Lawyers from France

351 quotes found

"There is scarcely any one who states purely arithmetical questions, scarcely any who understands them. Is this not because arithmetic has been treated up to this time geometrically rather than arithmetically? This certainly is indicated by many works ancient and modern. Diophantus himself also indicates this. But he has freed himself from geometry a little more than others have, in that he limits his analysis to rational numbers only; nevertheless the Zetcica of Vieta, in which the methods of Diophantus are extended to continuous magnitude and therefore to geometry, witness the insufficient separation of arithmetic from geometry. Now arithmetic has a special domain of its own, the theory of numbers. This was touched upon but only to a slight degree by Euclid in his Elements, and by those who followed him it has not been sufficiently extended, unless perchance it lies hid in those books of Diophantus which the ravages of time have destroyed. Arithmeticians have now to develop or restore it. To these, that I may lead the way, I propose this theorem to be proved or problem to be solved. If they succeed in discovering the proof or solution, they will acknowledge that questions of this kind are not inferior to the more celebrated ones from geometry either for depth or difficulty or method of proof: Given any number which is not a square, there also exists an infinite number of squares such that when multiplied into the given number and unity is added to the product, the result is a square."

- Pierre de Fermat

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"J.M. Child... has made a searching study of Barrow and has arrived at startling conclusions on the historical question relating to the first invention of the calculus. He places his conclusions in italics in the first sentence as follows Isaac Barrow was the first inventor of the Infinitesimal Calculus... Before entering upon an examination of the evidence brought forth by Child it may be of interest to review a similar claim set up for another man as inventor of the calculus... Fermat was declared to be the first inventor of the calculus by Lagrange, Laplace, and apparently also by P. Tannery, than whom no more distinguished mathematical triumvirate can easily be found. ...Dinostratus and Barrow were clever men, but it seems to us that they did not create what by common agreement of mathematicians has been designated by the term differential and integral calculus. Two processes yielding equivalent results are not necessarily the same. It appears to us that what can be said of Barrow is that he worked out a set of geometric theorems suggesting to us constructions by which we can find lines, areas and volumes whose magnitudes are ordinarily found by the analytical processes of the calculus. But to say that Barrow invented a differential and integral calculus is to do violence to the habit of mathematical thought and expression of over two centuries. The invention rightly belongs to Newton and Leibniz."

- Pierre de Fermat

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"One may regard Fermat as the first inventor of the new calculus. In his method De maximis et minimis he equates the quantity of which one seeks the maximum or the minimum to the expression of the same quantity in which the unknown is increased by the indeterminate quantity. In this equation he causes the radicals and fractions, if any such there be, to disappear and after having crossed out the terms common to the two numbers, he divides all others by the indeterminate quantity which occurs in them as a factor; then he takes this quantity zero and he has an equation which serves to determine the unknown sought. ...It is easy to see at first glance that the rule of the differential calculus which consists in equating to zero the differential of the expression of which one seeks a maximum or a minimum, obtained by letting the unknown of that expression vary, gives the same result, because it is the same fundamentally and the terms one neglects as infinitely small in the differential calculus are those which are suppressed as zeroes in the procedure of Fermat. His method of tangents depends on the same principle. In the equation involving the abscissa and ordinate which he calls the specific property of the curve, he augments or diminishes the abscissa by an indeterminate quantity and he regards the new ordinate as belonging both to the curve and to the tangent; this furnishes him with an equation which he treats as that for a case of a maximum or a minimum. ...Here again one sees the analogy of the method of Fermat with that of the differential calculus; for, the indeterminate quantity by which one augments the abscissa x corresponds to its differential dx, and the quantity ye/t, which is the corresponding augmentation [Footnote: Fermat lets e be the increment of x, and t the subtangent for the point x,y on the curve.] of y, corresponds to the differential dy. It is also remarkable that in the paper which contains the discovery of the differential calculus, printed in the Leipsic Acts of the month of October, 1684, under the title Nova methodus pro maximis et minimis etc., Leibnitz calls dy a line which is to the arbitrary increment dx as the ordinate y is to the subtangent; this brings his analysis and that of Fermat nearer together. One sees therefore that the latter has opened the quarry by an idea that is very original, but somewhat obscure, which consists in introducing in the equation an indeterminate which should be zero by the nature of the question, but which is not made to vanish until after the entire equation has been divided by that same quantity. This idea has become the germ of new calculi which have caused geometry and mechanics to make such progress, but one may say that it has brought also the obscurity of the principles of these calculi. And now that one has a quite clear idea of these principles, one sees that the indeterminate quantity which Fermat added to the unknown simply serves to form the derived function which must be zero in the case of a maximum or minimum, and which serves in general to determine the position of tangents of curves. But the geometers contemporary with Fermat did not seize the spirit of this new kind of calculus; they did not regard it but a special artifice, applicable simply to certain cases and subject to many difficulties, ...moreover, this invention which appeared a little before the Géométrie of Descartes remained sterile during nearly forty years. ...Finally Barrow contrived to substitute for the quantities which were supposed to be zero according to Fermat quantities that were real but infinitely small, and he published in 1674 his method of tangents, which is nothing but a construction of the method of Fermat by means of the infinitely small triangle, formed by the increments of the abscissa e, the ordinate ey/t, and of the infinitely small arc of the curve regarded as a polygon. This contributed to the creation of the system of infinitesimals and of the differential calculus."

