1758,
published
at
Vienna,
because,
advantage
;
of
profound
regret
to
everyone
Philip
Butler
largely
to
general
science
of
1763,
established
In
1736,
Boscovich
began
his
the
Venice,
revised,
enlarged
and
rearranged
and
original
edition
taken as the
in
the
Papal
States.
Boscovich
had
designed
Voyage astronomique
Italy
by
his
professorship
at
Rome,
of Venus
city
in
company
with
the
English
ambas-
complicated by
appointed
him
director
of
his
native
town,
his
beloved
Ragusa,
which
has
most
fitly
celebrated
the
letter,
dated
May
3rd,
1774,
to a
two
material
points
can
occupy
expressing
the
reason
why
such
induction
can
be
made),
that
two
material
points
cannot
occupy
the
same
local
point
simultaneously
material
points
1
perception
and
appetition
in
a
vis
viva.
Boscovich
opposes
this
idea
own
material
points.
of
bodies
forming
a
system
;
rearranged
material
points
is
finite,
whereas
the
number
even
goes
further
motion
in
a
straight
line,
whichever
point
relative
to
the
other.
If,
on
the
other
hand,
we
consider
with
Clerk
Maxwell
point
unimaginable.
Clerk
Maxwell,
in
ascribing
Boscovich
ascribed
vis,
as
used
by
the
mutual
vires,
ascribed
by
Boscovich
Boscovich's own
is
corroborated
by
of
his
no
mass,
 
and B
bodies have their velocities
;
the Newtonian sense
cause,
Boscovich is an
cosmic
system
definition
what
points
body,
by
the
reader,
after
a
study
curve of
equiangular spiral
major
axis
is
decreased
indefinitely,
equal
distance
on
title is : De Motu
overcoming
this
discrepancy
curve near
must be
points
are
the axis at
sight
of
this
latter
possi-
bility,
but
apparently
a curve
branch, however,
between
these
points
of
finally
of other
similar
plane
of
equal
points
are
conglomerated
steady
disturbed,
by
a
sufficiently
great
difference
follow on the
adds
that
there
are
no
signs
in
Nature
of
anything
approaching
perpendicular
velocity
upon
entering
the
 
is
equal
medium
mind,
are
full
of
would
appear
that
the
own
catalogue
Mention
 
leaves
present
in
the
seed
p.
115,
1.
some
difficulty
for
copies
of
progress,
& that
he
should
superintend
the
whole
thing
travelling
of the human
see
the
purpose
of
rendering
certain
passages
more
elegant
& clear
regirninis
curas
importunus
interpellator
advenio,
;
ubique
se
prodat
uniformis
agendi
ratio,
is
not
unimportant
as
altogether,
let
no
forces
producing
mutual
approach
at
things
disclosed
itself
single
volume,
the
matter
being
carried
out
during
have
said,
was
twofold
your
approval,
higher
geometry
the
heading
Supplements
a
image
points
depending
representation
requires
far
more
knowledge
of
algebraical
processes,
of
the
segments
requires
no
geometrical
proof,
but
only
a
knowledge
of
certain
terms,
which
either
belong
defined
when
they
speak
being
asymptotic
asymptote
to
any
arc which
highly
of
some
difficulty
for
copies
of
for
the
purpose
of
rendering
certain
passages
more
elegant
& clear
young
it
is
introduced,
explained,
some
for
copies
of
pub-
lished
in
progress,
& that
Vienna will soon
complicated
nature,
;
law of forces is an instance of this. I find
that between
employed
the
latter
In a
habere,
motusque
leges
passivas
illas,
ques
that it does not
quite
ignorant
of
geometry,
given
the
explanation
of
but
few
terms,
may
get
perfectly
good
idea
facts,
whilst
the
second
will
credit
Newton,
my Theory,
of
these,
ished,
vanish,
be
changed
decreases
approximately
scope
of
it
by
a
straightforward
argument
me
by
the
Newtonians,
particles
of
solids,
esse,
videatur
At this
principle
is
derived,
& where
real
quantities
lacking,
existence and
antecedent series of
having
nature
of
these
velocities &
to
their
changes.
Further,
principle
of
continuity
that,
when
one
body
a
this
complete
law
already
this kind.
First of
of this
law
of
inverse
squares
is
very
slight.
From
Art.
124
onwards,
this sort from the
is
more
likely
to
lead
to
perceive
them
by
any difficulty.
regard
to
space,
the
properties
of
light,
extension seems
especially
in
connection
with
the
curve
matters,
single
inviolate
elementary
system.
From
Art.
172
by
the
latter,
In Art.
put
in
general
calculation
forces
this also
221
that
follow,
I
much
Physics.
222
two
points
rods,
either
rigid,
flexible
or
elastic,
analogy
27
I
supply,
& I
bring
forward
treatment. In Art.
Theory
of
living
forces,
since
everything
can
be
explained
without
them
bodies,
relative force
these
same
resultant
forces
to
one
another
from the third
acting,
the
theorem
relating
to
preponderance
to
the
case
also,
mutually
act
upon
one
another
principles
is, that,
of its
be
equal
These
things
the
general
375,
concerned with the
399
particular
branch
attraction
is
greatest
at
actual
contact,
possible
for
various
shapes
of
one
particle
upon
another,
points
their
natural
positions
still
of
forces,
the
frequency
a
single
472
vision,
I
very
briefly
follow
next.
Then,
in
the
S3
and
alteration
are
investigated,
part
of
my
Theory.
I
one
thing
with
regard
simple
investigations.
Initially,
my
idea
not
only
those
more
especially
worth
mention,
which
my
mind
previously,
whilst
others
in
determinationem ad
are also
law,
which
it
pass
from
being
attractive
to
being
repulsive,
i.e.,
from
a
propensity
to
approach
force that varies
abxlute.
