People From Lyon

"In general this geometry instead of dealing with definite triangles, polygons, circles, etc., in the Euclidean manner, is based on a consideration of all points of a straight line, of all lines through a common point and of the possible effects of setting up an orderly one-to-one correspondence between them. In particular, Desargues makes a comparative study of the different plane sections of a given cone, deducing from known properties of the circle analogous results for the other conic sections."

"In his chief work Desargues enunciates the propositions:— 1. A straight line can be considered as produced to infinity and then the two opposite extremities are united. 2. Parallel lines are lines meeting at infinity and conversely. 3. A straight line and a circle are two varieties of the same species. On these he bases a general theory of the plane sections of a cone."

"Desargues contented himself with enunciating general principles remarking:—"He who shall wish to disentangle this proposition will easily be able to compose a volume.""

"He met Descartes while employed by Cardinal Richelieu at the , and they with others met regularly in Paris for the discussion of the new Copernican theory and other scientific problems."

"Perceiving that the practitioners of these arts ["...among others, the cutting of stones in architecture, that of sun-dials, that of perspective in particular"] had to burden themselves with the laborious acquisition of many special facts in geometry, he sought to relieve them by developing more general methods and printing notes for distribution among his friends."

"An interesting theorem bearing his name and typical of projective geometry is as follows:—If two triangles ABC and A'B'C' are so related that lines joining corresponding vertices meet in a point O, then the intersections of corresponding sides will lie in a straight line A"B"C". It remained for Monge, the inventor of descriptive geometry... and others more than a century later to carry this development forward. Desargues's work was indeed practically lost until Poncelet in 1822 proclaimed him the Monge of his century."

"One could say my life itself has been one long soundtrack. Music was my life, music brought me to life, and music is how I will be remembered long after I leave this life. When I die there will be a final waltz playing in my head that only I can hear."

"You have all Manner of News there: You have a good Fire, which you may sit by as long as you please: You have a Dish of Coffee; you meet your Friends for the Transaction of Business, and all for a Penny, if you don't care to spend more. (speaking of London coffeehouses in the late 1600s)"

"In the qualities of his heart too Montucla was truly estimable: remarkably modest in his manner and deportment; benevolent far beyond the means of his small fortune: of a very respectable personal appearance; he spoke with ease and precision, but unassuming and with simplicity; related anecdotes and stories in a pleasant and playful manner; and breathing, in all his conduct and deportment the sweetness of virtue, and the delicacy of a fine taste."

"John Stephen Montucla, member of the National Institute, and of the academy of Berlin, censor royal for mathematical books, and author of this new-modelled and enlarged edition of the Mathematical Recreations of Ozanam, was born at Lyons, the 5th of September 1725. His father was a banker, by whom he was intended for the same profession; but the science of calculations, to which he was early introduced, soon produced a discovery of the natural bent of his mind. In the Jesuits college at Lyons he laid a good foundation in the ancient languages, as well as in the mathematical sciences, which enabled him afterwards easily to acquire a competent acquaintance with the Italian, the German, die Dutch, and the English, .which he not only read, but also spoke very well."

"There is reason, however, to think that the author would have rendered it much more interesting, and have carried it to si higher degree of perfection, had he lived in an age more enlightened and better informed in regard to the mathematics and natural philosophy. Since the death of that mathematician, indeed, the arts and sciences have been so much improved, that what in his time might have been entitled to the character of mediocrity, would not at present be supportable. How many new discoveries in every part of philosophy? How many new phenomena observed, some of which have even given birth to the most fertile branches of the sciences? We shall mention only electricity, an inexhaustible source of profound reflection, and of experiments highly amusing. Chemistry also is a science, the most common and slightest principles of which were quite unknown to Ozanam. In short, we need not hesitate to pronounce that Ozanam's work contains a multitude of subjects treated of with an air of credulity, and so much prolixity, that it appears as if the author, or rather his continuators, had no other object in view than that of multiplying the volumes. To render this work, then, more worthy of the enlightened agt in which we live, it was necessary to make numerous corrections and considerable additions. A task which we have endeavoured to discharge with all diligence"

"No one ever squared the circle with so much genius, or, excepting his principal object, with so much success."

