Hisce volui tantum ostendere quam late pateat,
quamq; certa sit Lex tertia motus.
Nam si aestimetur Agentis actio
ex ejus vi et velocitate conjunctim;
et Resistentis reactio
ex ejus partium singularum velocitatibus
et viribus resistendi ab earum attritione,
cohaesione, pondere et acceleratione oriundis;
erunt actio et reactio,
in omni instrumentorum usu,
sibi invicem semper aequales.
Et quatenus actio propagatur per instrumentum
et ultimo imprimitur in corpus omne resistens,
ejus ultima determinatio determinationi reactionis
semper erit contraria.
Nam si aestimetur Agentis actio
ex ejus vi et velocitate conjunctim;
→「Agentis actio
= F(ejus vi) * V(ejus velocitate)」
Fはforce(力)
Vはvelocity(速度)
et Resistentis reactio
ex ejus partium singularum velocitatibus
et viribus resistendi ab earum attritione,
cohaesione, pondere et acceleratione oriundis;
→「Resistentis reactio
= V(ejus partium singularum velocitatibus)
*F(viribus resistendi ab earum attritione,
cohaesione, pondere et acceleratione oriundis)
Vはvelocity(速度)
Fはforce(力)
erunt actio et reactio,
in omni instrumentorum usu,
sibi invicem semper aequales.
→「actio in omni instrumentorum usu
= reactio in omni instrumentorum usu」
actioはaction(作用)
reactioはreaction(反作用)
Et quatenus actio propagatur per instrumentum
et ultimo imprimitur in corpus omne resistens,
ejus ultima determinatio determinationi reactionis
semper erit contraria.
→「ejus ultima determinatio
⇔ determinationi reactionis 」
~参考~
運動の第一法則
Corpus omne perseverare
in statu suo quiescendi vel movendi uniformiter
in directum, nisi quatenus a viribus impressis
cogitur statum illum mutare.
運動の第二法則
Mutationem motus proportionalem
esse vi motrici impressae,
et fieri secundum lineam rectam
qua vis illa imprimitur.
運動の第三法則
Actioni contrariam semper
et aequalem esse reactionem:
sive corporum duorum actiones
in se mutuo semper esse aequales
et in partes contrarias dirigi.
Ut corpora in concursu et reflexione idem pollent,
quorum velocitates sunt reciproce ut vires insitae:
sic in movendis Instrumentis Mechanicis agentia
idem pollent et conatibus contrariis se mutuo sustinent,
quorum velocitates secundum determinationem
virium aestimatae, sunt reciproce ut vires.
I was only willing to show by those examples
the great extent and certainty of
the third Law of motion.
For if we estimate the action of the agent
from its force and velocity conjunctly,
and likewise the reaction
of the impediment conjunctly
from the velocities of its several parts,
and from the forces of resistance
arising from the attrition, cohesion, weight,
and acceleration of those parts,
the action and reaction
in the use of all sorts of machines
will be found always equal to one another.
And so far as the action is propagated
by the intervening instruments,
and at last impressed upon the resisting body,
the ultimate determination of the action
will be always contrary
to the determination of the reaction.
For if we estimate the action of the agent
from its force and velocity conjunctly,
→「the action of the agent
= F(its force) * V(its velocity)」
Fはforce(力)
Vはvelocity(速度)
and likewise the reaction of
the impediment conjunctly
from the velocities of its several parts,
and from the forces of resistance arising
from the attrition, cohesion, weight,
and acceleration of those parts,
→「the reaction of the impediment
= V(the velocities of its several parts)
* F(the forces of resistance arising
from the attrition, cohesion, weight,
and acceleration of those parts)」
Vはvelocity(速度)
Fはforce(力)
the action and reaction
in the use of all sorts of machines
will be found always equal to one another.
→「the action in the use of
all sorts of machines
= the reaction in the use of
all sorts of machines」
actionは作用
reactionは反作用
And so far as the action is propagated
by the intervening instruments,
and at last impressed upon the resisting body,
the ultimate determination of the action
will be always contrary to
the determination of the reaction.
→「the ultimate determination of the action
⇔the determination of the reaction」
~参考~
運動の第一法則(inertia)
Every body perseveres in its state of rest,
or of uniform motion in a right line,
unless it is compelled to change that state
by forces impressed thereon.
uniform motion=力F(Force)
運動の第二法則
The alteration of motion is ever proportional
to the motive force impressed;
and is made in the direction of the right line
in which that force is impressed.
The alteration of motion=加速度a(Acceleration)
the motive force=力F(Force)
運動の第三法則
To every action there is always
opposed an equal reaction:
or the mutual actions of two bodies
upon each other are always equal,
and directed to contrary parts.
「every action」=F
「an equal reaction」=F
「To every action there is always
opposed an equal reaction:」
「or the mutual actions of two bodies
upon each other are always equal,
and directed to contrary parts.」
=「every action⇔an equal reaction」
=「F=-F」
And as those bodies are equipollent
in the congress and reflexion,
whose velocities are reciprocally
as their innate force:
so in the use of mechanic instruments,
those agents are equipollent,
and mutually sustain
each the contrary pressure of the other,
whose velocities,
estimated according to
the determination of the forces,
are reciprocally as the forces.