 
presented by
every way.
change
its
direction
deveniat
ad
immediatum
contactum
this
6
use
ln
Physics
any
point
or
regular
by
those,
who
think,
thoroughly,
it
struck
me
that,
if
The
cause
of
we
employ
a
straightforward
that
really
immediate
impulsive
action
of
he
idea'
one
body
on
another,
of
Continuity
continue
lineae
segmenta,
mutatio
greater
distance
in
space
than
front surface of the second
body
must
have
passed
beyond
body
time that
force of
my argument
any particles,
no matter
surface
bodies
QUO
pacto
nomen
25.
Hinc
autem
in
iis
ipsis
massa
quaedam
considerari
potest
duarum
dimensionum,
vel
in minimis
of
velocity.
Moreover,
there
is
in
truth
always
something
of
this
the
manner
boundary
*
with a
surface,
or
a
line,
or
any
quantity, namely,
for a
will be as
the
change
P
mts
suerit,
dimcultatem
ejusmodi
amoveri
posse
dicendo,
duas
r
myself
with
regard
conclusion that there could
layer
of
air,
(that
upon
those
arguments
that
persuade
it,
consists
in
the
idea
that,
in accessum
parts
of
continuous
time,
which
cor-
respond
to
these
parts
of
a
line,
themselves
also
continuous,
& instants
of
time,
which
are
AB to
passage
through
all
intermediate
stages
or
>
after
it
interval that can be
next
state
to
it,
some
momentary
addition
having
been
made
represents
it,
possible
for
a
passage
to
take
place
Passages
without
through
all
intermediate
55
place
account,
if
we
have
regard
mentioned,
velocities of
the
words
motions
take
place
in
continuous
lines
that
The
planets
horizon,
not
suddenly,
by
adopted.
changed
anguli,
sed
semper
mutatio
rivers,
in
the
leaves,
boughs
& branches
of
trees,
continuity
large
number
of
other
examples,
such
may
be
employed,
particularly,
which
can
be
examined
in
question
is
followed,
in
all
of
certain
bodies
penetrating
pass
through
of
bodies,
we
that
they
depend
on
ejus
conciliationis
exemplum,
compenetration,
or
enfolding,
or
be
deficient
in
inertia,
but
larger
masses
small
particles
account
of
its
being
parts
whole without
necessary
that,
property,
example
of
through
inductive
reasoning.
their
way,
by
saltu
spongiae
ingressa
respectu
ad
emuxum
1I
aquK
impenetrabilitatis,
some continuous
series such
that we
it
by
some
other
that
that these
complete parallel
of latitude
on the
of
the
beginning
second
oscilla-
tions
equal
parts,
& the
path
traversed
(or
the
time
spent
in
traversing
the
path)
is
taken
between
an
Examples
for some
the
gunpowder
has
to
be
inflamed
use of
puncta contigua, quorum
the
first
segment,
magnitudes
to each instant
to travel
it,
as
in
Fig.
6
it,
sudden
change,
happen,
comes about that
time two
the time
thing
will
both
exist
& not
exist,
instant,
namely
that
dissertation,
beginning
with
Art.
8
continuous motion from A
in two
instant
preceding
series
exist can
ordinate,
;
a
themselves
exclude
evident,
r
i
PLg
same
given,
& the
quantity,
Hence,
;
CL,
quas
evanescet,
ubi
puncto
C
localibus existendi
posteriores per
change
from
creation
or
annihilation,
or
production
real
the
the
other,
which
deeply
considered
points
C,L,
or
H,M ;
;
&
another,
But
they
kind,
as
CL,
are
called
positive
distances,
an
Fig.
8.
71
62.
 Hence
&stable conclusion that
last
;
velocities,
somewhat
more
carefully.
64.
The
term
velocity,
general by
Mechanicians is
place
accurately.
is
everywhere
intended
by
Mechanicians,
when
they
make
geometrical
measured
diagrams
for
any
way
it
is
potential
prescribed potential velocity.
ipsum,
quod
conditionatus
est.
Jam
vero
suo
termino
stare
possit.
Quovis
momento
66.
Praeterea
corporis,
vel
puncti
existentis
potest
utique
that
particular
propensity
is
for
other
reasons
altered
by
the
conjunction
part
existendi
ipsorum,
of B at
X
>>
HK.
For,
according
ejus
gravitate
in
terram
comparata
cum
;
the
preceding
velocities,
BE,
& the
first
of
the
subsequent
ference
of
velocities
velocities,
BF.
Now,
since
(as
contact with the
& motions.
72.
In
both bodies
Continuity,
mutual,
& act
m
one
of
the
two
bodies
only,
altering
the
of
the
body
in
opposite
directions,
bodies
only,
or
time,
& how.
This
point
will
equal
orbit
arising
the two
the
force
which
infinitum
excrescentium,
quo
casu
asymptotus
AB
non
transiret
per
initium
distantiae
binorum
corporum,
est
is,
quern
in
figura
i
proposui,
haberi
degrees
left
over
(for,
between
20
increased,
when
diminished,
also
compared
as
a
boundary
limit
to
forces
great
the
asymptote
that,
as
the
distances
are
indefinitely
diminished,
increase
indefinitely
particularum
repulsio
fuerit,
quin
will have an
limit-points,
i.e.,
attractions of universal
pushed
inwards,
the
the curve of
constitution
naturalis,
utut
praesup-
ponens
aliquid
factum
vi
agente
supra
Naturam.
they
during
to
quite
overthrown
by
that
same
bring
under
observation,
that
auction
6
correctly
whatever
occupies
even be
in
merely
a
remaining
points
^v
vr ..
points
of
space.
87.
ways
the
analogy
between
space
& time
is
impaired.
2^
pace
and
tlme
any
point
of
space,
in
which
elements
are
simple,
non-extended &
non-adjacent.
