Jean-Baptiste le Rond, genannt D’Alembert, war einer der bedeutendsten Mathematiker und Physiker des Jahrhunderts und ein Philosoph der Aufklärung. Gemeinsam mit Diderot war der Aufklärer Herausgeber der Encyclopédie. Er selbst beschäftigte. Jean-Baptiste le Rond ['ʒɑ̃ ba'tist lə ʁɔ̃ dalɑ̃'bɛːʁ], genannt D'Alembert, (* November in Paris; † Oktober ebenda) war einer der. Das d'Alembertsche Prinzip (nach Jean-Baptiste le Rond d'Alembert) der klassischen Mechanik erlaubt die Aufstellung der Bewegungsgleichungen eines. November Paris† Oktober ParisJEAN BAPTISTE LE ROND D'ALEMBERT war nicht nur ein bedeutender Mathematiker und Physiker des D'Alembert, mit einer Abhandlung über Probleme der Mechanik in ganz Europa bekannt geworden, schreibt eine programmatische Vorrede. Er.
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His father, however, located the baby and found him a home with a humble artisan named Rousseau and his wife. Destouches-Canon also saw to the education of the child.
In spite of the efforts of his teachers, he turned against a religious career and began studies of law and medicine before he finally embarked on a career as a mathematician.
A slight man with an expressive face, a high-pitched voice, and a talent for mimicry, he was known for his wit, gaiety, and gift for conversation, although later in life he became bitter and morose.
He seldom traveled, leaving the country only once, for a visit to the court of Frederick the Great. It was a critique of a mathematical text by Father Charles Reyneau.
He published rather hastily a pattern he was to follow all of his life in order to forestall the loss of priority; Clairaut was working along similar lines.
That accomplishment is often attributed to Newton, but in fact it was done over a long period of time by a number of men.
Finally, it was long afterward said rather simplistically that in this work he resolved the famous vis viva controversy, a statement with just enough truth in it to be plausible.
In terms of his own development, it can be said that he set the style he was to follow for the rest of his life. It is true that he was not always faithful to the principles he set down in the preface, but it is astonishing that he could carry his arguments as far as he did and remain faithful to them.
The main tenet of this epistemology was that all knowledge was derived, not from innate ideas, but from sense perception.
The criterion of the truth, for example, was still the clear and simple idea, although that idea now had a different origin.
In science, therefore, the basic concepts had to conform to this ideal. Space and time were such. So simple and clear that they could not even be defined, they were the only fundamental ideas he could locate.
Motion was a combination of the ideas of space and time, and so a definition of it was necessary.
The concept of mass, which he defined, as Newton had done, as quantity of matter, had to be smuggled into the treatise in a mathematical sense later on.
It should be remembered that Newton had stated his laws verbally in the Principia , and that expressing them in algebraic form was a task taken up by the mathematicians of the eighteenth century.
His proof was based on the simple ideas of space and time; and the reasoning was geometric, not physical, in nature. His second law, also proved as a problem in geometry, was that of the parallelogram of motion.
It was not until he arrived at the third law that physical assumptions were involved. The third law dealt with equilibrium, and amounted to the principle of the conservation of momentum in impact situations.
They will clearly balance one another, he declared, for there is no reason why one should overcome the other.
Other impact situations were reduced to this one; in cases where the masses or velocities were unequal, the object with the greater quantity of motion defined as mv would prevail.
This fact was what made his work a mathematical physics rather than simply mathematics. It was not so much a principle as it was a rule for using the previously stated laws of motion.
It can be summarized as follows: In any situation where an object is constrained from following its normal inertial motion, the resulting motion can be analyzed into two components.
The lost motion is balanced against either a fictional force or a motion lost by the constraining object. The latter case is the case of impact, and the result is the conservation of momentum in some cases, the conservation of vis viva as well.
In the former case, an infinite force must be assumed. Such, for example, would be the case of an object on an inclined plane.
