156 Dear
“Physico- mathematics” meant to Beeckman a curious amalgam of con-
jectural micro- mechanical explanations (of the sort that Descartes himself
subsequently made famous) and, at least in principle, mathematical for-
malisms to discipline the explanatory models so developed.^22 As the term
was adopted by others shortly thereafter, however, its application reverted
to the more widely understood categories associated with the middle sci-
ences of mixed mathematics. The attraction of this new term seems to have
derived, for many, from its provocative attachment of the prefi x “physico”
to the mathematical sciences that addressed aspects of the natural world.
Where Galileo had referred to himself as a “philosophical astronomer,”
so others began to refer to their own work as “physico- mathematics” or
“physico- mathematical,” and to convey much the same idea.^23
By the 1640s the term had become widespread among mathematical
and other philosophical writers, including several Jesuits, such as Atha-
nasius Kircher. One of the more infl uential loci for its use was the circle
around Marin Mersenne. Mersenne published two major works that em-
ployed it in their titles: Cogitata physico mathematica (1644) and its sequel,
usually known as Novarum observationum... tomus III (1647), but the
chief new part of which is called Refl exiones physico- mathematicae.^24 Both
works deal with a multiplicity of mixed mathematical sciences, includ-
ing the new mathematical science of falling bodies and projectiles. One
of Mersenne’s regular correspondents, Jean Le Tenneur, shortly thereaf-
ter published De motu naturaliter accelerato tractatus physico- mathematicus
(1649), which uses the term in very much the same way, here specifi cally
in relation to fall and acceleration.^25 Others, however, had begun to em-
phasize the prefi x as a way of designating a “mathematical” approach to
physics itself: Kircher, in his 1631 Ars magnesia, a “physico- mathematical”
disquisition on the nature and effects of magnets, used the structural
form of so- called theorems and problems to present largely qualitative
assertions based on accounts of experimental procedures.^26 In this usage,
“physico- mathematics” was concerned much more with a kind of experi-
mentalism than it was with mixed mathematics. In general, however, de-
spite the evident rhetorical fl exibility of the term, it usually designated
the well- understood terrain of mixed mathematics. Isaac Newton’s men-
tor and predecessor as Lucasian Professor at Cambridge, Isaac Barrow, in
a published version of his mathematical lectures originally given in the
1660s, explained the division of mathematics into “pure” and “mixed”
and noted that studies falling under the latter category were sometimes
dubbed, in Latin, physico- mathematicas.^27
The two terms, “mixed mathematics” and “physico- mathematics,”
acquired overlapping and fl exible, although constrained, senses in the