For
continuum
extcn-
e
Natura,
in
innmtum
6 *
ea
a
C011
start,
fact
Now,
that
this
even
contained
in
them,
as
is
points
of
matter,
point
of
matter,
in
any
direction
whatever
perceive,
J
i
o
rr
t
o
that it takes
quam
set of
place
in
which
it
puts
it
rather
than
in
the
place
of
another.
But
&
things,
instance
such
as
mind,
except
when
which
will
entirely
prevent
similarity.
Moreover
this
tendency
are
perfectly
homogeneous
many
above,
analysis
&
experiments.
This
will
be
presented
at
such small distances from one another that the intervals cannot be
perceived except
consisting
of
printed
letters,
the characters is
could
compose
lexicons,
as
many
languages
so
many
what
investigation,
the
similar
of
difference
amongst
themselves,
less unlike
one another
letters,
would
form
evitetur
hie
actio
alia
ejusmodi,
quae
quidem
longe
superant
humanum
captum,
sunt,
progignat
in
sunt
omnia,
phcajidam.
impost-
at
q
ue
determinata,
& ad
calculum
redacta
cum
phaenomenis
congruunt
ultra,
quam
sperare
liceret,
accuratissime.
Ego
quidem
ejusmodi
in
explicando,
95
consideration
of
Nature
i
proof
of
the
Theory
legitimate
r
i
of forces.
what
a
bountiful
8,
them are a
Moreover
all
perfectly
plain.
things
the
particles
composing
it,
or
why
repulsione
minimam
primam
attractionem
transitur.
statibus,
quern
aliquando
utique
continue
motu
puncti
b
ad
Lumine,
everywhere
raise these
right
down
to
zero,
in
which
there
is
the
propensity
for
preserving
the
original
straight
line
zero
up
to
the
prescribed
attractive
force,
by
the
points
as
as
ordinates
all
magnitudes,
less
the last ordinate dh.
pictorial
first
them
the case of a
;
per
continuam
mutationem
passes
over
attractive
negative
tum,
mirum
sane,
quantus
sit
is
ipse
an
curves
above we
are led
axis in
a few
r
second kind
by
multiplication
simple
Aestu,
& the
supplements
to
different
geometry,
referring
all
other
curves
to
that
one,
just
as
we
compare
i
expressed,
requires
a
deeper
knowledge
01
analysis
itselt.
Wnereiore
expression
he can indeed describe on the attractive side the which
has
can be divided into
resolution of forces. But all this will be as it
were
only
a
conception
gravitation decreasing
cohesion
is
immensely
greater
added the
the
res
But Clairaut found
carried far
gravitation
being
so
accurately
observed
were the
least because
of
my
of
his,
I
mean,
ing
to
Maupertuis,
with
regard
to
the
law
of
forces
decreasing
separate
particles
Nature
known
and did set
before Himself when
hoc,
qui
electus
est,
of the other
particular,
of
evidence
of
praestabunt nunquam
velocity
is
produced,
motion
is
changed,
or
the
motion
itself
their correct
134.
length
(that
being
the
length
in
itself
of
the
plane
mass,
plane
we
acquire
thing,
which
is such that it does not allow another indivisible and non-extended
thing
or
leaves
possible
so
own kind
of indivisible
there were
forces which
the
notion
of
simple
non-extended
points
Simple
and
into
physics.
had
an
&
another,
an
idea
they
have
acquired
through
right
put
words
117
proved
by
assuming
the
truth
of
the
contradictory
proposition.
For
other can
of the
merely
a
question
of
terminology.
of
before
temporal
any
sort
so
near
cannot be others
greatest
or
as all
aliqua
per
saltum,
alia
parte
reflexa,
ali
refracta,
sine
ullo
intermedio
flexu
cujuspiam.
through
all
magnitudes
in the
same manner.
continuity
of
motions
masses
certain
cases,
relating
uous
lines
  is
light
falls
upon
a
plane
mirror,
part
is
refracted &
part
is
reflected.
In
reflection &
inter-
refraction,
according
to
times,
& even
only begin
distances
whatever.
of
Continuity.
Hence
in
diffusion
in
my
Theory
observes
98.
Sed
the
angles
angle.
147.
It
seems
to total
be done
is
not
continuous
an increment
term
thing
separate parts
man.
Also,
since
kind,
in
which
aggregates
of
things
are
taken,
separated
was
for
this
very
reason
that,
nothing
without
the
inclusion
altogether
false
wise affect
know in
think and will
the
question,
represented
in
Fig.
i,
cannot think
Cartesians in
senses,
rest,
& that
the
daily
motions
of
the
Sun
source of
fewer occasions
scope
whether
properties
of this kind would be intrinsic in the matter of which
the
bodies
are
composed,
mcnis>
formed.
Further,
these
ideas,
of the
formed
1111
which
groups
of
points
groups
of
points,
tenacious
masses :
n t i 11-1 i i T i i i i
n
&
third
part,
repulsion
at
smaller
it),
more
fully,
per
eas
squares
of
the
distances,
expounded,
may
go
away
to
infinity.
There
will
not
(*)
to
infinity,
W
thus
in
arcum
asymptoticum
attractivum,
may possibly
curve
is
winding,
is
exceedingly
small
compared
any
applied
to
MQ
can
approach
so
closely
to
the
straight
lines
MQ,
QV
any
given
area,
even
although
QV
little further on.
area
should
that the
it
is
derived
the
simple
inverse
ratio
of
the
abscissse,
ibunt
ialves
of
the
dis-
. .
same
approaches.
These
points
attractive
to
the
equal
;
&
limit-points
of
the
first
kind,
are
indeed
they
will
ipso, quod
Transitus
per
infi-
185.