The normal motion would be vertically downward; this motion car. One would be a component down the plane the motion actually taken and the other would be normal to the surface of the plane the motion destroyed by the infinite resisting force of the plane.
Then one can easily describe the situation in this case, a trivial problem. One must have the conditions of constraint.
The minus sign indicates deceleration, and the constant g packs in the other factors involved, such as mass.
One could therefore define force in terms of the velocity of an object. It involved convention, not reality, for universal causes the metaphysical meaning of the idea of force were not known, and possibly not even knowable.
He did not throw the word away, but used it only when he could give it what today would be called an operational definition.
He simply refused to give the notion of force any metaphysical validity and, thus, any ontological reality. He employed mathematical abstractions and hypothetical or idealized models of physical phenomena and was careful to indicate the shortcomings of his results when they did not closely match the actual events of the world.
The metaphysician, he warned in a later treatise, too often built systems that might or might not reflect reality, while the mathematician too often trusted his calculations, thinking they represented the whole truth.
But just as metaphysics was suspect because of its unjustified claim to knowledge, so mathematics was suspect in its similar claim.
Not everything could be reduced to calculation. Geometry owes its certainty to the simplicity of the things it deals with; as the phenomena become more complicated, the results become less certain.
Unfortunately, in this case they diverted him from the path that was eventually to produce the principle of the conservation of energy.
A major question that beset all philosophers of the Enlightenment was that of the nature of matter. Here again, he was frustrated, repeating time after time that we simply do not know what matter is like in its essence.
Since this kind of atom could not show the characteristic of elasticity, much less of other chemical or physical phenomena, he was sorely perplexed.
In this way, he could explain elasticity, but he never confused the model with reality. Possibly he sensed that his model actually begged the question, for the springs became more important that the atom itself, and resembled nothing more than a clumsy ether, the carrier of an active principle.
The sources of his interest in fluids were many. Second, there was a lively interest in fluids by the experimental physicists in the eighteenth century, for fluids were most frequently invoked to give physical explanations for a variety of phenomena, such as electricity, magnetism, and heat.
There was also the problem of the shape of the earth; What shape would it be expected to take if it were thought of as a rotating fluid body?
Clairaut published a work in which treated the earth as such, a treatise that was a landmark in fluid mechanics.
Furthermore, the vis viva controversy was often centered on fluid flow, since the quantity of vis viva was used almost exclusively by the Bernoullis in their work on such problems.
Finally, of course, there was the inherent interest in fluids themselves. He was actually giving an alternative treatment to one already published by Daniel Bernoulli , and he commented that both he and Bernoulli usually arrived at the same conclusions.
He felt that his own method was superior. Bernoulli did not agree. In it appeared the first general use of partial differential equations in mathematical physics.
Euler later perfected the techniques of using these equations. Here the wave equation made its first appearance in physics. The precession of the equinoxes , a problem previously attacked by Clairaut, was very difficult.
He was rightly proud of his book. He was not awarded the prize; indeed, it was not given to anybody. The Prussian Academy took this action on the ground that nobody had submitted experimental proof of the theoretical work.
There has been considerable dispute over this action. It was in this essay that the differential hydrodynamic equations were first expressed in terms of a field and the hydrodynamic paradox was put forth.
This implied that whatever the forces exerted on the front of the object might be, they would be counteracted by similar forces on the back, and the result would be no resistance to the flow whatever.
The paradox was left for his readers to solve. He found himself forced to assume, in order to avoid the necessity of allowing an instantaneous change in the velocity of parts of the fluid moving around the object, that a small portion of the fluid remained stagnant in front of the object, an assumption required to prevent breaking the law of continuity.
In spite of these problems, the essay was an important contribution. But it is often difficult to tell where the original idea came from and who should receive primary recognition.