"Mathematics and philosophy are cultivated by two different classes of men: some make them an object of pursuit, either in consequence of their situation, or through a desire to render themselves illustrious, by extending their limits; while others pursue them for mere amusement, or by a natural taste which inclines them to that branch of knowledge. It is for the latter class of mathematicians and philosophers that this work is chiefly intended j and yet, at the same time, we entertain a hope that some parts of it will prove interesting to the former. In a word, it may serve to stimulate the ardour of those who begin to study these sciences; and it is for this reason that in most elementary books the authors endeavour to simplify the questions designed for exercising beginners, by proposing them in a less abstract manner than is employed in the pure mathematics, and so as to interest and excite the reader's curiosity. Thus, for example, if it were proposed simply to divide a triangle into three, four, or five equal parts, by lines drawn from a determinate point within it, in this form the problem could be interesting to none but those really possessed of a taste for geometry. But if, instead of proposing it in this abstract manner, we should say: "A father on his death-bed bequeathed to his three sons a triangular field, to be equally divided among them: and as there is a well in the field, which must be common to the three co-heirs, and from which the lines of division must necessarily proceed, how is the field to be divided so as to fulfill the intention of the testator?" This way of stating it will, no doubt, create a desire in most minds to discover the method of solving the problem; and however little taste people may possess for real science, they will be tempted to try iheir ingenuity in finding the answer to such a question at this."

"Montucla says, speaking of France, that he finds three notions prevalent among cyclometers: 1. That there is a large reward offered for success; 2. That the longitude problem depends on that success; 3. That the solution is the great end and object of geometry. The same three notions are equally prevalent among the same class in England. No reward has ever been offered by the government of either country. The longitude problem hi no way depends upon perfect solution; existing approximations are sufficient to a point of accuracy far beyond what can be wanted. And geometry, content with what exists, has long passed on to other matters. Sometimes a cyclometer persuades a skipper who has made land in the wrong place that the astronomers are at fault, for using a wrong measure of the circle; and the skipper thinks it a very comfortable solution! And this is the utmost that the problem has to do with longitude."

"Affections are more solid and lasting among spirits than among men, because they are not subordinated to the caprices of material interests and self-love."

"If demons existed, they would be the work of God; but would it he just on the part of God to have created beings condemned eternally to evil and to misery? If demons exist, it is in your low world, and in other worlds of similar degree that they are to be found. They are the human hypocrites who represent a just God as being cruel and vindictive, and who imagine that they make themselves agreeable to Him by the abominations they commit in His name."

"During life, a spirit is held to the body by his semi-material envelope, or perispirit. Death is the destruction of the body only, but not of this second envelope, which separates itself from the body when the play of organic life ceases in the latter. Observation shows us that the separation of the perispirit from the body is not suddenly completed at the moment of death, but is only effected gradually, and more or less slowly in different individuals. In some cases it is effected so quickly that the perispirit is entirely separated from the body within a few hours of the death of the latter but in other cases, and especially in the case of those whose life has been grossly material and sensual, this deliverance is much less rapid, and sometimes takes days, weeks, and even months, for its accomplishment. This delay does not imply the slightest persistence of vitality in the body, nor any possibility of its return to life, but is simply the result of a certain affinity between the body and the spirit which affinity is always more or less tenacious in proportion to the preponderance of materiality in the affections of the spirit during his earthly life."

"The line of march of all spirits is always progressive, never retrograde. They raise themselves gradually In the hierarchy of existence they never descend from the rank at which they have once arrived. In the course of their different corporeal existences they may descend in rank as men, but not as spirits. Thus the soul of one who has been at the pinnacle of earthly power may, in a subsequent incarnation, animate the humblest day-labourer, and vice versa ; for the elevation of ranks among men is often In the inverse ratio of that of the moral sentiments. Herod was a king, and Jesus, a carpenter."

"Spirits incarnate themselves as men or as women, because they are of no sex and, as it is necessary for them to develop themselves in every direction, both sexes, as well as every variety of social position. furnish them with special trials and duties, and with the opportunity of acquiring experience. A spirit who had always incarnated itself as a man would be only known by men, and vice versa."

"As spirits transport themselves from point to point with the rapidity of thought, they may be said to see everywhere at the same time. A spirit's thought may radiate at the same moment on many different points; but this faculty depends on his purity. The more impure the spirit, the narrower is his range of sight. It is only the higher spirits who can take in a whole at a single glance."

"A master who had been cruel to his slaves might become a slave in his turn, and undergo the torments he had inflicted on others. He who has wielded authority may, in a new existence, be obliged to obey those who formerly bent to his will. Such an existence may be imposed upon him as an expiation if he have abused his power. But a good spirit may also choose an influential existence among the people of some lower race, in order to hasten their advancement; in that case, such a reincarnation is a mission."

"Intellectual superiority is not always accompanied by an equal degree of moral superiority, and the greatest geniuses may have much to expiate. For this reason, they often have to undergo an existence inferior to the one they have previously accomplished, which is a cause of suffering for them the hindrances to the manifestation of his faculties thus imposed upon a spirit being like chains that fetter the movements of a vigorous man. The idiot may be said to be lame in the brain, as the halt is lame in the legs, and the blind, in the eyes."