Hi
quidem
F i i r i i i i f i
i
6
g
cl
i
to or
another
than
they
stronger
than
others,
or
weaker,
in
any
manner
its
tangent,
or
the
ordinate,
or
any
other
straight
the axis
Yet,
that
these
point
of
curva
censeo
removendos
made
on
the
opposite
that
be
both
attractive &
repulsive,
conditione
ab
ipso,
impediente
transitum
area
repulsiva
mnnita,
:
per
intervalla
aequalia,
prout
fuerint
sub
arcu
attractivo,
vel
repulsive.
Quoniam
away
squares
case,
even
if
limit-point
becomes
equal
to
the
area
under
the
for the
several short
^ ^abeat^maxU
be obtained
original
position,
will
immediately
afterwards
retrace
their
paths
they
at,
that
of
the
velocity
j^sfderabSH-han^e;
projectorum.
P
er
directiones,
quae
is
an
important
use
Fig.
problem
already
solved
by
Newton
of
gravity
is
plane,
measured
in
any
direction,
will
be
equal
to
the
general
theore-
the
direction
tantummodo
every
point
the far
treated
algebraically,
point
would
points
7
The
1
great
be
determined,
both
in
position
the
same,
the
laws
with
respect
to
different
rr
distances,
will be of
direction of
the force
for
each
sequalitatis, adeoque
quocunque
punctorum
qu;is
mas- _
be
easily
demonstrated.
For,
small
mass
that
in
Fig.
i,
more
simple
case
perpendicular
point,
there
may
be
altogether
different
forces
tances.
for
several
points
are
now
attractive,
centre of
the mass
duplicate
by
a
mass
considerably
forces
that
are
approximately
equal
disposition
of
the
points,
or
their
number,
may
be
for
either
mass.
213.
It
in the
different,
as
punctum
d,
sumaturque
refers to
produced
itself the matter is
Fig.
i
by
the
two
points
point
the
equation
of
the
curve
in
Fig.
directionem
CC',
oppositam
C'C.
Deinde
facile
patebit,
vim
direction
CC',
required
in
Fig.
I
for
difference
of
the
two
corresponding
Fig.
27,
weu
let
equal
to
half
the
poterunt
: vel
enim
punctum
before,
the axis
at all
third a
point,
if
they
were
both
situated
single
system
straight
owing
i r V.
by
But
acts
perpendicularly,
so
that,
for
instance,
the
point
acting
in
u f i n i
torted
by
parallel
to
AB,
or
parallel
to
the
forces.
laws of
a
kind,
that
no
one
of
them
is
8
three distances
equilibrium.
For,
if
in
Fig.
i
we
take
Az,
Au
equal
to
AO,
BO
of
Fig.
32,
then
Nz,
repelled
from
O
the
the
force
directed
action
.is towards
the ver-
angle
LCI
will
be
equal
of
the
ellipse
is
disturbed
somewhat
in
addition,
owing
to
centrifugal
force.
232.
Fig.
ATT- i T A ^i i /^XT i i r
-i
limit-points
a
repulsion
for
the
intra
perimetrum
mediam,
factis
BC',
AC'
minoribus,
quam
ellipsis,
this
ellipse
is
equal
they
perimeter. Exactly
Art.
ellipses
use for
truly
corresponding
along
the
perimeter
to
a
limit-point
of
other
conjugati
accelerabit,
& ita
porro,
;
innuam.
H,a
tiis
hmitum,
suao
q
u
great
conjugate
axis
with
which
connection
with
they
are
urged
towards
that
flexible
rods;
a.
at
the
possible
of
a
solid
rod,
in
which,
if
the
lowest
set
or
points
is
inclined,
all
the
points
a
single
distance
corresponding
to
a
limit-point
position
majores,
sed
adhuc
multo
magis
mobiles,
atque
variabiles,
ex
quibus
pendent
chemica;
operationes,
& ex
quibus
haec
ipsa
crassiora
corpora
componuntur,
manner,
greater,
& useful
properties
of
the
centre
of
 ntr?
of
 gravity^
gravity.
will move
motion in
gravity
of
any
number
of
points,
Definition
the
situated
in
191
taken
together
are
equal
to
Of
to
the
corresponding
to the sums
Consequently,
in
what
follows,
whenever
speak
of
distances,
will
exceed
the
sum
for
those
lying
on
the
planes
multiplied
demonstrations,
by
the distances from one of them over the
sum
of
the
distances
from
the
other
is
equal
to
the
which
the
distances
the
measured,
distances on
the
other
side
of
just
have
every
point
that
of
all
the
points
of
the
first
class,
like
E,
by
points
lying
on
the
near
side
of
PV,
quae
resolvitur
6
l
v
in
s
beyond
.
,
.
, ,
the
the
positives
over
the
negatives.
In
precisely
the
same
manner,
we
may
three
planes,
determining
equilibrium,
centre
of
magnitude
muni
methodo.
is here
of
magnitude
in
any
one
points
belonging
to
the
mass
A,
the
negatives
being
to
divided in the
reciprocal
ratio
of
the
sum
of
the
first
two
;
many
continuous
figures.
Thus,
in
Fig.
38,
base.
For,
the
straight
line
BD
GE
gravity,
that,
although
the
areas
FAGH,
FBH
are
unequal,
yet
If,
task
interval that
is the
generaliter,
& admodum
facile,
ac
luculenter
demon-
stratur.
[122]
Concipiamus
vires
singulas
a
part
same
thing.
as it
of
the
magnitude
the
same
different
pairs
of
points
in
time
points
pair,
whilst
all
the
others
remain at rest. Then at the end of the last of these intervals of
time,
each
point
single
will
represent
had existed no velocities
together,
at
the
time,
of
the
mutual
forces,
which
may
be
assumed
not
change
the
distance
solis initialibus
time,
& then
moves
demonstration,
some other
is
approach,
the
approaches
of
the
masses.
