360 12. MODERN GEOMETRIESTwo modern applications of the truncated icosahedron: a mole-
cule of buckminsterfullerene ("buckyball"); a soccer ball.strange and inefficient way of painting, it does illustrate the use of projection very
vividly, even if it was only a "thought experiment." 8
2.3. Girard Desargues. The mathematical development of the theory of projec-
tion began with the work of Girard Desargues (1593-1662). In 1636, one year before
the publication of Descartes' Geometrie, Desargues published a pamphlet with the
ponderous title An Example of One of the General Methods of S.G.D.L? Applied
to the Practice of Perspective Without the Use of Any Third Point, Whether of
Distance or Any Other Kind, Lying Outside the Work Area. The reference to a
"third point" was aimed at the primary disadvantage of Alberti's rules, the need to
use a point not on the canvas in order to get the perspective correct. Three years
later he produced a Rough Draft of an Essay on the Consequences of Intersecting a
Cone with a Plane. In both works, written in French rather than the more custom-
ary Latin, he took advantage of the vernacular to invent new names, not only for
the conic sections, 10 as Durer had done, but also for a large number of concepts
that called attention to particular aspects of the distribution and proportions of
points and lines. He was particularly fond of botanical names, 11 and included tree,
trunk, branch, shoot, and stem, among many other neologisms. Although the new
language might seem distracting, using standard terms for what he had in mind
would have been misleading, since the theory he was constructing unified concepts
that had been distinct before. For example, he realized that a cylinder could be
regarded as a limiting case of a cone, and so he gave the name scroll to the class
consisting of both surfaces. Desargues had very little need to refer to any specific
conic section; his theorems applied to all of them equally. As he said (Field and
Gray, 1987, p. 102—I have changed their roll to scroll):
8 According to Strauss (1977, p. 31), painters of Durcr's time who actually tried to build such
devices found them quite impracticable.
9 Sieur Girard Desargues Lyonnois.
10 He gave the standard names, but suggested deficit, equalation, and exceedence as alternatives.
11 Ivins (1947, cited by Field and Gray, 1987, p. 62) suggested that these names were inspired by
similar names in Alberti's treatise.