"When a spirit has reached the end of the term assigned by Providence to his errant life, he chooses for himself the trials which he determines to undergo in order to hasten his progress - that is to say, the kind of existence which he believes will be most likely to furnish him with the means of advancing and the trials of this new existence always correspond to the faults which he has to expiate. If he triumphs in this new struggle, he rises in grade; if he succumbs, he has to try again."

"You often say, 'I have had a strange dream, a frightful dream, without any likeness to reality' You are mistaken in thinking it to be so; for it is often a reminiscence of places and things which you have seen in the past, or a foresight of those which you will see in another existence, or in this one at some future time. The body being torpid, the spirit tries to break his chain, and seeks, in the past or in the future, for the means of doing so."

"The spirit acquires an increase of knowledge and experience in each of his corporeal existences. He loses sight of part of these gains during his reincarnation in matter, which is too gross to allow of his remembering them in their entirety; but he remembers them as a spirit. It is thus that some somnambulists give evidence of possessing knowledge beyond their present degree of instruction, and even of their apparent intellectual capacity. The intellectual and scientific inferiority of a somnambulist in his waking state, therefore, proves nothing against his possession of the knowledge he may display in his lucid state. According to the circumstances of the moment and the aim proposed, he may draw this knowledge from the stores of his own experience, from his clairvoyant perception of things actually occurring, or from the counsels which he receives from other spirits; but, in proportion as his own spirit is more or less advanced, he will make his statements more or less correctly."

"If there be a doctrine that should win over the most incredulous by its charm and its beauty, it is that of the existence of spirit-protectors, or guardian-angels. To think that you have always near you beings who are superior to you, and who are always beside you to counsel you, to sustain you, to aid you in climbing the steep ascent of self-improvement, whose friendship is truer and more devoted than the most intimate union that you can contract upon the earth-is not such an idea most consoling? Those beings are near you by the command of God. It is He who has placed them beside you. They are there for love of Him, and they fulfil towards you a noble but laborious mission. They are with you wherever you may be; in the dungeon, in solitude, in the lazar-house, even in the haunts of debauchery. Nothing ever separates you from the friend whom you cannot see, but whose gentle impulsions are felt, and whose wise monitions are heard, in the innermost recesses of your heart."

"In the case of those who are killed in battle, as in all other cases of violent death, a spirit, during the first few moments, is in a state of bewilderment, and as though he were stunned. He does not know that he is dead and seems to be taking part in the action. It is only little by little that the reality of his situation becomes apparent to him."

"Écoute les savants, mais ne les écoute que d'une oreille!... Que l'autre soit toujours prête à recevoir les doux accents de la voix de ton ami céleste!"

"Either one or the other [ analysis or synthesis ] may be direct or indirect. The direct procedure is when the point of departure is known-direct synthesis in the elements of geometry. By combining at random simple truths with each other, more complicated ones are deduced from them. This is the method of discovery, the special method of inventions, contrary to popular opinion."

"There is synthesis when, in combining therein judgments that are made known to us from simpler relations, one deduces judgments from them relative to more complicated relations. There is analysis when from a complicated truth one deduces more simple truths."

"The experimental investigation by which Ampère established the law of the mechanical action between electric currents is one of the most brilliant achievements in science. The whole, theory and experiment, seems as if it had leaped, full grown and full armed, from the brain of the 'Newton of electricity.' It is perfect in form, and unassailable in accuracy, and it is summed up in a formula from which all the phenomena may be deduced, and which must always remain the cardinal formula of electro-dynamics."

"La vérité ne se possède pas, elle se cherche."

"... en matière scientifique, on a souvent des prédécesseurs beaucoup plus anciens qu'on ne le pense a priori."

"Les pierres du chantier ne sont en vrac qu’en apparence, s’il est, perdu dans le chantier, un homme, serait-il seul, qui pense cathédrale."

"Toute nation est égoïste. Toute nation considère son égoïsme comme sacré."

"If it is true that wars are won by believers, it is also true that peace treaties are sometimes signed by businessmen."

""Navigating by the compass in a sea of clouds over Spain is all very well, it is very dashing, but—" And I was struck by the graphic image: "But you want to remember that below the sea of clouds lies eternity." And suddenly that tranquil cloud-world, that world so harmless and simple that one sees below on rising out of the clouds, took on in my eyes a new quality. That peaceful world became a pitfall. I imagined the immense white pitfall spread beneath me. Below it reigned not what one might think — not the agitation of men, not the living tumult and bustle of cities, but a silence even more absolute than in the clouds, a peace even more final. This viscous whiteness became in my mind the frontier between the real and the unreal, between the known and the unknowable. Already I was beginning to realize that a spectacle has no meaning except it be seen through the glass of a culture, a civilization, a craft. Mountaineers too know the sea of clouds, yet it does not seem to them the fabulous curtain it is to me."