For,
by
the
theorem,
the
common
centre
of
gravity
of
the
they
do
not,
but
only
the
& the distances
masses,
adapted
to
force
of
impenetrability,
alterum,
globi
body
impinging
body
which
is
following
put
its
velocity
c
sphere
will
continue
to
>
centres
of
gravity,
;
indeed
everywhere
in
elementary
books.
I
myself
have
followed
plane
usual method
vaiere.
pressure
impeded,
the
other
equilibrium
eum
sustinet
fili
respond-
such
that,
when
combined
with
BO,
will
give
a
attraction towards
of the
of
all
compounded
into
BG
(in
Now,
since
the
General
summing
in
gives
everything
empty space
in the
is
found,
equal
given
habeatur
effectus
non
aequalis
suae
will
rightly
govern
such
resolution,
which
will
complete
the
composition.
For,
the
straight
lines
AB,
BC,
triangles
AEB,
PFC
are
equal,
& thus
account
to
the
usual
merely
a
stress
globum
approaching
is
enormous,
...
point
such
as
Q
was
reached
where
extended,
such
inequality
the
vertical,
the
same
angle.
T>T i i 11 i i i r i
regard
the
ascent;
IT r
planes,
but
when
d^ed
we have
to
L L '1.
perpendicular
;
^ fo^e^with
pairs,
triangle
;
&
triangle
respect
to
it,
or
they
will also
directed towards
the same
The
proof
along
its
diagonal.
Such
equality
will
be
;
base,
force
is
given
in
all
cases.
cum
distantia
a
the
sines
of
the
angles
CB
A,
CAB
is
to the motive
force for
B as
motive
forces
direction,
as
triangle
the
third,
the
quavis
alia
directione
;
&
these
by
means
of
mutual
forces,
triangle
upon
inverse ratio
to
be
externae,
sed
in
pluribus
autem oriuntur tria
also
acting,
not
on
three
masses
only,
nuniDer
01
masses
i i r
.further,
chosen
from
C,
since
the chosen
; then,
.
perpendiculares
distantias
possit
tota
massa
tanquam
eadem
Theoria,
plura pondera,
haec,
retardare
Q
nation
of
the
oscillate
more
quickly,
the one
then known
in the
as
well,
but
similar,
possible
way.
330.
Suppose
QM
Tus
Jensen
P
any
such
in
the
plane
FOR,
perpendicular
The
i 1^1- i i_ T J J
-U
tne
application
to
values
of
the
sines
q
same,
with
a
gene-
at
any
quapiam,
vel
piano,
vel
of
oscillation,
is substituted
that which
distance
point
of
abo
*
formula for
1 r
>~\ i i i A i i i A A T> rn/~\
the force
Benvenuto,
he
expounded
it
first
utcunque
dispersis,
& cum
omnibus
directionibus
agens.
Ax
AP
-f
B
x
quacunque,
repulsiva
inter
secundum,
A,
B,
&c.,
which
are
proceeding
with
their
several
become
endless,
& it
is
quite
to the
cancelled
by
repulsive
equal
the
particles
next
to
it,
pertain,
must
be
equal
in
acre,
quae
hyperbolae
conicae
Apollonianae.
by
a
contrary
particles
like
N
equal
to
amount
of
fluid
superincumbent
fluid
upheld,
even
though
this
is
immensely
great,
pressure
of
the
fluid,
upon
the
balance
water
being
volatile
become
fixed,
& Hales
elastlc
va
especially
gave
a
very
full
proof
of
this),
the
arc
are
diminished
satisfy
the
conditions
logistic
curves.
If
corresponding
to
any'
AC,
third,
much the
in
the
subduplicate
ratio
For,
then
the
velocity may
the whole altitude
sequantur
superiores
leges,
pens
many
things
which
opened
part
beginning
species.
of
the
first
part.
After
that,
from
to which class
immediately
from
this
principle
is
taken
into
account,
the
first
case
is
infinitely
more
improbable
than
the
second.
Hence,
in
any
projection
whatever
of
mass
against
mass
there
is
of
these
asymptotes,
cannot
with
any
finite
of the
regular pyramid
globus sciopeto
movet :
cur
lumini
tormentarns
globis
impetuntur.
In
this
case,
not
projected
with
communicated to
to
the
path
the
ball,
is
bombarded
with
the
slightest.
Merely
a
hole,
approximately
equal
to
& vacuo
spatio,
quod
est
purum
nihil.
Constat
per
were
born,
during
infancy
is
infinitely
is
the same
absolutely
mtthematically,
points
plane
eiegans
anaiogia
theticse,
quae
inde
deducuntur,
[171]
sunt
verse,
punctis
ponatur
tertium
novum
ad
aequalem
distantiam
ex
parte
altera
physical
sense,
by
The
sum
equal
distances,
we
can
say
that
one
distance
is
name double
congruence
idea
of
it
is,
even
m
has
its
boundaries
investigate
regard
which
that has even
is
m
the
idea
of
it
in
my
1
heory
of
different
heterogeneous
substances.
Again
if
considered
to
its internal
considered
as
being
necessary
to
only
something
solid
;
points
&
be
excluded
by
the
argument
of
infinite
improbability,
which
I
used
in
the
there
respect
gravity,
whether
this
is
at
rest
or
travelling
uniformly
Art. 88
be
reduced
to
the
twisting
any
Perhaps
even
the
positions
of
no
matter
how
small,
would
problem.
Now,
oppositas,
grasp,
determination
is
the
fixed
stars)
 
arise
&
mind;
& that
Free
of
continuity
without
any
break
not
in
it
should
be
remarked
that
by
means
of
this
Hence,
the
point
as
law
especially
the
existence
of
these
to
the
source
indefinitely
without
infinite
divisibility
any
occupies
a
distinct
part
of
space
sion.
is
itself
distinct,
then,
from
the
divisibility
of
continuous
space,
the
infinite
divisibility
of
divisibility,
yet
I
do
number
of
points
greater
than
Universe
to
the
phenomena
of
Nature,
particles,
changed.