But they all sought claims to priority, and they guarded their claims with passion. It appeared in three volumes, two of them published in and the third in His efforts did not remain limited to purely scientific concerns, however.
Actually, the first part is an exposition of the epistemology of sensationalism, and owes a great deal to both John Locke and Condillac.
All kinds of human knowledge are discussed, from scientific to moral. The sciences are to be based on physical perception, and morality is to be based on the perception of those emotions, feelings, and inclinations that men can sense within themselves.
As a history, it has often quite properly been attacked for its extreme bias against the medieval period and any form of thought developed within the framework of theology, but this bias was, of course, intentional.
All knowledge is related to three functions of the mind: memory, reason, and imagination. Reason is clearly the most important of the three.
To him, the things used by philosophers—even mathematical equations—were very useful, even though the bulk of the public might find them mysterious and esoteric.
Yet it was more than simply a popularization. Music was still emerging from the mixture of Pythagorean numerical mysticism and theological principles that had marked its rationale during the late medieval period.
The first two were reprinted along with two more in ; a fifth and last volume was published in They make an odd mixture, for some are important in their exposition of Enlightenment ideals, while others are mere polemics or even trivial essays.
It was clearly an article meant to be propaganda, for the space devoted to the city was quite out of keeping with the general editorial policy.
These collections of mathematical essays were a mixed bag, ranging from theories of achromatic lenses to purely mathematical manipulations and theorems.
Included were many new solutions to problems he had previously attacked—including a new proof of the law of inertia.
His concept of the limit did not seem to be any more clear to his contemporaries than other schemes invented to explain the nature of the differential.
This evaluation must be qualified. No doubt he sensed the power of mathematics. He was rather in the tradition of Descartes.
Space was the realization of geometry although, unlike Descartes. It was for this reason that he could never reduce mathematics to pure algorithms, and it is also the reason for his concern about the law of continuity.
It was for this reason that the notion of perfectly hard matter was so difficult for him to comprehend, for two such particles colliding would necessarily undergo sudden changes in velocity, something he could not allow as possible.
The mathematical statement is:. The application of mathematics was a matter of considering physical situations, developing differential equations to express them, and then integrating those equations.
Mathematical physicists had to invent much of their procedure as they went along. For every such first, one can find other men who had alternative suggestions or different ways of expressing themselves, and who often wrote down similar but less satisfactory expressions.
He used, for example, the word fausse to describe a divergent series. The word to him was not a bare descriptive term.
There was no match, or no useful match, for divergence in the physical world. Convergence leads to the notion of the limit; divergence leads nowhere—or everywhere.
Here again his view of nature, not his mathematical capabilities, blocked him. He considered, for example, a game of chance in which Pierre and Jacques take part.
Pierre is to flip a coin. He considered the possibility of tossing tails one hundred times in a row. Metaphysically, he declared, one could imagine that such a thing could happen; but one could not realistically imagine it happening.
He went further: heads, he declared, must necessarily arise after a finite number of tosses. In other words, any given toss is influenced by previous tosses, an assumption firmly denied by modern probability theory.
Jacques and Pierre could forget the mathematics; it was not applicable to their game. Moreover, there were reasons for interest in probability outside games of chance.
It had been known for some time that if a person were inoculated with a fluid taken from a person having smallpox, the result would usually be a mild case of the disease, followed by immunity afterward.
Unfortunately, a person so inoculated occasionally would develop a more serious case and die. The question was posed: Is one more likely to live longer with or without inoculation?
There were many variables, of course. For example, should a forty-year-old, who was already past the average life expectancy, be inoculated?
What, in fact, was a life expectancy? How many years could one hope to live, from any given age, both with and without inoculation?
It was not, as far as he was concerned, irrelevant to the problem. Unfortunately, Euler was never trusted by Frederick, and he left soon afterward for St.
Petersburg , where he spent the rest of his life. The work was seen through the press by Voltaire in Geneva, and although it was published anonymously, everyone knew who wrote it.
