Lenses and Waves

THE 'PROJET' OF 1672 117
mechanical philosophy notwithstanding, this ‘physical’ understanding of rays
and their behavior would crucially affect the investigations of Huygens and
other seventeenth-century opticians. Kepler and Descartes set off where
Alhacen and Witelo had left off. A law of reflection was known, as well as
diverse mathematical properties of radiated light, but refraction remained to
be understood only qualitatively. The thirteenth-century synthesis left
perspectiva as a comprehensive body of knowledge – Alhacen’s theory of
vision, solutions to various problems of reflection and so on – riddled with
some persistent, well-known problems like the pinhole image. 39 The sixteenth
century witnessed major developments in optics, but mainly in its practical
parts that bore on Galileo’s telescopic achievements rather than Kepler’s and
Descartes’ theoretical pursuits. 40
4.1.2 KEPLER ON THE MEASURE AND THE CAUSE OF REFRACTION
The heritage of medieval perspectiva Kepler received, consisted of a welldefined
set of aims and criteria for geometrical optics: mathematical analysis
of the behavior of light rays. 41 In Paralipomena he took up this heritage and
transformed it radically. In chapter two we have seen how he created a new
theory of image formation by rigorously applying the principle of rectilinear
propagation of light rays. We now turn to his account of the causes
underlying the behavior of light rays. Here the same approach is
recognizable. In Kepler’s view, the mathematically established properties of
things are real and should be directive in physical considerations. Kepler’s
conception of the nature of light can be seen as a realist reading of
perspectivist’s mathematical ideas which he then rigorously employed in the
investigation of the behavior of light. 42
At the start of this section I cited the opening lines of Paralipomena, where
Kepler pointed out the relative freedom of reasoning he would employ in
these matters pertaining to physics. In the first chapter, ‘De Natura Lucis’, he
expounded the general concepts and principles pertaining to his account of
optics. On the whole, his theory of light was the perspectivists’ theory of
multiplication of species enriched with neoplatonist metaphysics. 43 According
to Kepler, light is an incorporeal substance which has two aspects, essence
and quantity, by which it has two operations (‘energias’), illumination and
local motion, respectively. 44 Radiation is the form of propagation: light
spreads in all directions and does so spherically. Light rays are the radii of
this sphere and thus rectilinear. Light itself can be regarded as the twodimensional
surface of an expanding sphere. The mathematical structure of
39
Lindberg, Theories, 122-132.
40
Dupré, Galileo, 17-19.
41
Lindberg, “Roger Bacon”, 249-250.
42
The following discussion owes much to Buchdahl’s illuminating discussion of Kepler’s method:
Buchdahl “Methodological aspects”. References are to the original text, corresponding pages in the
Gesammelte Werke in parentheses. Except where noted, translations are by Donahue from Kepler, Optics.
43
Lindberg, “Incorporeality”, 240-243.
44
Kepler, Paralipomena, 13 (KGW2, 24)