Academics From France

"L'histoire est un roman dont le peuple est l'auteur."

"On étouffe les clameurs, mais comment se venger du silence?"

"Un désespoir paisible, sans convulsions de colère et sans reproches au ciel est la sagesse même."

"Tout homme a vu le mur qui borne son esprit."

"Les acteurs sont bien heureux, ils ont une gloire sans responsabilité."

"L'existence du Soldat est (après la peine de mort) la trace la plus douloureuse de barbarie qui subsiste parmi les hommes."

"The questions here dealt with have occupied me since my earliest youth, when my interest for them was powerfully stimulated by the beautiful introductions of Lagrange to the chapters of his Analytic Mechanics..."

"Analytic mechanics... was brought to the highest degree of perfection by Lagrange. Lagrange's aim is ('... 1788) to dispose, once and for all, of the reasoning necessary to resolve mechanical problems, by embodying as much as possible of it in a single formula. This he did. Every case... can now be dealt with by a very simple, highly symmetrical and perspicuous schema; and whatever reasoning is left is performed by purely mechanical methods. The mechanics of Lagrange is a stupendous contribution to the economy of thought."

"Full use of Lagrange's own made the unification of the varied principles of statistics and dynamics possible—in statistics by the use of the principle of virtual velocities, in dynamics by the use of . This led... to generalized coordinates and to the equation of motion in their "Lagrangian" form... Newton's geometrical approach was now fully discarded; Lagrange's book was a triumph of pure analysis."

"Who has studied the works of such men as Euler, Lagrange, Cauchy, Riemann, , and Weierstrass, can doubt that a great mathematician is a great artist? The faculties possessed by such men, varying greatly in kind and degree with the individual, are analogous with those requisite for constructive art. Not every mathematician possesses in a specially high degree that critical faculty which finds its employment in the perfection of form, hi conformity with the ideal of logical completeness; but every great mathematician possesses the rarer faculty of constructive imagination."

"Lagrange, in one of the later years of his life, imagined that he had overcome the difficulty [of the parallel axiom]. He went so far as to write a paper, which he took with him to the Institute, and began to read it. But in the first paragraph something struck him which he had not observed : he muttered II faut que fy songe encore, and put the paper in his pocket."

"The mathematician is perfect only in so far as he is a perfect being, in so far as he perceives the beauty of truth; only then will his work be thorough, transparent, comprehensive, pure, clear, attractive and even elegant. All this is necessary to resemble Lagrange."

"The treatment of the kinetics of a material system by the method of generalised coordinates was first introduced by Lagrange, and has since his time been greatly developed by the investigations of different mathematicians. Independently of the highly interesting, although purely abstract science of theoretical dynamics which has resulted from these investigations, they have proved of great and continually increasing value in the application of mechanics to thermal, electrical and chemical theories, and the whole range of ."

"Lagrange, struck with the circumstance that the calculus had never given any inequalities but such as were periodical, applied himself to the investigation of a general question, from which he found by a method peculiar to himself and independent of any approximation, that the inequalities produced by the mutual action of the planets must in effect be all periodical; that the periodical changes are confined within narrow limits; that none of the planets ever has been or ever can be a comet moving in a very eccentric orbit; but that the planetary system oscillates as it were round a medium state from which it never deviates far: that amid all the changes which arise from the mutual actions of the planets, two things remain perpetually the same, viz. the length of the greater axis of the ellipse which the planet describes, and its periodical time round the sun; or, which is the same thing, the mean distance of each planet from the sun and its mean motion remain constant. The plane of the orbit varies, the species of the ellipse and its eccentricity change, but never, by any means whatever, the greater axis of the ellipse, or the time of the entire revolution of the planet. The discovery of this great principle, which we may consider as the bulwark that secures the stability of our system, and excludes all access to confusion and disorder, must render the name of Lagrange for ever memorable in science, and ever revered by those who delight in the contemplation of whatever is excellent and sublime. After Newton's discovery of the elliptic orbits of the planets from gravitation, Langrange's discovery of their periodical inequalities is, without doubt, the noblest truth in physical astronomy, and in respect of the doctrine of final causes, it may truly be regarded as the greatest of all."