Now,
can
be
changed
simultaneously
directionibus,
sed
summa
earum
respondet
ad
sensum
summae
punctorum
;
&
distances,
but
only
to
its
up
a
huge
resistance
the
points
usually
employed
by
mechanicians
;
systema
pertinentium
distantiae
maximae
a
Sole,
incipiat
recedere
plurimum
ab
hyperbola
habente
ordinatas
reciprocas
quadratorum
distantiae,
of
equilibrium,
the
lever,
the
balance
& the
principles
of
machines
masses
acting
mutually
upon
one
another
mass.
Others
reply
to
this,
b
y
Newton,
things
that
actually
exist,
I
proportional
to
the
masses,
light
absolutely proved
water,
which
we
407.
exactly
what
happens
in
plane,
they
will
be
explained
the case.
this
attraction
from
some
j^
m
}]i|
s
^pi
a
*a
compressing
;
virium.
a
vl
repulsiva
ejusmodi
cohaesiones
ipsae
esse
diversissimae
fere ad
at a
any
another that would
points
was
nearly
perpendicular
t^enTis
appressae
non
acqui-
Theoria Newton-
very great
simultaneously
;
polished
are
drawn
apart
perpendicularly,
o.
polished
Theoria
commodius
accidit,
quam
in
communi,
particula
disponi
puncta
in
sphaeram,
in
alia
in
pyramidem,
vel
quadratum,
vel
299
any
force,
however
arcs
having
given
direction
extension
horizontal
the
beam,
was
very great
differences to
be found.
that calls our attention
can be derived arising
jacere
ad
plagas
admodum
diver'sas
in
eadem
etiam
particula,
space
corresponds
a
limit-point
of the
a
great
may
be
very
centre
For,
the
outer
surface.
In
;
the forces which one
particles
acting
upon
sitam
attrahant,
circumducenda in
along
them,
in
Art.
402.
But
I
will
themselves
to
angle.
For,
particles
throughout
force,
that
impedient.
Hinc
impresso
motu
particulis
aliquot,
poterunt
ipsae
the
weight
the
clepsydras
of
the
ancients
To
of
latter
equilibrium
the
particles,
mover
remotae
a 
aua
ac
ngurarum
irregulantas,
impediunt
ejusmodi
liberum
motum,
qui
of the
-HT TII particles
particles
alone,
these
particles
will
expand.
Indeed,
what
is
more,
there
original
state,
just
walls of a vessel the air contained within it. When
this
compressing
which
it
may
appear
strange
that
takes
away
one after
fluidum
ejusmodi
incurritur
ita
exempium
in
parai-
the neck
Also,
be
imparted
to
any
part
evident,
regard
to
parallelepipeds
any
The
same
thing
for
figures
whatever
the
limit-point,
ductilibus,
[200]
velut
in
plumbo.
adhaereant,
in
illis
nimirum
locis
tantummodo,
in
quibus
se
attrahunt,
in
minimis
distantiis
duas
an
amplitude
that
is
not
altogether
small
side of
bodies.
But,
before
The
nature &
we
pass
have to
one
side,
but
greater
different
points
of
the
particles,
from
which
particles
found
so
frequently
as
only
in
may
be
possible
corpuscularians,
such
asGassendi
can
with
an
infinite
tenacity
parts
of
their
of
shape,
it recedes
only slightly
from the
ut
inserted
of
vapours
r
i
i-rr-
i
tne
same
force -
forces
T>
tiam
fluidorum :
vidimus
442.
forces
exactly,
the
number
impressed
on
the
particles
;
&
owing
to the
same
time,
but
greater.
Hence
resistance
in
agreement
317
determination
relate
to
the
distinction
stay
changed
;
of a
appellation
the
slightest
change
of
shape
thing),
we
place
its own
discuss transformations. For
diminished,
reduced
by
compression
increases,
the
with transformations
towards the
end. Fire
is also
another law
Theory
the
general
theory
tlon &
precipita-
certam
solids
salt,
is
precipitated.
It
is
quite
easy
to
get
a
spheres
greater,
then,
saturated
to
that
distance
Hence
were
continuous
fluid
a
stronger
force,
dissolved,
single
mass,
particles
of
The
general
explanation
takes
place
a
them.
For,
invicem
recedunt,
sub
omni
repulsive
augent,
semper
magnitudinis.
In
accessu
tamen
in
utroque
casu
ad
compenetrationem
sane
nunquam
deveniretur :
in
springs
restrained &
constricted
by
little
prevented by
of
connection.
For,
on
recession,
points
space
is
in
the
second
case,
very
large,
but
finite,
it
will
indeed
be
possible
limit-point,
the
in
explosione
subita
will also
approach
ation.
;
&
remain for a
rest,
coming
up
to
slight
differences
that
may
originally heterogeneous,
get
inquiry
is
laid
open
&
fn
u
^'It
powder,
with
their
minutest
particles
quite
inert
explicationem
autem
diminishing
these
oscillations
by
great
fermentation
is some
only
rarefies
through
very
small
468.
We
can
of considerable
; these,
as
they
fall,
will
drag
with
*9*
of
the
moun
very
'
only by
substance
mixed
with
them,
these
would
vigorous
fire,
analogy,
would
be
dissipated
by
prejudices
ever so much
earths,
;
earth
vinegar,
they
would
be
were substances which
long
time
without
slightest
fashion,
of the
excellent
geometer
La
Grange
has
published
on
the
subject.
homogeneis
vix
ullum
esse,
si
quod
est,
colligitur
pluribus
indiciis
ingenti
attractive
juxta
guum,
separation,
with
the
law
of
a
constant
ratio
between
the
more
easily
transmitted,
which
by
Fr.
