







Fig. 2.1
Masaccio, Trinity (ca. 1425). Fresco. Church of Santa Maria
Novella, Florence. 
ook
at Masaccio's Trinity (Figure 2.1), the most accomplished painting
by the first artist to use rigorous perspective.^{1} Why it looks
compellingly threedimensional will be explained in Chapter ??. In this chapter,
we will discuss the geometry that underlies perspective; in Chapter we will
look at the origins of perspective.
We, in the late twentieth
century,take photography for granted as the prototypical physical embodiment
of picture taking, and perspective as its mathematical model. But for the
artistsscientists of the Renaissance the introduction of perspective required
a complex mesh of innovations: They had to envisage the very concept of "taking"
a picture, to understand the optics implied by this operation, to abstract
the geometry underlying the optics, and finally to discover ways of translating
these abstractions into practical rules of thumb that anyone could apply in
order to draw scenes in perspective. In the Introduction, we have already
encountered Alberti's description of his key concept of taking a picture.
Let us quote it again:
First of all, on the surface on which I am going to paint, I draw a rectangle
of whatever size I want, which I regard as an open window through which the
subject to be painted is to be seen (See Figure 2.2).






Fig. 2.2 Representation of Alberti's
window (perspective drawn using a front picture plane). Engraving
(modified) from G. B. Vignola, La due regole della prospettiva
practica, 1611..



Before we analyze the relation between the Alberti window
and perspective, a distinction must be made between the study of perspective
as the theory of picture taking and the practice of drawing in perspective.
In the remainder of this chapter, we will deal mostly with the theory of perspective,
that is, with the nature of the geometric transformation that allows us to
represent a threedimensional scene on a twodimensional surface, and with
certain features that all perspective representations have in common. After
presenting these notions in some detail, we will dwell briefly on the procedure
that Alberti invented, but because this is a very complicated topic to which
numerous textbooks have been devoted, the reader should not expect to learn
from this book how to draw a perspectivally correct representation.^{2}