He continued to live with her until her death in His later life was filled with frustration and despair, particularly after the death of Mlle.
What political success they had tasted they had not been able to develop. Original Works. Paris, ; and the Bastien ed.
Paris, The most recent and complete bibliographies are in Grimsley and Hankins see below. Secondary Literature. Paris, France, 29 October , mathematics, mechanics, astronomy, physics, philosophy.
Other scientific writings appeared in the form of letters to Joseph-Louis Lagrange in the Memoirs of the Turin Academy and in those of the Berlin Academy between and He held the positions of sous-directeur and directeur in and respectively.
As an academician, he was in charge of reporting on a large number of works submitted to the Academy, and he sat on many prize juries.
In particular, one may believe that he had a decisive voice concerning the choice of works about lunar motion, libration, and comets for the astronomy prizes awarded to Leonhard Euler , Lagrange, and Nikolai Fuss between and In [ 5 ] d'Alembert's ideas, as presented in this preface, are described Rational mechanics was a science based on simple necessary principles from which all particular phenomenon could be deduced by rigorous mathematical methods.
Clearly a rivalry quickly sprung up and d'Alembert stopped reading the work to the Academy and rushed into print with the treatise. The two mathematicians had come up with similar ideas and indeed the rivalry was to become considerably worse in the next few years.
D'Alembert stated his position clearly that he believed mechanics to be based on metaphysical principles and not on experimental evidence.
He seems not to have realised in his reading of Newton 's Principia how strongly Newton based his laws of motion on experimental evidence.
For d'Alembert these laws of motion were logical necessities. This work gave an alternative treatment of fluids to the one published by Daniel Bernoulli.
D'Alembert thought it a better approach, of course, as one might expect, Daniel Bernoulli did not share this view.
D'Alembert became unhappy at the Paris Academy , almost certainly because of his rivalry with Clairaut and disagreements with others.
His position became even less happy in when Maupertuis left Paris to take up the post of head of the Berlin Academy where, at that time, Euler was working.
In around d'Alembert's life took a rather sudden change. This is described in [ 4 ] as follows:- Until  he had been satisfied to lead a retired but mentally active existence at the house of his foster-mother.
In he was introduced to Mme Geoffrin, the rich, imperious, unintellectual but generous founder of a salon to which d'Alembert was suddenly invited.
He soon entered a social life in which, surprisingly enough, he began to enjoy great success and popularity. He was contracted as an editor to cover mathematics and physical astronomy but his work covered a wider field.
When the first volume appeared in it contained a Preface written by d'Alembert which was widely acclaimed as a work of great genius.
Buffon said that:- It is the quintessence of human knowledge In fact he wrote most of the mathematical articles in this 28 volume work.
He was a pioneer in the study of partial differential equations and he pioneered their use in physics. Euler , however, saw the power of the methods introduced by d'Alembert and soon developed these far further than had d'Alembert.
In fact this work by d'Alembert on the winds suffers from a defect which was typical of all of his work, namely it was mathematically very sound but was based on rather poor physical evidence.
In this case, for example, d'Alembert assumed that the winds were generated by tidal effects on the atmosphere and heating of the atmosphere played only a very minor role.
Clairaut attacked d'Alembert's methods [ 5 ] :- In order to avoid delicate experiments or long tedious calculations, in order to substitute analytical methods which cost them less trouble, they often make hypotheses which have no place in nature; they pursue theories that are foreign to their object, whereas a little constancy in the execution of a perfectly simple method would have surely brought them to their goal.
A heated argument between d'Alembert and Clairaut resulted in the two fine mathematicians trading insults in the scientific journals of the day.
The year was an important one for d'Alembert in that a second important work of his appeared in that year, namely his article on vibrating strings.
The article contains the first appearance of the wave equation in print but again suffers from the defect that he used mathematically pleasing simplifications of certain boundary conditions which led to results which were at odds with observation.
