11 / 198
10
The conception of such illustrations is to endow perspective and painting more generally with
status – not as a material craft but as a “liberal art” that has rational and even scientific foundations.
Paintingcanjustlybeseenbranchofpracticalmathematics,akintomusicwithitsPythagoreanharmonies.
Some of the books, most notably German ones of the 16
th
century, regale us with surreal compositions
of geometrical solids of an regular and bizarre kind, as a kind of plastic music.*
2
We can extend the
intellectual motivation that drives such pages more broadly to the agendas of the academies of art that
rose across Europe following the lead of the Florentine Academia del Disegno in 1563. The message
was also directed to a broader society, not least via royal and powerful patrons, as typified by the
dedication of a number of the grander books. At telling example is Joshua Kirby’s publication in 1754
of the perspective system of Brook Taylor, a noted mathematician. The resulting volume with its witty
frontispiece by Hogarth was dedicated to George III*
3
.
The introductions that the authors provided for their volumes typically mirror the implicit intellectual
claims of the frontispiece and social aspirations of the dedication. The idea is to show that art is a
learned discipline. Authors characteristically claim that what is to follow surpasses other treatises in
novelty, optical and geometrical accuracy, intelligibility and practicality
Some basic geometry and sometimes some basic optics typically follows, though more of the former
than the latter. There may well be some basic Euclid, especially of simple geometrical shapes, basic
constructions such as similar triangles, and three-dimensional illustrations of geometrical solids (most
notably the five regular or “Platonic” polyhedra).*
4
The Euclidian and Platonic connotations were
useful and served to make a philosophical point about the “ideal” status of geometry and therefore of
art. Next we would expect to witness the basic geometry of projecting simple forms that are behind
the picture plane on to that plane, given a fixed point located at a given distance from the front of
the plane. The really serious books depict compound solids in perspective and show how the ground
plans and elevation of a complex objects, especially architectural components or whole buildings, can
be projected at any given angle on to the picture surface. We might expect on occasion to find provide
alternative and abbreviated methods, some aimed at encouraging young devotees.
There are some set-piece examples that recur across the treatises, acting like five-finger exercises on
the piano. Early Italian examples include mazzocchi, the facetted doughnut frames that supported
voluminous hats, first illustrated by Uccello and Piero della Francesca*
5
. Lutes are favourite subjects,
portrayed at various angles.*
6
Spiral staircases - a real challenge - serve to certify the author’s
competence.*
7
We find pictures of optical instruments, most obviously in books that discuss
surveying*
8
and even artists’ easels*
9
. There are also arrays of the letters of the alphabet depicted as
sculptural objects and placed in diverse orientations.*
10
The choices seem to be based upon stock ideas
of what a trained perspectivist was expected to accomplish.
A number of treatises deal in more detail with the issue of placing complex semi-regular or irregular
forms, most notably the human body, systematically foreshortened as if seen from the fixed viewpoint.
The most accurate method was to project the human body in plan and elevation, as demonstrated
by Cousin,*
11
but there was also a short-hand technique of reducing figures to a series of box-like
components within which the detailed forms could be foreshortened.*
12
Complementing the projections of the bodies, a number of the treatises deal with the geometry of
shadows cast by various bodies under illumination from given sources of light.*
13
Mechanical or optical devices or instruments for the achieving of perspective constructions in an
automated manner are illustrated and discussed by some of the authors. The simplest are the glass and
“veil”, which allow the direct transcription of the seen thing from a fixed view point on to a flat surface*
14
.
*
2
184, 345
*
3
348
*
4
1, 14, 25, 26, 72, 83, 90-92, 164, 167, 259, 357
*
5
282
*
6
1
*
7
17, 80
*
8
2, 22, 93, 95, 263, 277, 278
*
9
183, 330
*
10
61, 213
*
11
87-89
*
12
209, 304
*
13
35, 107, 110
*
14
103, 195