149THE QUADRIVIUM AND “MIXED MATHEMATICS”
The category “mixed mathematics” is nowadays perhaps best known by
historians from its use by d’Alembert in the “Discours préliminaire” to the
great eighteenth- century Encyclopédie. Its origin is sometimes attributed
to Francis Bacon, d’Alembert’s great hero, at the start of the seventeenth
century.^1 However, the concept and its associations were well established
long before the eighteenth century and were not rooted in the works
of Bacon.
From the sixteenth century well into the nineteenth, “mixed math-
ematics” designated an approach to making natural knowledge that dis-
tinguished it from qualitative natural philosophy. The latter had been
associated with causal explanations for phenomena, which before the
seventeenth century had frequently been denied to the mathematical sci-
ences; mathematics, on this view, had been useful for describing and co-
ordinating the quantitative characteristics of things, including geometri-
cally describable features, but not for addressing questions concerning the
natures of things themselves. Mathematics might tell you how something
behaved, but not why: geometrical optics, for example, could describe the
refl ection of images from mirrors, but could not tell you what light was
and why it behaved in the ways it did.
Mixed mathematics was so called because it combined “pure” math-
ematics with specifi c subject- matters usually considered by physics. Pure
CHAPTER 6Mixed Mathematics
Peter Dear