C.
Benvenuti,
a
Society,
particles,
be
much
diminished
by
such
a
large
emission
of
light
of
oscillation
within
the
confines
i i
iuvat.
Quoniam
tate,
quovis
tempore
quia
accurate
335
fly
off,
they
should
the
different
positions
first,
& the
points
of
the
as
centre,
nay,
;
&
rays
of
light
come
compenetration.
Hence,
disturbance
of
their
forces
extending
over
; for,
plane,
inequality,
no
matter
regard
to
particles
occur,
that
pertains
to
gravity,
are
like
them,
at
distances
se
invicem
punctorum
particulam
componentium,
finite,
and
points
of
matter,
in
accordance
with,
my
Theory,
are
perfectly
simple
understanding
the
mutual
penetration
of
light
water,
turning
into
ice
interrupted
by
continuous
bubbles,
the
principles
for
same cause.
If the
been
premised.
great
velocity
of
light
is
enough
in the
media traversed.
-1
from
it
equal
to
particle
particle
surface
of
separation
equal
to
the
radius
486.
Now,
&
i
i t i i r ^ T i i i r i r i
from the
by
a
ray
of
light
esset
progressus
est,
 
stronger
equal
density;
the
medium,
But
sulphurous
the same refraction as it had in the first instance.
Moreover,
of
its
r
seconds
at a
very great
T> i i i < i 11 -1 r v i_
L
naturalibus,
vel
artificialibus
phosphoris,
nam
of
the
angles
of
incidence
particle
of
light
is
same for
particulae
dispositionibus.
in one
different
particles,
have
quite
different
of
forces
axis
particle
at
length
difference
in
the
fits
ipsa
Benvenutiana
dissertatione.
innuisse
353
different
circumstances.
beyond
us,
observation
alone.
This
Newton
accomplished
seen
much
better
also
easily
be
deduced
always
have
angle
of
incidence
to
the
sine
these
things
is
enough.
501.
particles
of
light
my
Theory
there
the
body
orbibus
sit
eadem,
translata :
quod
nisi
fiat,
distantiam
propagatur
intervening
medium.
Moreover,
I
have
fully
explained,
ear-drum
invicem,
sed
recedent,
quo
recessu
incipiet
retardari
etiam
punctum
primum
dexterum,
ac
paullo
post
extinguetur
tota
velocitas
id
punctum
iterum
incipit
regredi
versus
dexteram,
erit
aliquod
e
dexteris,
quod
tune
referendas
v -j i -j
357
on
retardation,
the
point
beginning
to
move
particles
of them attracts it more at smaller distances & less at
greater
distances,
equal
r
of
this
diffusion
between
different
parts
superficiem
descensum
sit,
permanens
habeatur
caloris
gradus,
ut
in
fodinis,
ad
exiguam
etiam
praeci-
tem :
conjungatur,
vel
ad
illam
satis
wood,
marble,
of a
naturally
electric
can
take
place
cooled
more
rapidly,
works
in
an
exactly
opposite
one side
further surface & enter the
other
will
pass
through
time
But
this
fact
which
in
conjunction
omnibus
hisce
repulsive
even
this
can
take
is
causes,
the
modern
philosophers,
differences could
r
parent
compene-
trabilitate
reah,
tioneessenumerum,
corporum
formae
erunt
combmatio
punctorum
points,
there
would
anv
us, or,
space
having
own
power
of
perception,
or
even
of
imagination,
of
the
things
that
the
number
Ftitute'the
;
changes
that
the
primary
combinations
between
specie'?
transformed.
Thus,
when
principiis petitam,
inveniretur
massa,
quae
ceteras
be
possible
. .
,
'
form of a
knowledge
of
the
structure
of
particular
bodies
connection,
relating
found it
vires inducentes
tam,
qua
videamus
mtimam,
habent ad
mind &
matter,
that,
I
will
proceed
^fought*
10
or
S
'wilt
must
cogitationis,
vulgus,
operations,
even to
colour.
a
definite
term
union,
has
The
intercourse
of
i   i c i i-n- r i f i i V/T
the mind
of the mind are transmitted to certain motions of the
body,
& vice
versa
is free.
;
will,
law,
there
will
points
a
power
of
compenetration
with
matter.
For,
I
point
of
matter, &,
points,
with
respect
off,
place
; but,
once
fingers, by
the motions
number of
mind;
but
I
think
there
should
Motion
can
never
be
legibus
consistentem.
Error
materiae adhuc
ceteris manentibus
: sed ratio
The The
error made
pass
through
all
points
of
matter,
that is
immensely higher
than the
sed eo determinante
haberi
terminantem
requi-
place
in
certain
points
Universe
the
arms
of
the
man,
come
by
a
Being
Moreover,
in
general,
stages
to
which
the
knowledge
very regularity
seriously
persuade
himself
way,
if
other
parallels
like
ghf
are
drawn,
ationem
ad
existendum,
eternal
motion,
nor
can
it
have
passing
through
all
the
points
For
a
stone,
which
the
instant,
exist,
is
determinately.
Moreover,
this
preceding
exist,
but
precedes
it.
Consequently,
state.
a
fourth,
determination
the
549.
1
have
employed
this
argument
for
many
sint
nomina
centum,
possibilium
numero,
matter is altered
of
series.
But
my
argument
is
superior
class,
must
number. Also
regular
series
from
among
the
irregular
series
who
;
&
non-existence,
the individual
particular
form
for
a
statue.
552.
Now,
if
anyone
will
especially,
giving
forth
properties
suitable
for
sound,
for
breathing,
even
for
the
the
im-
submini-
starent
can never understand no
needs of
we are
settled
of
greater
perfection.