"An ancient writer said that arithmetic and geometry are the wings of mathematics; I believe one can say without speaking metaphorically that these two sciences are the foundation and essence of all the sciences which deal with quantity. Not only are they the foundation, they are also, as it were, the capstones; for, whenever a result has been arrived at, in order to use that result, it is necessary to translate it into numbers or into lines; to translate it into numbers requires the aid of arithmetic, to translate it into lines necessitates the use of geometry."

"Newton was the greatest genius that ever existed, and the most fortunate, for we cannot find more than once a system of the world to establish."

"It took them only an instant to cut off that head, but France may not produce another like it in a century."

"As long as algebra and geometry proceeded along separate paths, their advance was slow and their applications limited. But when these sciences joined company, they drew from each other fresh vitality and thenceforward marched on at a rapid pace toward perfection."

"The value of his work [Mécanique Analytique] consists in the exposition of a general method by which every mechanical question may be stated in a single algebraic equation. The entire history of any mechanical system, as for example, the solar system, may thus be condensed into a single sentence; and its detailed interpretation becomes simply a question of algebra. No one who has not tried to cope with the difficulties presented by almost any mechanical problem can form a just appreciation of the great utility of such a labor-saving and thought-saving device. It has been well called 'a stupendous contribution to the economy of thought.'"

"I cannot say whether I will still be doing geometry ten years from now. It also seems to me that the mine has maybe already become too deep and unless one finds new veins it might have to be abandoned. Physics and chemistry now offer a much more glowing richness and much easier exploitation. Also, the general taste has turned entirely in this direction, and it is not impossible that the place of Geometry in the Academies will someday become what the role of the Chairs of Arabic at the universities is now."

"We have already various treatises on Mechanics, but the plan of this one is entirely new. I intend to reduce the theory of this Science, and the art of solving problems relating to it, to general formulae, the simple development of which provides all the equations necessary for the solution of each problem. I hope that the manner in which I have tried to attain this object will leave nothing to be desired. No diagrams will be found in this work. The methods that I explain require neither geometrical, nor mechanical, constructions or reasoning, but only algebraical operations in accordance with regular and uniform procedure. Those who love Analysis will see with pleasure that Mechanics has become a branch of it, and will be grateful to me for having thus extended its domain."

"The great masters of modern analysis are Lagrange, Laplace, and Gauss, who were contemporaries. It is interesting to note the marked contrast in their styles. Lagrange is perfect both in form and matter, he is careful to explain his procedure, and though his arguments are general they are easy to follow. Laplace on the other hand explains nothing, is indifferent to style, and, if satisfied that his results are correct, is content to leave them either with no proof or with a faulty one. Gauss is as exact and elegant as Lagrange, but even more difficult to follow than Laplace, for he removes every trace of the analysis by which he reached his results, and studies to give a proof which while rigorous shall be as concise and synthetical as possible."

"Lagrange... was the first to draw sharply the line of demarcation between physics and metaphysics. The mechanical ideas of Descartes, Leibnitz, Maupertius, and even of Euler, had proved to be more or less hazy and unfruitful from a failure to separate those two distinct regions of thought. Lagrange put an end to this confusion, for no serious attempt has since been made to derive the laws of mechanics from a metaphysical basis."

"The mere reading of the life of Jesus, as we have represented it according to documents which Christians consider inspired, must be sufficient to undeceive every thinking being. But it is the property of superstition to prevent thinking: it benumbs the soul, confounds the reason, perverts the judgment, renders doubtful the most obvious truths, and makes a merit with its slaves of despising inquiry, and of relying on the word of those who govern them."

"Men are naturally disposed to listen to, and believe those who make them hope for an end to their miseries. Misfortunes render them timorous and credulous, and lead them to superstition. A fanatic easily makes conquests among a wretched people. It is not then wonderful that Jesus should soon acquire partizans, especially among the populace who in every country are easily seduced."

"Our hero knew the weakness of his fellow-citizens. They wanted prodigies, and he, in their eyes, performed them. A stupid people, totally strangers to the natural sciences, to medicine, or to the resources of artifice, easily mistook very simple operations for miracles, and attributed effects to the finger of God which might be owing to the knowledge Jesus had acquired during the long interval that preceded his mission. Nothing is more common than the combination of enthusiasm and imposture; the most sincere devotees, when they intend to advance what they believe to be the word of God, often countenance frauds which they style pious. There are but few zealots who do not even think crimes allowable when the interests of religion are concerned. In religion, as at play, one begins with being dupe, and ends with being knave. Thus on considering things attentively, and comparing the different accounts of the life of Jesus, we must be persuaded that he was a fanatic, who really thought himself inspired, favored by Heaven, sent to his nation; in short, that he was the messiah, who, to support his divine mission, felt no difficulty to employ such deceptions as were best calculated for a people to whom miracles were absolutely necessary; and whom, without miracles, the most eloquent harangues, the wisest precepts, the most intelligent counsels, and the truest principles could never have convinced. A medley of enthusiasm and juggling constitute the character of Jesus, and it is that of all spiritual adventurers who assume the name of Reformers, or become the chiefs of a sect."

"The dogma of the resurrection of Jesus is only attested by men whose subsistence depended on that absurd romance; and as roguery continually belies itself, these witnesses could not agree among themselves in their evidence. They tell us, that Jesus had publicly predicted his own resurrection. He ought therefore to have risen publicly; he ought to have shewn himself, not in secret to his disciples, but openly to priests, pharisees, doctors, and men of understanding, especially after having intimated, that it was the only sign which would be given them. Was it not acknowledging the falsehood of his mission, to refuse the sign by which he had solemnly promised to prove the truth of that mission? Was it reasonable to require the Jews to believe, on the word of his disciples, a fact which he could have demonstrated before their own eyes? How is it possible for rational persons of the present age to believe, after the lapse of eighteen hundred years, on the discordant testimonies of four interested evangelists, fanatics, or fabulists, a story which they could not make be believed in their own time; except by a small number of imbecile people, incapable of reasoning, fond of the marvellous, and of too limited understandings to escape the snares laid for their simplicity."

"Jesus, to whom miracles cost nothing when every thing was arranged for performing them, did not risk himself by working them impromptu, or in the presence of those he judged acute enough to examine them."

"Jesus caused a fig-tree to die in twenty-four hours to punish it for not producing figs at a season when it was physically impossible for it to bear any; that is about the month of March. As all the actions of the messiah, even when they appear foolish to ordinary men, have an important signification in the eyes of devotees illuminated by faith, we ought to perceive in the miracle of this fig-tree one of the fundamental dogmas of the Christian religion symbolically represented. The fig-tree cursed is the mass of mankind, whom, according to our theologists, the God of mercy curses, and condemns to eternal flames, for having neither faith nor grace, which they could not possibly acquire of themselves, and which God does not seem to have been willing to give them. Thus we find that the ridiculous passage of the fig-tree in the gospel, is intended to typify one of the most profound dogmas of the Christian religion."

"Doubt is not a pleasant condition, but certainty is an absurd one. What is most repellent in the System of Nature — after the recipe for making eels from flour — is the audacity with which it decides that there is no God, without even having tried to prove the impossibility. If God did not exist, he would have to be invented. But all nature cries aloud that he does exist: that there is a supreme intelligence, an immense power, an admirable order, and everything teaches us our own dependence on it."

"the ways of God are not as those of men. The Deity ought never to act in a natural way, or be easily understood. It is the essence of religion that men should not comprehend any part of the divine conduct. This furnishes to their spiritual guides the pleasure of explaining it to them for their money."

"It must be acknowledged, that the impossibility of comprehending the doctrine of Jesus furnishes a good reason for denying that it can be divine. It cannot be conceived why a God, sent to instruct men, should never distinctly explain himself. No Pagan oracle employed terms more ambiguous, than the divine missionary chosen by Providence to enlighten nations."

"In the whole gospel system, the devil is more sly and powerful than both God the Father and God the Son: he is always successful in thwarting their designs, and succeeds in reducing God the Father to the dire necessity of making his dear Son die in order to repair the evil which Satan had done to mankind. Christianity is real manichaeism, wherein every advantage is on the side of the bad principle, who, by the great number of his adherents renders nugatory all the purposes of the Deity."

"Christians, docile to the lessons of their divine master, which they dare not examine, have made perfection consist in a total abandonment of those objects which nature has rendered dearest to man. Christianity seems intended only to create discord, detach men from every thing on earth, and break the ties which ought to unite them. There is, according to Jesus, but one thing needful; namely, to be attached to him exclusively: a maxim very useful in meriting heaven, but calculated to destroy every society on the earth."

"Jesus charged people of property with the maintenance of his apostles. Their successors have taken sufficient advantage of this, and through it assumed an authority to exercise the most cruel extortions on impoverished nations."

"the miracles of the messiah were calculated to convince those only who did not [Pg 82]see them. Thus it is, that these miracles are believed at present by people who would not credit those performed in their presence."

"It is very strange that men should deny a Creator and yet attribute to themselves the power of creating eels."

"The worshipers of God find, above all in the order of the universe, an invincible proof of this existence of an intelligent and wise being, who governs it. But this order is nothing but a series of movements necessarily produced by causes or circumstances, which are sometimes favourable, and sometimes hurtful to us: we approve of some, and complain of others."

"a protestant is bound to believe the gospel to be divine: and the examination of it is permitted only, while he finds there what the ministers of his sect have resolved that he shall find. Beyond this, he is regarded as an ungodly man, and often punished for the weakness of his intellect."

"Jesus, with a view, no doubt, of sweetening the lot of his apostles, recommended compassion to the listening multitude, of which he, as well as his party, stood in the greatest need. It is readily perceived, that the messiah felt the most imperious necessity to preach charity to his auditors; for he lived on alms, and his success depended on the generosity of the public, and the benefactions of the good souls who hearkened to his lessons."

"There is a science that has for its object only things incomprehensible. Contrary to all other sciences, it treats only of what cannot fall under our senses, Hobbes calls it the kingdom of darkness. It is a country, where every thing is governed by laws, contrary to those which mankind are permitted to know in the world they inhabit. In this marvelous region, light is only darkness; evidence is doubtful or false; impossibilities are credible: reason is a deceitful guide; and good sense becomes madness. This science is called Theology, and this theology is a continual insult to this reason of man."

"Everything that passes in the world, proves to us, in the clearest manner, that it is not governed by an intelligent being."

"The universe can be only what it is; all sensible being there enjoy and suffer, that is, are moved sometimes in an agreeable, and sometimes in a disagreeable manner. these effects are necessary; they result necessarily from causes, which act only according to their properties."

"The preacher recommended peace and concord; dispositions necessary to a new born, weak, and persecuted sect; but this necessity ceased when this sect had attained strength enough to dictate the law."

"To wonder at the order of nature, is to wonder that any thing can exist; it is to be surprised at one's own existence."

"Pascal proves nothing in favour of Religion, unless that a man of genius may be foolish on some subjects, and is but a child, when he is weak enough to listen to his prejudices."

"Religion has ever filled the mind of man with darkness, and kept him in ignorance of his real duties and true interests. It is only by dispelling the clouds and phantoms of Religion, that we shall discover Truth, Reason, and Morality. Religion diverts us from the causes of evils, and from the remedies which nature prescribes; far from curing, it only aggravates, multiplies, and perpetuates them."

"Suns are extinguished or become corrupted, planets perish and scatter across the wastes of the sky; other suns are kindled, new planets formed to make their revolutions or describe new orbits, and man, an infinitely minute part of a globe which itself is only an imperceptible point in the immense whole, believes that the universe is made for himself."

"All children are born Atheists; they have no idea of God."

"We are quite surprised at finding, that Moses and the ancient Hebrew writers have no where mentioned the dogma of a future life, which now-a-days forms one of the most important articles of the Christian religion. Solomon speaks of the death of men by comparing it with that of brutes. Some of the prophets, it is true, have spoken of a place called Cheol, which has been translated Hell (Enfer); yet it is evident, that this word implies merely sepulchre or tomb. They have also translated the Hebrew word Topheth into Hell: but on examining the word, we find that it designates a place of punishment near Jerusalem, where malefactors were punished, and their carcases burned. It was after the Babylonish captivity that the Jews knew the dogma of another life, and the resurrection, which they learned of the Persian disciples of Zoroaster. In the time of Jesus, that dogma was not even generally received. The Pharisees admitted it, and the Sadducees rejected."