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A
modern
branch
of
mathematics
having
achieved
the
art
of
dealing
with
the
infinitely
small
can
now
yield
solutions
in
other
more
complex
problems
of
motion
which
used
to
appear
insoluble
.
This
modern
branch
of
mathematics
,
unknown
to
the
ancients
,
when
dealing
with
problems
of
motion
admits
the
conception
of
the
infinitely
small
,
and
so
conforms
to
the
chief
condition
of
motion
(
absolute
continuity
)
and
thereby
corrects
the
inevitable
error
which
the
human
mind
can
not
avoid
when
it
deals
with
separate
elements
of
motion
instead
of
examining
continuous
motion
.
In
seeking
the
laws
of
historical
movement
just
the
same
thing
happens
.
The
movement
of
humanity
,
arising
as
it
does
from
innumerable
arbitrary
human
wills
,
is
continuous
.
To
understand
the
laws
of
this
continuous
movement
is
the
aim
of
history
.
But
to
arrive
at
these
laws
,
resulting
from
the
sum
of
all
those
human
wills
,
man
's
mind
postulates
arbitrary
and
disconnected
units
.
The
first
method
of
history
is
to
take
an
arbitrarily
selected
series
of
continuous
events
and
examine
it
apart
from
others
,
though
there
is
and
can
be
no
beginning
to
any
event
,
for
one
event
always
flows
uninterruptedly
from
another
.
The
second
method
is
to
consider
the
actions
of
some
one
man
--
a
king
or
a
commander
--
as
equivalent
to
the
sum
of
many
individual
wills
;
whereas
the
sum
of
individual
wills
is
never
expressed
by
the
activity
of
a
single
historic
personage
.
Historical
science
in
its
endeavor
to
draw
nearer
to
truth
continually
takes
smaller
and
smaller
units
for
examination
.
But
however
small
the
units
it
takes
,
we
feel
that
to
take
any
unit
disconnected
from
others
,
or
to
assume
a
beginning
of
any
phenomenon
,
or
to
say
that
the
will
of
many
men
is
expressed
by
the
actions
of
any
one
historic
personage
,
is
in
itself
false
.
It
needs
no
critical
exertion
to
reduce
utterly
to
dust
any
deductions
drawn
from
history
.
It
is
merely
necessary
to
select
some
larger
or
smaller
unit
as
the
subject
of
observation
--
as
criticism
has
every
right
to
do
,
seeing
that
whatever
unit
history
observes
must
always
be
arbitrarily
selected
.
Only
by
taking
infinitesimally
small
units
for
observation
(
the
differential
of
history
,
that
is
,
the
individual
tendencies
of
men
)
and
attaining
to
the
art
of
integrating
them
(
that
is
,
finding
the
sum
of
these
infinitesimals
)
can
we
hope
to
arrive
at
the
laws
of
history
.
The
first
fifteen
years
of
the
nineteenth
century
in
Europe
present
an
extraordinary
movement
of
millions
of
people
.
Men
leave
their
customary
pursuits
,
hasten
from
one
side
of
Europe
to
the
other
,
plunder
and
slaughter
one
another
,
triumph
and
are
plunged
in
despair
,
and
for
some
years
the
whole
course
of
life
is
altered
and
presents
an
intensive
movement
which
first
increases
and
then
slackens
.
What
was
the
cause
of
this
movement
,
by
what
laws
was
it
governed
?
asks
the
mind
of
man
.
The
historians
,
replying
to
this
question
,
lay
before
us
the
sayings
and
doings
of
a
few
dozen
men
in
a
building
in
the
city
of
Paris
,
calling
these
sayings
and
doings
"
the
Revolution
"
;
then
they
give
a
detailed
biography
of
Napoleon
and
of
certain
people
favorable
or
hostile
to
him
;
tell
of
the
influence
some
of
these
people
had
on
others
,
and
say
:
that
is
why
this
movement
took
place
and
those
are
its
laws
.
