mathematics; and the great painter Leonardo da Vinci (1452-1519) had
discovered the principles of mechanics, though without gaining much
influence over the work of his contemporaries. It was reserved for the
triple star which has been mentioned to overthrow Scholasticism. The
conceptions with which the Scholastic-Aristotelian philosophy of nature
sought to get at phenomena--substantial forms, properties, qualitative
change--are thrown aside; their place is taken by matter, forces working
under law, rearrangement of parts. The inquiry into final causes is
rejected as an anthropomorphosis of natural events, and deduction from
efficient causes is alone accepted as scientific explanation. Size, shape,
number, motion, and law are the only and the sufficient principles of
explanation. For magnitudes alone are knowable; wherever it is impossible
to measure and count, to determine force mathematically, there rigorous,
exact science ceases. Nature a system of regularly moved particles of
mass; all that takes place mechanical movement, viz., the combination,
separation, dislocation, oscillation of bodies and corpuscles; mathematics
the organon of natural science! Into this circle of modern scientific
categories are articulated, further, Galileo's new conception of motion
and the conception of atoms, which, previously employed by physicists, as
Daniel Sennert (1619) and others, is now brought into general acceptance
by Gassendi, while the four elements are definitively discarded (Lasswitz,
_Geschichte der Atomistik_, 1890). Still another doctrine of Democritus
is now revived; an evident symptom of the quantification and mechanical
interpretation of natural phenomena being furnished by the doctrine of the
subjectivity of sense qualities, in which, although on varying grounds,
Kepler, Galileo, Descartes, Gassendi, and Hobbes agree.[1] Descartes and
Hobbes will be discussed later. Here we may give a few notes on their
fellow laborers in the service of the mechanical science of nature.

[Footnote 1: Cf. chapter vi. in Natorp's work on _Descartes'