Euler had learnt of d'Alembert's work in around through letters from Daniel Bernoulli. When d'Alembert won the prize of the Prussian Academy of Sciences with his essay on winds he produced a work which Euler considered superior to that of Daniel Bernoulli.
Certainly at this time Euler and d'Alembert were on very good terms with Euler having high respect for d'Alembert's work and the two corresponded on many topics of mutual interest.
However relations between Euler and d'Alembert soon took a turn for the worse after the dispute in the Berlin Academy involving Samuel König which began in The situation became more relevant to d'Alembert in when he was invited to became President of the Berlin Academy.
Another reason for d'Alembert to feel angry with Euler was that he felt that Euler was stealing his ideas and not giving him due credit.
In one sense d'Alembert was justified but on the other hand his work was usually so muddled that Euler could not follow it and resorted to starting from scratch to clarify the problem being solved.
The Paris Academy had not been a place for d'Alembert to publish after he fell out with colleagues there and he was sending his mathematical papers to the Berlin Academy during the s.
Euler was strongly opposed to this and wrote to Lagrange see [ 5 ] You will never be anything but a philosopher - and what is that but an ass who plagues himself all his life, that he may be talked about after he is dead.
Destouches secretly paid for the education of Jean le Rond, but did not want his paternity officially recognised.
D'Alembert first attended a private school. The chevalier Destouches left d'Alembert an annuity of livres on his death in In his later life, d'Alembert scorned the Cartesian principles he had been taught by the Jansenists : "physical promotion, innate ideas and the vortices".
The Jansenists steered d'Alembert toward an ecclesiastical career, attempting to deter him from pursuits such as poetry and mathematics.
Theology was, however, "rather unsubstantial fodder" for d'Alembert. He entered law school for two years, and was nominated avocat in He was also interested in medicine and mathematics.
Jean was first registered under the name "Daremberg", but later changed it to "d'Alembert". The name "d'Alembert" was proposed by Frederick the Great of Prussia for a suspected but non-existent moon of Venus.
D'Alembert was also a Latin scholar of some note and worked in the latter part of his life on a superb translation of Tacitus , for which he received wide praise including that of Denis Diderot.
In this work d'Alembert theoretically explained refraction. He authored over a thousand articles for it, including the famous Preliminary Discourse.
D'Alembert "abandoned the foundation of Materialism "  when he "doubted whether there exists outside us anything corresponding to what we suppose we see.
In , he wrote about what is now called D'Alembert's paradox : that the drag on a body immersed in an inviscid , incompressible fluid is zero.
In , an article by d'Alembert in the seventh volume of the Encyclopedia suggested that the Geneva clergymen had moved from Calvinism to pure Socinianism , basing this on information provided by Voltaire.
The Pastors of Geneva were indignant, and appointed a committee to answer these charges. Under pressure from Jacob Vernes , Jean-Jacques Rousseau and others, d'Alembert eventually made the excuse that he considered anyone who did not accept the Church of Rome to be a Socinianist, and that was all he meant, and he abstained from further work on the encyclopaedia following his response to the critique.
D'Alembert wrote a glowing review praising the author's deductive character as an ideal scientific model. He saw in Rameau's music theories support for his own scientific ideas, a fully systematic method with a strongly deductive synthetic structure.
Because he was not a musician, however, d'Alembert misconstrued the finer points of Rameau's thinking, changing and removing concepts that would not fit neatly into his understanding of music.
Although initially grateful, Rameau eventually turned on d'Alembert while voicing his increasing dissatisfaction with J.Jean-Baptiste le Rond, genannt D'Alembert, (* November in Paris; † Oktober in Paris) war einer der bedeutendsten. Dynamik 2 1. Prinzip von d'Alembert. Freiheitsgrade. Zwangsbedingungen. Virtuelle Geschwindigkeiten. Prinzip der virtuellen Leistung.