162 Dear
Newton thought that he had established a substantive natural philosophi-
cal point by means of the experimental techniques of mixed mathematics.
He could not have done so if natural philosophy were not already widely
regarded, in the Cartesian tradition, as mechanically (and hence math-
ematically) intelligible.IN THE EIGHTEENTH CENTURY
The post- Newtonian philosophical dispensation, as adopted in the open-
ing decades of the eighteenth century in England, integrated mathematics
with physics through the medium of “experimental philosophy,” and the
result was “mixed mathematics” or, sometimes, “physico- mathematics.”
The Newtonian lecturer Jean Desaguliers remarked that Newton himself
“look’d upon Geometry as no farther useful than as it directs us how to
make Experiments and Observations, and draw Consequences from them
when made; so that the Improvement of Philosophy must be the result of
mix’d Mathematics, that is, of Mechanics and Geometry.”^41 Perhaps even
more tellingly, John Harris, in his largely scientifi c and technical diction-
ary, the Lexicon technicum, described “Mixt Mathematicks, which is inter-
woven every where with Physical Considerations.”^42 By contrast, the fi rst
edition of Chambers’s Cyclopedia (1728) still represented the mixed math-
ematics as consisting of such traditional areas as optics, music, mechan-
ics, astronomy, and geography, as well as hydrostatics and pneumatics,
but, curiously, listing statics itself (including the “Doctrine of Motion”)
as a branch of mathematics along with arithmetic and geometry, quite
distinct from the “Artifi cial and Technical” parts of knowledge into which
mixed mathematics fell.^43 Chambers’s taxonomy of knowledge continued
to make a sharp demarcation between contemplative and practical knowl-
edge, therefore: “Staticks is wholly scientifi cal, as it takes up with the mere
Contemplation of Motion: Mechanicks, on the contrary, is an Art, as it
reduces the Doctrines of Staticks into Practice.”^44 His formal defi nition of
mixed mathematics echoes that of Harris but tellingly excises the refer-
ence to physics. “Mix’d Mathematics consider Quantity as subsisting in
material Beings, and as continually interwove.”^45
Indeed, mixed mathematics had never traditionally been understood
as dealing with physical causes, and Chambers’s defi nition easily and un-
controversially reverted to the primary meaning prior to the advent of
physico- mathematics. That understanding is refl ected in the avant- garde
Encyclopédie, and not only in d’Alembert’s quasi- Baconian discussions of