- Pierre de Fermat

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"Lastly, let each of us consider how far he is bound in duty to others, and in good faith pay what we owe. In the same way, let the people pay all due honour to their rulers, submit patiently to their authority, obey their laws and orders, and decline nothing which they can bear without sacrificing the favour of God. Let rulers, again, take due charge of their people, preserve the public peace, protect the good, curb the bad, and conduct themselves throughout as those who must render an account of their office to God, the Judge of all… Let the aged also, by their prudence and their experience, (in which they are far superior,) guide the feebleness of youth, not assailing them with harsh and clamorous invectives but tempering strictness with ease and affability. Let servants show themselves diligent and respectful in obeying their masters, and this not with eye-service, but from the heart, as the servants of God. Let masters also not be stern and disobliging to their servants, nor harass them with excessive asperity, nor treat them with insult, but rather let them acknowledge them as brethren and fellow-servants of our heavenly Master, whom, therefore, they are bound to treat with mutual love and kindness. Let every one, I say, thus consider what in his own place and order he owes to his neighbours, and pay what he owes. Moreover, we must always have a reference to the Lawgiver, and so remember that the law requiring us to promote and defend the interest and convenience of our fellow-men, applies equally to our minds and our hands."

- John Calvin

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"The worship of images is intimately connected with that of the saints. They were rejected by the primitive Christians; but St Irenæus, who lived in the second century, relates that there was a sect of heretics, the Carpocratians, who worshipped, in the manner of Pagans, different images representing Jesus Christ, St Paul, and others. The Gnostics had also images; but the church rejected their use in a positive manner, and a Christian writer of the third century, Minutius Felix, says that “the Pagans reproached the Christians for having neither temples nor simulachres;” and I could quote many other evidences that the primitive Christians entertained a great horror against every kind of images, considering them as the work of demons. It appears, however, that the use of pictures was creeping into the church already in the third century, because the council of Elvira in Spain, held in 305, especially forbids to have any picture in the Christian churches. These pictures were generally representations of some events, either of the New 5 In his Treatise given below. 11 or of the Old Testament, and their object was to instruct the common and illiterate people in sacred history, whilst others were emblems, representing some ideas connected with the doctrines [008] of Christianity. It was certainly a powerful means of producing an impression upon the senses and the imagination of the vulgar, who believe without reasoning, and admit without reflection; it was also the most easy way of converting rude and ignorant nations, because, looking constantly on the representations of some fact, people usually end by believing it. This iconographic teaching was, therefore, recommended by the rulers of the church, as being useful to the ignorant, who had only the understanding of eyes, and could not read writings.6 Such a practice was, however, fraught with the greatest danger, as experience has but too much proved. It was replacing intellect by sight.7 Instead of elevating man towards God, it was bringing down the Deity to the level of his finite intellect, and it could not but powerfully contribute to the rapid spread of a pagan anthropomorphism in the church."

