancient
people
who
gave
their
name to the land
of
Russia.
Stoglavy
Sobor-the
joint sitting
("sobor")
of
the
higher clergy
of the
Russian Orthodox
Church,
Czar
Ivan IV the Terrible
and
representatives
of
the
govern-
ment, that took place in Moscow nJanuary-February
1551. It
owes the name
"Stoglavy"
("Hundred
Chaptered")
to the
code
of its
decisions,
which was
divided into 100
chapters. During
the sixteenth and
seventeenth
centuries,
the
result
of the
Stoglavy
Sobor
made
up
the
basic code
of life
for the Russian Ortho-
dox
clergy
and
its relations with
society.
The
Stoglavy
Sobor unified church rites and
instituted control over
the work of
book-writers nd
icon-painters.
Trinity-in
Christian
doctrine,
the
triunity
of
the
Father,
the Son
and
the
Holy Spirit
as three
persons
in one
Godhead.
The
idea of
triplicity
was first for-
mtilated at the
Council
of
Nicaea
in
325 that ac-
cepted
the
"Credo,"
the
symbol
of
faith,
obligatory
for all
Christians.
triplicity-the
basic
theological
doctrine
of the
Trinity,
the essence of
which
is
made
up by
the
dog-
mata
of
Triunity,
Homoousios,
Non-Amalgamation
and
Inseparability.
Triunity-one
of
the main
dogmata
of the
triplicity,
asserting
on the
one hand that God is
unique
and
on the other
hand that God
comprises
the
Trinity:
God
the
Father,
God the Son and God the
Holy
Ghost. The idea of
Triunity
s often
expressed
in
the
following paradoxical
equalities:
1
=
3 and 3
=
1.
Manuscript
received
26
March
1997.
112
Voloshinov,
The
Old Testament
Trinity
Thi d l d d f 194 95 59 195 Th 20 F b 2014 17 42 13 PM
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