Advances in Historical Studies
2013. Vol.2, No.3, 126-130
Published Online September 2013 in SciRes (http://www.scirp.org/journal/ahs) http://dx.doi.org/10.4236/ahs.2013.23016
Copyright © 2013 SciRe s . 126
Lagrange as a Historian of Mechanics
Agamenon R. E. Oliveira
Polytechnic School of Rio de Janeiro, Federal University of Ri o d e J ane iro, Rio de Janeiro, Brazil
Received August 5th, 2013; revised September 6th, 2013; accepted September 15th, 2013
Copyright © 2013 Agamenon R. E. Oliveira. This is an open access article distributed under the Creative Com-
mons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, pro-
vided the original work is p roperly cited.
In the first and second parts of his masterpiece, Analytical Mechanics, dedicated to static and dynamics
respectively, Lagrange (1736-1813) describes in detail the development of both branches of mechanics
from a historical point of view. In this paper this important contribution of Lagrange (Lagrange, 1989) to
the history of mechanics is presented and discussed in tribute to the bicentennial year of his death.
Keywords: History of Mechanics; Epistemology of Physics; Analytical Mechanics
Introduction
Lagrange was one of the founders of variational calculus, in
which the Euler-Lagrange equations were derived by him. He
also developed the method of Lagrange multipliers which is a
manner of finding local maxima and minima of a function sub-
jected to constraints. He developed the method for solving dif-
ferential equations known as the parameter variation method. In
addition, he applied differential calculus to the theory of prob-
abilities and did notable work in obtaining the solution of alge-
braic equations. Furthermore, in calculus Lagrange introduced a
new approach for the interpolation of the Taylor (1685-1731)
series. His famous treatise known as the Theory of Analytical
Functions contains the path that leads to the foundation of
group theory, anticipating the work of Evariste Galois (1811-
1832).
In mechanics Lagrange studied specific problems, such as
the three-body problem related to motion of the earth, sun and
moon. By means of his Analytical Mechanics, he transformed
Newtonian mechanics (Newton, 1952) into a branch of analysis,
Lagrangian mechanics, which was a result of the application of
the variational calculus to mechanical principles. Through this
work, rational mechanics was able to fulfill the long desired
Cartesian aim of becoming a branch of pure mathematics.
In relation to problems later called applied mechanics, La-
grange, in the works known as the Mélanges de Turin, studied
the propagation of sound, making an important contribution to
the theory of vibrating strings. He used a discrete mass model
to represent string motion consisting of n masses joined by
weightless strings. Then he solved the system of n + 1 differen-
tial equations, when n tends to infinity to obtain the same func-
tional solution proposed by Euler (1707-1783). Lagrange also
studied the integration of differential equations and made vari-
ous applications to topics such as fluid mechanics, where he
introduced the Lagrangian function
Lagrange’s Analytical Mechanics was published in 1788,
crowning a series of works and other important contributions
previously developed by d’Alembert (1717-1783) and Euler
(Euler, 1952). This book presents a model of formalized theory
in the same meaning that is now understood by modern physi-
cists. The logical unity of this theory is based on the least action
principle. However, the two dimensions of formalization and
unification are the main characteristics of Lagrange’s method.
Lagrange: A Biographical Note
Joseph-Louis Lagrange was born in Turin on January 25,
1736, under the name of Giuseppe Lodovico Lagrangia (Figure
1). His father was Giuseppe Francesco Lodovico Lagrangia and
was Treasurer of the Office of Public Works and Fortifications
in Turin. His mother was Teresa Grosso, the only daughter of a
medical doctor from Cambiano near Turin. Lagrange was the
eldest of their 11 children, but one of only two to live to adult-
hood.
Turin became the capital of the kingdom of Sardinia in 1720,
sixteen years before Lagrange’s birth. His family had French
connections on his father’s side. His grandfather was a French
Figure 1.
Joseph-Louis Lagrange (1736-1813).

A. R. E. OLIVEIRA
Copyright © 2013 SciRe s . 127
cavalry captain who had left France to work for the Duke of
Savoy. For this reason, Lagrange always leant towards his
French ancestry. When he was young he signed his name Lo-
dovico LaGrange or Luigi Lagrange, using the French form of
his family name.
Lagrange’s interest in mathematics began when he read a
copy of Halley’s 1693 work on the use of algebra in optics. He
was also attracted to physics by the excellent teaching of Fran-
cesco Ludovico Beccaria (1716-1781) at the College of Turin,
leading him to decide to follow a career in mathematics.