- John Calvin

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"The aversion of the first Christians to the images, inspired by the Pagan simulachres, made room, during the centuries which followed the period of the persecutions, to a feeling of an entirely different kind, and the images gradually gained their favour. Reappearing at the end of the fourth and during the course of the fifth centuries, simply as emblems, they soon became images, in the true acceptation of this word; and the respect which was entertained by the Christians for the persons and ideas represented by those images, was afterwards converted into a real worship. Representations of the sufferings which the Christians had endured for the sake of their religion, were at first exhibited to the people in order to stimulate by such a sight the faith of the masses, always lukewarm and indifferent. With regard to the images of divine persons of entirely immaterial beings, it must be remarked, that they did not originate from the most spiritualised and pure doctrines of the Christian society, but were rejected by the severe orthodoxy of the primitive church. These simulachres appear to have been spread at first by the Gnostics,—i.e., by those Christian sects which adopted the most of the beliefs of Persia and India. Thus it was a Christianity which was not purified by its contact with the school of Plato,—a Christianity which entirely rejected the Mosaic tradition, in order to attach itself to the most strange and attractive myths of Persia and India,—that gave birth to the images."

- John Calvin

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"“The practice of employing images as ornaments and memorials to decorate the temple of the Lord is in a most especial manner approved by the Word of God himself. Moses was commanded to place two cherubim upon the ark, and to set up a brazen figure of the fiery serpent, that those of the murmuring Israelites who had been bitten might recover from the poison of their wounds by looking on the image. In the description of Solomon's temple, we read of that prince, not only that he made in the oracle two cherubim of olive tree, of ten 83 Vide supra, p. 17. 101 cubits in height, but that ‘all the walls of the temple round about he carved with divers figures and carvings.’ “In the first book of Paralipomenon (Chronicles) we observe that when David imposed his injunction upon Solomon to realise his intention of building a house to the Lord, he delivered to him a description of the porch and temple, and concluded by thus assuring him: ‘All these things came to me written by the hand of the Lord, that I may understand the works of the pattern.’ “The isolated fact that images were not only directed by the Almighty God to be placed in the Mosaic tabernacle, and in the more sumptuous temple of Jerusalem, but that [132] he himself exhibited the pattern of them, will be alone sufficient to authorise the practice of the Catholic Church in regard to a similar observance.”—(Hierurgia, p. 371.) All this may be briefly answered. There was no representation of the Jewish patriarchs or saints either in the tabernacle or in the temple of Solomon, as is the case with the Christian saints in the Roman Catholic and Græco-Russian Churches; and the brazen serpent, to which the author alludes, was broken into pieces by order of King Hezekiah as soon as the Israelites began to worship it."

- John Calvin

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"From a reading of The Institutes of Christian Religion, The Tracts, and much of the Correspondence of Calvin, I am impressed with the fact that Calvin allowed very little place in his life for purely aesthetic enjoyment of art. His whole attention was directed to theological matters and the precise, and to him the inevitable, relation which these theological matters bore to human conduct. His was a keen, penetrating mind, sharpened by legalistic training, which had never gone through the torment of doubt that so affected Luther. Calvin based every thought on the scriptures. He did not speak for himself, but was only the interpreter of the Scriptures. On the one hand this made him very humble, but on the other since he was admittedly the most astute theologian of his day, he could not conceive of anyone doubting the truth and the authority of his interpretations. Little did he realize that he was attempting to set up a new form of religious tyranny, and in many respect succeeding. Calvin was completely ignorant of any approach to truth except by the way of logic and cold reason. There was nothing of the mystic about him as there was in Luther. He was lacking in imagination and in a sensitiveness to visual and aural beauty. In vain may one search for a single reference in his works to the beauty of Lake Geneva or of the Alps. Any man who would set out looking for a wife with a blue print of the desired qualities of his future mate in his hand, asking his friends for candidates, lacks qualities which we expect to find in a normal human being. But Calvin was not a normal human being. He was an organizing genius, wholly concerned with the matters of theology and conduct. His condemnation of Servetus has usually been cited as an example of his hardness of heart. