lements than a curve
is composed of straight lines.

In a general way, the most radical progress a science can achieve is
the working of the completed results into a new scheme of the whole, by
relation to which they become instantaneous and motionless views taken
at intervals along the continuity of a movement. Such, for example, is
the relation of modern to ancient geometry. The latter, purely static,
worked with figures drawn once for all; the former studies the varying
of a function--that is, the continuous movement by which the figure is
described. No doubt, for greater strictness, all considerations of
motion may be eliminated from mathematical processes; but the
introduction of motion into the genesis of figures is nevertheless the
origin of modern mathematics. We believe that if biology could ever get
as close to its object as mathematics does to its own, it would become,
to the physics and chemistry of organized bodies, what the mathematics
of the moderns has proved to be in relation to ancient geometry. The
wholly superficial displacements of masses and molecules studied in
physics and chemistry would become, by relation to that inner vital
movement (which is transformation and not translation) what the position
of a moving object is to the movement of that object in space. And, so
far as we can see, the procedure by which we should then pass from the
definition of a certain vital action to the system of physico-chemical
facts which it implies would be like passing from the function to its
derivative, from the equation of the curve (_i.e._ the law of the
continuous movement by which the curve is generated) to the equation of
the tangent giving its instantaneous direction. Such a science would be
a _mechanics of transformation_, of which our _mechanics of translation_
would become a particular case, a simplification, a projection on the
plane of pure quantity. And just as an infinity of functions have the
same differential, these functions differing from each other by a
constant, so perhaps the integration of the physico-chemical elements
of properly vital action might determine that action only in part--a
part would be left to indetermination. But such an integration can be no
more than dreamed of; we do not pretend that the dream will ever be
realized. We are only trying, by carrying a certain comparison as far as
possible, to show up to what point our theory goes along with pure
mechanism, and where they par