Returning to Mécanique Analytique, it was written by La-
grange during his period in Berlin and was approved for public-
cation by a committee from the Academy of Sciences consist-
ing of Laplace (1749-1827), Cousin, Legendre (1752-1833) and
Condorcet (1743-1794). This book summarized all the work
done in the field of mechanics since the time of Newton
(1642-1727), being notable for its use of the theory of different-
tial equations. In 1810, he commenced a thorough revision of
his masterpiece, but he was able to complete only about two-
thirds of this before his death in Paris, on April 10, 1813. He
was buried in the same year in Panthéon in Paris. The French
inscription on his tomb reads:
Joseph-Louis Lagrange. Senator. Count of the Empire.
Grand Officer of the Legion of Honour. Grand Cross of
the Imperial Order of the Reunion. Member of the Insti-
tute and the Bureau of Longitude. Born in Turin on 25
January. Died in Paris on 10 April 1813.
Science and the French Revolution
The French revolution has a great importance as a funda-
mental transformation of European society from the social,
political and scientific viewpoints. Besides the intellectual and
cultural changes before the takeover of power by the bourgeoi-
sie in France with direct consequences to the scientific produc-
tion over a long period of his history, we should also mention
other factors and aspects of this context.
The first important thing to note is the need of the new re-
gime for new institutions in order to criticize and fight against
the ideas of the ancien regime. These new institutions also ap-
peared within the educational system as the best way to change
mentalities and to prepare new technical and political elite to
give continuity to the project of a new society announced by the
Revolution.
The transformations in the educational system of France im-
plied significant modifications in technical and professional
education, because new creeds, new knowledges and new tech-
nologies had progressed, making it necessary to teach them.
The development of engineering and its teaching is important in
this context. A reformation of engineering instruction was nec-
essary also because war with other European countries had
stimulated the construction of fortifications, roads and bridges,
and the development of artillery. This new context propelled
France to apply scientific principles to industry, with the result
that the new engineering had to provide universal scientific
knowledge as well as tools and methods applicable in a diverse
range of practical situations (Belhoste, 2003). As we know,
Lagrange played an important role in the context of these
transformations. He was the first professor of analysis, ap-
pointed for the opening of the École Polytechnique in 1794. In
1795 the École Normale was founded with the aim of training
school teachers. Lagrange taught courses on elementary ma-
thematics there.
Historical Considerations in Analytical
Mechanics
First Part: Statics
Lagrange began his history of statics by defining this disci-
pline associated with the concept of force. He states:
Statics is the science of forces in equilibrium. We think, in
general, of force or power as a cause, anything that im-
presses or tend to impress motion on the body under con-
sideration; it is also by the quantity of impressed motion,
or by its tendency, that a force or power must be esti-
mated.
According to him, the objective of statics is to provide the
laws that govern equilibrium. In this sense equilibrium appears
as the destruction of several forces that oppose and annihilate
them. These laws are based on three general principles, namely:
a) the equilibrium of the lever; b) the composition of motions; c)
virtual velocities. It is, thus, in the context of the historical de-
velopment of these three principles that Lagrange rebuilds the
history of statics.
Lagrange considers Archimedes (287 - 212 b. C.) as the only
scholar from ancient times who had produced a theory of Me-
chanics, which is contained the latter’s two books named
Aequiponderantibus. Archimedes was also the author of the
principle of the lever (Dijksterhuis, 1987). In modern times the
contributions of Stevin (1548-1620), in his Statics, and Galileo
(1564-1642), in his Dialogues (Discorsi) about motion, had
transformed Archimedes’ demonstration into a much more
simple and useful concept (Galileo, 1988). However, it seemed
to Lagrange that ancient mathematicians did not know of a
method to generalize the principle of the lever to other simple
machines, notably the inclined plane. This problem is also
posed to the first modern mathematicians. Stevin presented the
first exact solution to this problem independent of the lever
theory. These considerations led him to the impossibility of
perpetual motion. (See Elements of Statics and Hypomnemata
Mathematica)
The second fundamental principle of equilibrium is the
composition of motions. It is assumed that when two forces are
acting in different directions on a body, these two forces are
equivalent to one following the diagonal of the parallelogram.
In all cases when there are several forces, the composition of
two forces leads to a single force representing the whole system.
For the equilibrium condition this force must be zero if there is
no fixed point. This conclusion is found in any book of Statics,
particularly in Varignon’s new mechanics (Blay, 1992). In ad-
dition he derived a theory of machines using this principle
alone.
The origin of this principle is attributed by Lagrange to Gali-
leo, specifically in the second Proposition of the Fourth Journey
in his Dialogues (Discorsi). Lagrange remarks that Galileo does
not consider the entire importance of the Principle in his theory
of equilibrium.
The theory of composed motions can also be found in the
writings of Descartes (1596-1650), Roberval (1602-1675),
Mersenne (1588-1648), and Wallis (1616-1703). As mentioned
above, Varignon (1654-1722) used this principle for machines
in equilibrium. His project of a new mechanics, presented in

A. R. E. OLIVEIRA
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128
1687, had this objective.
Let us look at the third principle, virtual velocities. This is
understood as the velocity acquired by a body whose equilib-
rium is not maintained. The principle states that for the equilib-
rium the powers are in inverse ratio to the virtual velocities,
estimated in the direction of the powers. Lagrange attributes the
discovering of this principle to Galileo in his Dialogues (Dis-
corsi). (See the Scholium of the second proposition of the third
Dialogue) In this context, Galileo also defines the moment of
some weight or of some power applied to a given machine as an
action, energy, or impetus to move the machine in a way that
equilibrium is maintained between two powers with the condi-
tion that the moments are equals and in contrary sense. The
moment is always proportional to a power (force) multiplied by
its virtual velocity.
This notion of moment that came from Galileo was adopted
by Wallis in his Mechanics, published in 1669. He emphasizes
the principle of equality of moments as the main foundation for
Statics, and thus applies this theory to machines. In parallel,
Descartes summarizes Statics in a unique principle, which in
fact is the same as proposed by Galileo, though presented in a
new and general form. This principle is based on the force nec-
essary to elevate a weight to a height. Afterwards it was used
extensively to evaluate the capacity of a given machine or to
compare machines with different capacities. The birth of ap-
plied mechanics, mainly with Lazare Carnot (1753-1823), uses
this mechanical model extensively (Oliveira, 2012).
Another important principle described by Lagrange is Tor-
ricelli’s principle. He was a famous disciple of Galileo and his
principle is directly related to Galileo’s concepts, or even are a
consequence of Galileo’s analysis. The principle states that
when a system of bodies is in equilibrium its center of gravity
is in the lowest position. In the condition of equilibrium the
center gravity cannot go up or down due to infinitely small va-
riations of position.
Lagrange enunciated the principle of virtual velocities in a
general form as follows:
If in any system of bodies or material points, any one of
them is submitted to forces, but the system is in the posi-
tion of equilibrium and therefore we apply any small mo-
tion, as a consequence each point describes an infinitely
small space which will express its virtual velocity; the ad-
dition of all forces multiplied by the displacement of its
points of application following the direction of the force
will be always zero, since we adopt as positive the dis-
placements in the direction of the forces and as negative
the displacements in opposite sense to the forces.
Lagrange also remarks that was Jean Bernoulli (1667-1748)
the first to realize the great generality of the principle of virtual
velocities, as well as its usefulness to solve statics problems. He
mentions the letter addressed by Jean Bernoulli to Varignon in
1717 about this principle and other important developments,
such as that of Maupertuis (1698-1759), who in 1740 proposed
to Paris Academy of Sciences the name of the Law of Res t, and
Euler who developed in his Memorials to the Berlin Academy
in 1754.
Second Part: Dynamics
As in the previous section, Lagrange begins this topic defin-
ing dynamics by the effect that forces can cause on bodies, by
accelerating or decelerating them. In addition, this science was
entirely developed by modern mathematicians and physicists.
Again, the name of Galileo arises as the one who presented the
first fundamental concepts of dynamics. In addition, Galileo
developed the kinematics of the free fall of heavy bodies, in
which the law of inertia is also constantly present in the free fall,
but also the motion of projectiles. Before Galileo forces were
only discussed in the context of equilibrium conditions. In spite
of the simplicity involving the falling of heavy bodies and the
motion of projectiles, the determination of the laws governing
these phenomena were unknown until Galileo. He took the first
step and opened the way to advancing mechanics. Lagrange
then refers to Galileo’s master piece, calling it the Dialogues
About the New Science, published in Leiden in 1637. Obviously,
he means the Discorsi.
Following the development of mechanics, Lagrange studied
Huygens’ contributions, especially the latter’s findings on pen-
dulum motion and the mathematization of centrifugal force,
which were fundamental steps towards the discovery of uni-
versal gravitation. Huygens’ construction of a bridge between
Galileo and Newton was of great importance (Taton, 1982).
Mechanics became a new science due to Newton’s book
known as Mathematical Principles, which appeared for the first
time in 1687. With the invention of infinitesimal calculus it was
possible to transform the laws of motion into analytical equa-
tions.
The theory of motion produced by driven forces is based on
general laws of any motion impressed on a given body. These
laws are derived from known principles which are inertia force
and composed motion. As in Statics, Lagrange looks for gen-
eral principles governing dynamics phenomena using the cate-
gory of force as a unifying concept. Thus, he identifies these
two already mentioned principles as the most general and fun-
damental. It is in the context of these two principles where La-
grange develops his historical considerations.
Galileo realized that the first principle enunciated and de-
rived from the laws governing the motion of projectiles through
the composition of horizontal motion with constant velocity
with the vertical up and down motion modified by gravity ac-
celeration. The case of falling bodies with the velocity acquired
being proportional to the elapsed time, or the vertical displace-
ment proportional to the time squared, was an important
achievement made by Galileo using geometrical considerations
in addition to experimental measurements with inclined planes.
After Galileo, Huygens (1629-1695) discovered the laws of
centrifugal forces of bodies in circular motion with constant
velocity, and used this knowledge to compare forces. As a re-
sult weight on the surface of the earth could be calculated as a
centrifugal force. This was done in his Horologium Oscilato-
rum, published in 1673 (Huygens, 1673).
Newton generalized this theory to any kind of curve, thereby
developing the science for varied motions with accelerated
forces. He used a geometrical method and occasionally ana-
lytical calculation, though instead of differential methods he
applied the series method. After Newton the majority of ma-
thematicians that developed the theory of motion only gen-
eralized Newton’s theorems, introducing differential expres-
sions to solve many kinds of problems.
Lagrange then explains how to solve a dynamical problem by
using three different perpendicular directions and decomposing
forces and accelerations in these directions. The forces in any
direction can be calculated by equating on one side forces and

A. R. E. OLIVEIRA
Copyright © 2013 SciRe s . 129
on the other the second the differential of space divided by the
first differential of time squared. For curved trajectories, the
decomposition had to be done in normal and tangential direc-
tions. Lagrange does not mention that it was Euler who applied
this for the first time in 1752 in a manner different to Newton’s
second law (Truesdell, 1983).
Lagrange describes how the problem of shocks between hard
bodies was studied, explaining the result of these interactions
by means of the analysis of quantities of motion. He mentions
that it was Descartes who first realized the principle behind this
phenomenon. However, as confirmed by Lagrange, Descartes
made a mistake in the application of the principle because he
considered that the absolute quantity of motion was always
conserved. After Descartes, Wallis was the first to have a clear
idea of the principle and used it to discover the laws for the
communication of motion in the context of shocks between
hard and elastic bodies, as presented in his Philosophical
Transactions, published in 1669, as well as in the third part of
his treatise De Motu, which appeared in 1671.
One of the most important passages of Lagrange’s text is
dedicated to the d’Alembert principle. The Treatise of Dynam-
ics written by d’Alembert and published in 1743 presented a
general and direct method to solve, or at least to obtain the
equations for, practically any dynamic problem (d’Alembert,
1743). The method proposed transformed the laws of bodies in
motion to its equilibrium, thereby relating dynamics to statics.
The principle enunciated by d’Alembert generalizes the work of
some previous mathematicians, such as Jacques Bernoulli (1654-
1705), with great simplicity.
We can enunciate the principle by studying the motion of
various bodies which tend to move with velocities and in a
direction so that changes in both are caused by their inte ractions.
It is possible to visualize these motions as composed by what
was really acquired and others that are destroyed in the interac-
tions. If we consider only the final motions the bodies animated
with them are in equilibrium.
It is important to emphasize that d’Alembert made useful ap-
plications to mechanical problems. However, this principle
does not provide the necessary equations to solve different dy-
namical problems but rather provides the means to derive the
equations from the conditions of equilibrium. Thus, by com-
bining the principle with known principles of equilibrium, such
as the lever principle or that of the composition of forces, we
can find the equations for each problem with the help of some
more or less complicated constructions. The difficulty is to
evaluate the forces destroyed.
As discussed previously, the principle of virtual velocities
leads us to a very simple analytical method to solve static prob-
lems. This same principle combined with the d’Alembert prin-
ciple also provides a similar method to solve dynamical prob-
lems. Explaining this approach in more detail, the application
of the principle of virtual velocities consists of the following
methodology. For a given system containing several bodies that
can be reduced to points being acted upon by any kind of force,
if we apply to the system a small motion, each body displaces
an infinitesimal space. If we multiply each force by the dis-
placement of its point of application and add them for the
whole system, the result is zero.
If we suppose the system is in motion, and considering that
the velocities of each body can be decomposed in three fixed
and perpendicular directions, the decreasing of these velocities
will represent the motions lost along the same directions and
their increasing will be the motions lost in the opposite direc-
tions. Thus, these lost motions will be expressed in general by
the mass multiplied by the element of velocity and divided by
the time element, and they will have contrary directions to the
velocities. Using this approach it is possible to obtain a general
formula to represent the motions of bodies which will provide a
solution for any dynamic problem.
One of the advantages of the above mentioned formula is that
it immediately offers the general equations which encompass
the principles and known theorems about the conservation of
living forces, the conservation of the motion of the center of
gravity, the conservation of the moments of rotation motion, or
the principle of areas and the principle of least action. These
principles can be considered the general achievements of the
dynamic laws and are the primary principles of this science.
With this statement Lagrange proposed to explain its origins
and developments.
The first mentioned principle, the conservation of living
forces, was first presented by Huygens, but in a different form
to how it is now known. In its origins, the principle represented
the equality between the descending and raising of the center of
gravity of several heavy bodies, in which descending in a group
but raising separately, using the known properties of the gravity
center, the space displaced by this center in any direction is
expressed by adding the products of the mass of each body by
the space displaced in the same direction divided the total mass.
On the other hand, using Galileo’s theorems, the vertical dis-
placement of a heavy body is proportional to the square of the
velocity acquired in free descent, as well as what can be
reached by raising it to the same height. Based on these consid-
erations, Huygen’s principle can consider the motion of heavy
bodies in which the sum of the products of the masses by the
square of the velocities at each time is the same, since that the
bodies motion be conjunctly in any way, or that they displaces
freely to the same vertical heights. Huygens made these re-
marks in a short paper on the methods used by Jacques Ber-
noulli and the Marquis l’Hopital (1661-1704). Obviously, the
principle postulated by Huygens is a particular application of
the more general principle of conservation of energy, a concept
which would appear only in the middle of the nineteenth cen-
tury.
After these achievements, Daniel Bernoulli (1700-1782) de-
rived from this principle the laws of fluid motion in vessels,
which had not been previously dealt with. He reached this gen-
eral principle in the Berlin memorials, published in 1748 (Ber-
noulli, 1968).
The great advantage of this principle is that it easily provides
an equation between the velocities of the bodies and the vari-
ables which calculate their position in space in such a manner
that, due to the characteristics of the problem, all these vari-
ables are reduced to one, with this equation being sufficient to
solve completely the problem.
The second principle is due to Newton who, at the beginning
of his Principia, demonstrated that the state of rest or motion of
the center of gravity of several bodies does not change through
their reciprocal action. This implies that the center of gravity of
the system is at rest or in uniform linear motion unless it meets
some exterior obstacle. Obviously this principle is useful to
determine the center of gravity motion independently of indi-
vidual bodies’ motions, as it can provide three equations be-
tween the bodies’ coordinates and time.
The third principle, more recent than the other two, seems to

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have been discovered simultaneously in different ways by Euler,
Daniel Bernoulli, and Le Chevalier d’Arcy (1723-1779). Ac-
cording to Euler and Daniel Bernoulli, this principle involves
considering the motion of several bodies around a fixed center.
Hence, the sum of the products of the mass of each body by the
circular velocity around the center is always independent of the
mutual action among the bodies and is conserved unless some
exterior obstacle is found.
The principle enunciated by d’Arcy, which appeared in the
Memorial he presented to the Paris Academy of Sciences in
1746, is that the sum of the products of the mass of each body
by the area described by its vector radius around the fixed cen-
ter is always proportional to time. This principle generalizes
Newton’s theorem about areas due to any centripetal forces.
Finally, the fourth principle called the least action, in an
analogy with Maupertuis’ principle with the same name which
had become famous. It involved considering the motion of sev-
eral bodies acting among them and then taking the sum of the
products of the masses by the velocities and the spaces de-
scribed is a minimum. Maupertuis had derived this from the
laws of the reflection of light and refraction, as well as of me-
chanical shocks. These studies appear in two Memorials, one
presented to the Academy of Sciences of Paris in 1744 and the
other to the Berlin Academy (Maupertuis, 1744).
Before being completely established as a principle, Euler
made the first approach to it in his treatise on isoperimetric
curves, printed in Lausanne in 1744, postulating that in the
trajectories described by central forces, the integral of the ve-
locity multiplied by the curve element is always a maximum or
a minimum. This property which Euler did not recognize except
for isolated bodies, as he mentioned, was extended to any mo-
tion of bodies acting among themselves, leading to this new
general principle in which the sum of the products of the
masses by the integrals of the velocities multiplied by the space
elements is const ant and a maximum or a mini mum. It is a sim-
ple consequence of mechanical laws. This principle combined
with the principle of the conservation of living forces following
the rules of variational calculus directly provides all the neces-
sary equations to solve each problem giving rise to a method to
solve problems of motion.
Final Remarks and Conclusion
One of the aims most sought by physicists along the years
has been the finding of a principle, the simplest possible, or
some basic fundamental principles, which could fit all natural
phenomena. Some tried to do this, as Lagrange’s analysis
demonstrates. D’Alembert did the same. In his Preliminary
Discourse in the Treatise on Dynamics, one reads: If the prin-
ciple of the inertia of force, of composed motion, and of equi-
librium, are essentially different from each other, as we cannot
prohibit happening; and if, on the other hand, these three prin-
ciples are sufficient for mechanics, one can reduce this science
to the least number of principles possible, and assume that on
these three principles there can be established all the laws of
motion for any body in any circumstances, as I have accom-
plished in this work.
In his famous Fundamental Principles of Equilibrium and
Motion, published in 1803, Lazare Carnot states: There are two
ways to see mechanics and its principles. The first one is by
considering it as a theory of forces, the causes that impress
motion. The second is by considering it as a theory of motions
themselves. Here an important remark has to be made. Lagran-
gian mechanics is the development of mechanics using the
second approach, the analysis of motions by themselves as
defined by Carnot. However, with respect to history of me-
chanics, Lagrange adopts the concept of force to both statics
and dynamics to explain its internal development, obviously
because of the late development of the other concepts associ-
ated with motion that we know nowadays as the methods of
energy.
Another important contribution in the historical considera-
tions of mechanics made by Lagrange is that it highlights some
developments which are not completely clear in the current
literature. One example is his correct interpretation of d’Alem-
bert’s principle. As we know, from reading most mechanics or
physics textbooks, this principle is always presented as a me-
thod to reduce a dynamical problem into a statics one. Lagrange,
as in the original version of the d’Alembert principle, only con-
siders the possibility of equilibrium where motions are de-
stroyed. In other words, equilibrium means the conservation of
the quantity of motion.
Lastly, the importance attributed by Lagrange to include in
his masterpiece historical considerations about the development
of mechanics, only confirms that the internal development of
science is not independent of its historical development.
REFERENCES
Belhoste, B. (2003). La formation d’une technocratie. Paris: Belin, rue
Féron.
Bernoulli, D. (1968). Hydrodynamics. New York: Dover Publication,
Inc.
Blay, M. (1992). La science du mouvement: De galilée à lagrange.
Paris: Belin, rue Féron.
D’Alembert, J. L. (1921). Traité de dynamique. Paris: Gauthiers-Villars
et Cie Éditions.
Dijksterhuis, E. J. (1987). Archimedes. Princeton, NJ: Princeton Uni-
versity Press.
Euler, L. (1952). Methodus inveniendi lineas curvas maximi minimive
proprietates gaudentes. In leonhardi euleri opera omnia, s. I, vol.
XXIV, Lausanne.
Galileu, G. (1988). Discurso sobre as duas novas ciências, museu de
astronomia e ciências afins, Rio de Janeiro.
Huygens, C. (1673). Horologium oscilatorum. Paris: Albert Blanchard
Library.
Lagrange, J. L. (1989). Mécanique analytique. Paris: Éditins Jacques
Gabay.
Maupertuis, P. L. M. (1744). Accord des différents lois de la nature qui
avaient jusqui’ici paru incompatibles. Memoires de l’Academie des
Sciences de Paris.
Newton, I. (1952). Mathematical principles of natural philosophy.
London: Great Books of t h e Western World .
Oliveira, A. R. E. (2012). The role of the concept of work in the devel-
opment of appl ied mechanics. Rome : SISFA.
Taton, R. (1982). Huygens et la France. Paris: Librairie Philosophique
J. Vrin.
Truesdell, C. (1983). Essays in th e history of mechanics. Berlim: Springer-
Verlag.