The
theme;
what
up
of
perfectly
indivisible
points,
which
are
non-extended,
set
apart
is
it
does
distance,
points
proper
care
owing
to
this
prejudice
be able
from one
magnitude
said with
is
a
given
after'
the
first
instant,
the
point
distance &
position
with
respect
to
the
third
as
the
of
points
points
of
position
space
in
&
any
portion
of
matter,
as
indefinite
punctorum
materiae
existentium
est
aliquando
fuerit
c
f . .
excluded from
seventh & the
points
of
space
necessarily
induced
by
the
exclusion
of
the
seventh &
eighth
cases
seem to be
the same time
any
thing,
there
to
whether
all
those
points
of
position
remark
that,
if
velocity,
the
repulsive
is emitted & travels
&
Fieri
autem
posset,
ut
totus
rotation.
Similarly,
motion
principle
of
the
unchangeability
measure,
;
&
congruent
with
a
hundred
times,
to
be
the
position,
translation
Although,
when
moved
in
position,
constitute
the
being
altered
to
:
reckoned
as
same
these
equal
distances,
just
for
the
reasons
of
time
can
distance,
considered
i
principles
of
the
ordinary
Cartesian
algebra
Potion,
of
the
squares
of
any
one
imaginary,
& a
equal
to
29.
Next,
this
curve
ita,
ut
curva
per
omnia
ejusmodi
puncta
transeat,
& idem
poterit
'
scissae,
therefore,
the
Hence,
if
equal
abscissae
second order.
Hence, branch
direction
given
by
AB.
satisfied.
Now,
the
ways,
they
any
obtained
quite
easily,
;
&
the
other
equations.
come
to
a
single
addition,
the axis
tis
modis.
praestan
poterit
: ac
promde
observe
ways,
this
can
There
is
stm
left
be
brought
about
in
an
same
points
it
time. The
comes
ar
perpendicular.
Thus,
the
angle
AN/,
which
it
been
found
L
we
had
in
can
be
may
be
smaller
or
greater
that,
when
any
order
of
osculation,
the
difference
of
^f
s
r
of
mfimtesi
be
observed
that,
whenever
the
tangent
to
the
curve
that
This
relation
de.
has
finite
angle
to
the
axis,
the
any
way,
less,
there
may
be
one
can
be
asymptotic
arc
either
limit-
point.
i i Vni
parameters
that
nunquam
in the
of
a
single
power
of
agamst
it
men,
a
straight
all.
singly,
method
fashion,
as
intimately
itself
equally
simple.
power,
we
men
proprietas qusedam
quaedam
virtus,
quae
a
etiam,
si
eo,
quod
illius
relationem
same time
is
some
property
is
bound
to
progress,
i i
11- r
absolutely
bound
to
depend
on
distances
alone,
beyond
property
of
matter,
but
established
by
Author
; for,
limitation
distance.
Now,
what
very
sublata omni
procursu,
any
sort,
they
will
SiatT
^hen*
5
*the
: &
greater)
the
two
points,
would
require
of
its
velocity.
points
of
the
surface,
or
the
sphere,
centrum virium P
ratio
ad
demon-
sint,
consequentur
beyond
F,
equal
to
FD,
which
is
correspondingly
the
spherical
surface,
the
inverse
whole
For,
the
curve,
even
higher
powers,
with
which
still
worse
for
the
forces
may
higher
P
wers
r
inverse ratio of the
surfaces.
Imagine
parts proportional
to the
greater
sphere
the action of
the
points
situated
at
A,
of the forces on A
& D has
D,
two
extremes
on
respectively,
lo
cancel
these,
we
must
have
acting
compounded
parallel
forces
transferred
together
fieri,
& sine
nova
massarum
in
eodem
piano,
i
n
quo
peculiari
tinen.
in
duas,
alteram
perpendicularem
were
situated
lying
in
thoroughly,
& in
general.
i 11 i
give
the
same
figure,
have
same
system
perpendicular
the centre
equal
to
Calculation
giving
the
thin
rod.
m
m
*P
oscilla-
tion,
part
is
gravity.
Thus,
proportion
same,
of
gravity
percussion
I
say
that
point,
parallel
uniform
motion,
of time.
will therefore
r -1
Evan esc entia
required
equated
to
zero,
on
cancelling
the
common
factor
V/(P
X
PQ
2
given,
ipsi
axi
perpendiculari
transeunte
per
centrum
gravitatis
habebitur,
ducendo
singulas
perpendicularem
centri
gravitatis
communis
ab
eodem
plano.ty
Deductio
casus,
[304]
jaceant
pro
centro
percussionis
congruit
prorsus
cum
inventa
pro
centro
oscillationis,
work itself.
115. If
of
percussion
checked
of the
percussion
any
one
of
the
solution
itself,
that
the
the
centre
of
gravity
to
that
point
in
with
6f
velocity
of
motion,
that the
Q
with
the
direction &
speed
with
velocity
will
be
found
a
the
system
motion of the mass
straight
t f MI u AI i i i r i
motion left
x
parte opposita
by
the
given,
after
cancelling
terms
of
of
the
subduphcate
axis,
;
tiones
centn
per
percussion.
centre
of
percussion,
to
percussion
was
taken,
truly
wonderful
fertility
179
De
combinationibus
punctorum,
;
systems
part
358
Impenetrability
411 25
Author
to
Father
Scherffer
443
93
WE,
as
Jesu.
Habetur
secunda
Nicolaus,
Typis,
Jesu
in
Collegio
J
739
Romano.
Romae,
ex
Typographia
Komarek.
Extat
Jesu
in
Collegio
Romano.
Romae :
Typis
Generosi
Salomoni.
De
Lentibus,
hac
postrema
.
1742,
dato
1742
per
ordine
di
Nostro
Signore
Benedetto
XIV,
in
4.
In
fine
opusculi
habentur
subscripta
omnium
trio,
nomina.
itidem
poema
Heroicum
ejusdem
adnotationibus bina