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### Vermeer

### Vermeer

**Vermeer's view of the Little Street**

**Abstract**

The goal of this article is to refute the generally accepted theory
of camera obscura and its claimed usage
by Johannes
Vermeer. It
will prove that
behind
Vermeer's
perspectival space stands sophisticated geometrical system. Upon
analyzing *The
Geographer *it
becomes clear that Vermeer used window as a picture plane for his
external scene of *The
Little Street. *The geometry
also reveals that the viewing point of *The
Little Street*
is
distant
of
about
11.5
meters from
the building on the other side,
implying
that the
paintings
was
created on Voldersgracht Street.

**The Geographer**

Vermeer's
pictures
has been examined
and
inspected
closely
from
every possible angle to
find out more about their construction. Infrared
reflectography and
other scientific techniques
that has been used in recent years
can peek under the surface to
reveal some hidden
secret. Yet
Vermeer's canvases contain no underdrawings or
any other hints.
He
made his preparatory and
structural
drawings, not on the canvas, but on a sheet of paper, the similar
sheet
of paper we
can see in *The
Geographer. *If
there is not
much
below the surface, we
should examine
the surface once again
more closely.

Many attempts have been made to confirm the theory of camera obscura, but all have been unconvincing. Vermeer's concept of space, his precise placement of the objects within the depth of picture in correlation to the real space, is a matter of a perspective system and its skillful implementation. There was no camera obscura behind his perspective mastery.

After visit to Vermeer's studio in June 1669 Pietr Teding van Berkhout wrote that the most "extraordinary and curious aspect" of Vermeer's art consists in "perspective." 1 There is nothing "extraordinary and curious" about retracing image projected by the camera obscura and van Berkhout was certainly referring to Vermeer ability construct the space geometrically.

Fortunately,
Vermeer
left
many clues in
his paintings which demonstrate his expertise and excellent knowledge
of
the Renaissance perspective system.
To
obtain the right proportions and scale in his painting *The**
Geographer*
Vermeer used the same perspective system as in many of
his earlier
paintings. The
system Vermeer
employed
to construct his perspectival space
is
described
in
more details in
my
earlier study
*Vermeer
and art of the Renaissance perspective*.2

Upon
analyzing *The**
Geographer *some
interesting and
unexpected
consequences emerge.
This
picture provides lucid testimony
of his geometrical method.
He
was
not
tracing upside
down images in
a cramped space,
he
was using
a
secret
knowledge and
scientific
and rational
reasoning.

Utilizing a compass, Vermeer set the F point at the distance based on sacred geometry and on the Golden ratio. That is, if the side of the base square AB is 1, then the distance from the F point to the vanishing point V is 1.618.

Subsequently the tiers point or lateral points are derived and constructed from the focal point or F point.3

The
space of *The**
Geographer *is
not deep and
in this particular case the cube's
back
wall (EFGH)
aligns
with the
room's back wall. The
side of the cube measures
198cm,
which
corresponds to 7
Amsterdam's voet at that time.4
7
x
28.3
= 198cm.
If
we know the measurement of the front wall, then we know all other
walls too,
because
they
are
all
equal,
and can orientate
ourselves
in
three-dimensional
space
of
the picture.

In the picture we can see a compasses in man's hand and a tool that closely resembles a compass lying on wooden box. Neither is there by chance and both aims (green lines) to the important points in the perspective construction. One arm of the compass aims to the corner of the base square, point B. The other arm aims to the point J, where the large circle (determining the F point) and line j coming from the left corner of the bottom square meet. The line j determines the tiers point T2. One arm of a tool on the wooden box aims to where the horizon and smaller φ circle meet, point K. Its other arm aims to the tiers point, point T2.

When we look more closely on individual parts of the image we find sufficient evidence of the level of precise planning involved. The resulting consequences will transfer our attention unexpectedly outside of the picture frame.

If
we know the dimensions of the cube (7
Dutch feet)
we
can find out dimension of any objects within the picture. The
subject of this analysis is *The
Geographer' *view,
it
is his
view
from the window and
dimension of the window we will find out as
follows.

The width of the window is foreshortened and therefore we have to apply the principles of projection. Drawing lines (red lined) from lateral point or tiers point through the marked points on 45° diagonal we arrive at the unforeshortened distance at the base line. Using proportionality constant of a1/a2 x 198cm we get 44cm.

Things
will get interesting, when we focus our attention to the window "The
Geographer" is looking out (marked
red).
Again
using proportionality constant we find out that the length of the
window comes to around
83cm.
Nothing
special about it, but if
we measure the dimension of the window without its two upper
segments, without those segments covered by the curtain, and then
apply same proportionality constant formula of
b1/b2 x 198cm, we
arrive at the dimension of around
54cm.
One
of the few Vermeer's exterior
scenes *The
Little Street*
measures exactly 54.3 x 44cm. It
is no matter of chance that Vermeer
conceived the window in *The
Geographer*
as a picture plane for *The
Little Street. *It
is he
himself who
is
looking out of the window and across the street while constructing
the perspectival layout for *The
Little Street. *The
presence of a globe does not necessarily mean we
are looking at a geographer.
Vermeer
with a compass, painter's indispensable tool, in his hand is just
telling us that he is constructing
*The
Little Street*.
*The
Geographer *or*
The Astronomer *could
be Vermeer's lost self-portrait, item 3 from Dissius auction,5
which is now presumed missing.