"Each man must look to himself to teach him the meaning of life. It is not something discovered: it is something molded. These prison walls that this age of trade has built up round us, we can break down. We can still run free, call to our comrades, and marvel to hear once more, in response to our call, the impassioned chant of the human voice."

"I had a vision of the face of destiny. Old bureaucrat, my comrade, it is not you who are to blame. No one ever helped you to escape. You, like a termite, built your peace by blocking up with cement every chink and cranny through which the light might pierce. You rolled yourself up into a ball in your genteel security, in routine, in the stifling conventions of provincial life, raising a modest rampart against the winds and the tides and the stars. You have chosen not to be perturbed by great problems, having trouble enough to forget your own fate as man. You are not the dweller upon an errant planet and do not ask yourself questions to which there are no answers. You are a petty bourgeois of Toulouse. Nobody grasped you by the shoulder while there was still time. Now the clay of which you were shaped has dried and hardened, and naught in you will ever awaken the sleeping musician, the poet, the astronomer that possibly inhabited you in the beginning. The squall has ceased to be a cause of my complaint. The magic of the craft has opened for me a world in which I shall confront, within two hours, the black dragons and the crowned crests of a coma of blue lightnings, and when night has fallen I, delivered, shall read my course in the stars."

""I swear that what I went through, no animal would have gone through." This sentence, the noblest ever spoken, this sentence that defines man's place in the universe, that honors him, that re-establishes the true hierarchy, floated back into my thoughts."

"Transport of the mails, transport of the human voice, transport of flickering pictures — in this century, as in others, our highest accomplishments still have the single aim of bringing men together. Do our dreamers hold that the invention of writing, of printing, of the sailing ship, degraded the human spirit? It seems to me that those who complain of man's progress confuse ends with means. True, that man who struggles in the unique hope of material gain will harvest nothing worth while. But how can anyone conceive that the machine is an end? It is a tool. As much a tool as is the plough. The microscope is a tool. What disservice do we do the life of the spirit when we analyze the universe through a tool created by the science of optics, or seek to bring together those who love one another and are parted in space?"

"Precisely because it is perfect the machine dissembles its own existence instead of forcing itself upon our notice. And thus, also, the realities of nature resume their pride of place. It is not with metal that the pilot is in contact. Contrary to the vulgar illusion, it is thanks to the metal, and by virtue of it, that the pilot rediscovers nature. As I have already said, the machine does not isolate man from the great problems of nature but plunges him more deeply into them. Numerous, nevertheless, are the moralists who have attacked the machine as the source of all the ills we bear, who, creating a fictitious dichotomy, have denounced the mechanical civilization as the enemy of the spiritual civilization. If what they think were really so, then indeed we should have to despair of man, for it would be futile to struggle against this new advancing chaos. The machine is certainly as irresistible in its advance as those virgin forests that encroach upon equatorial domains."

"Have you looked at a modern airplane? Have you followed from year to year the evolution of its lines? Have you ever thought, not only about the airplane but about whatever man builds, that all of man's industrial efforts, all his computations and calculations, all the nights spent over working draughts and blueprints, invariably culminate in the production of a thing whose sole and guiding principle is the ultimate principle of simplicity? It is as if there were a natural law which ordained that to achieve this end, to refine the curve of a piece of furniture, or a ship's keel, or the fuselage of an airplane, until gradually it partakes of the elementary purity of the curve of a human breast or shoulder, there must be the experimentation of several generations of craftsmen. In anything at all, perfection is finally attained not when there is no longer anything to add, but when there is no longer anything to take away, when a body has been stripped down to its nakedness."

"Être homme, c'est précisément être responsable. C'est connaître la honte en face d'une misère qui ne semblait pas dépendre de soi. C'est être fier d'une victoire que les camarades ont remportée. C'est sentir, en posant sa pierre, que l'on contribue à bâtir le monde."

"A goal without a plan is just a wish."

"[...] Car une civilisation repose sur ce qui est exigé des hommes, non sur ce qui leur est fourni."

"Even our misfortunes are a part of our belongings"

"Ne confonds point l’amour avec le délire de la possession, lequel apporte les pires souffrances. Car au contraire de l’opinion commune, l’amour ne fait point souffrir. Mais l’instinct de propriété fait souffrir, qui est le contraire de l’amour."

"L'avenir, tu n'as point à le prévoir mais à le permettre."

"Ce qui embellit le désert, dit le petit prince, c'est qu'il cache un puits quelque part..."