*The
Little Street*
and
so called *The
Geographer *are
interconnected and bound
together
by a window, by
the
Vermeer's
view, which starts inside
of
the room and
ends
outside on
the street.

The testimony of meticulous planning is also brought to us by the wooden box. The dimensions wooden box, which Vermeer put it in the foreground and elevated the floor level, is 28.3 x 45.7 x 22.5cm. These dimensions are derived from already mentioned proportions of the Golden Ratio. 28.3 x 1.618 = 45.7 and 28.3/√1.618 = 22.5. Vermeer ingeniously placed the box so that its base sits outside of the picture plane and thus entering our space. He suggests that image space itself does not end with a frame, that things happen outside, and that the boundaries of the picture plan can be crossed. Elevated floor level gives different data thus tiers point of the box are closer to the vanishing point.

Also
notice
also slight tilt of the floor, this was
caused by shift
of
a tracing
paper, which
contained a geometric construction. This
thin paper was pinned to the canvas at the vanishing point
and a slight rotation about the axis caused the tilt. It is very
similar to a
tilt we
can see in
*T**he
M**usic
**L**esson*
and very likely done
intentionally
as
a slight hint
of imperfection, as
a human touch to an otherwise perfect perspective.

**The Little Street**

Using
the Renaissance perspective tool, we not only managed to reveal the
identity of the person in the picture, but we can also try to find
out where Vermeer is looking. One
of the consequences of Vermeer's view through the window is that we
are able by
reverse analysis
to define the viewing distance of
*The
Little Street. *The
first step is to convert the dimensions of the canvas or window
(without two segments) to a square. Then,
using the
system of the Renaissance perspective perspective
dividing
space further into
the depth,
we can
figure
out the necessary dimensionscontained
in the picture,
including
the
distance of
the viewer. The
viewer is in
this case
Vermeer
himself. A
divider
in his hand suggest
he is constructing
perspectival scheme and
window's dimensions imply that the scheme is of
*The
Little Street.*

The space divided into squares (or cubes) can be easily calculated: 450 cm (396 x 1.136) - the distance from the viewing point to the first square + 396 cm - first foreshortened square + 300 cm - to the opposite wall. This all equals 1146 cm or 11.46 meters or in original measuring unit it would be 15.9 + 14 + 10.6 = 40.5 Dutch feet.

According to the google distance finder the width of the Voldersgracht Street plus the canal at this point is 10.6 meters.6 We know that Vermeer is 55 centimeters away from the picture plane, from the window. There is around 30 cm remaining, which have to be taken into account for the width of the wall. It comes out to 10.6 + 0.55 + 0,3 = 11.45 meters or 40.5 Dutch feet or 37.5 US feet from the opposite wall to the eye of the beholder, Vermeer's eye itself.

This assertion is in complete accordance with Philip Steadman and Pieter Swillens, who first suggested that the painting shows a building in the Voldersgracht Street, just across from the building where Vermeer lived before his marriage.7

To simplify the layout I only provided the square grid, which is enough to figure out other dimensions. For example, the woman in the passageway is around 17.5 meters away from Vermeer.

Or that the ground floor of the building on the right is 5.2 meters high.

As you could see Vermeer was not constrained to one viewing distance or one focal point. He based his F point positions on the proportional variations of Golden ratio and its square root.

For
*The Little Street*
he utilized
the same scheme as for
*The Music Lesson*,
where
F point
has
been
derived from √φ.
And for *The Geographer*
he used same scheme as for *The
Art of Panting, *where
the F point has
been
derived from √5/2.

**Conclusion**

Today, most scholars disagree with the theory of camera obscura or lucida, but still hardly accept the fact that anyone would be able to find a universal geometric system that refutes this erroneous theory. In the meanwhile the general public is deluded by growth of studies and books about how old masters crammed in a small hot dark boxes were tracing upside down images.

The best Renaissance and Baroque minds have contributed to the method of spatial construction and thanks to their scientific knowledge, the paintings of superior and enduring authenticity have been created. It was my aim to disclose some of the secrets hidden in Vermeer's masterpieces, because the Renaissance Perspective system was recognizable as an intellectual and visual tool for several centuries and stands at the beginning of the artistic era unparalleled in the world.

Finally, I would like to hope, based upon these new facts, that the art of old masters will be perceived with an increased visual alertness and the criteria for their comprehension will become more objective and scientifically substantiated.8

**NOTES**

1.
Philip Steadman, (2002).
*Vermeer's
Camera**.*
Oxford
University Press, p55. ISBN 0-19-280302-6

2. https://www.renaissanceperspective.eu

3. More about how to determine the tiers points, which leads to the construction of the base cube and consequent quadrature, at www.renaissanceperspective.eu

4. https://en.wikipedia.org/wiki/Dutch_units_of_measurement#Length

5.
Elizebeth
Neurdenburg, "Johannes Vermeer. Eenige opmerkingen naar
aanleiding van de nieuwste studies over den Delftschen
Vermeer,"*Oud-Holland* 59,
1942,

6. https://www.mapdevelopers.com/distance_finder.php

7. https://www.essentialvermeer.com/delft/little-street-steadman/little-street-steadman.html

8. https://www.renaissanceperspective.eu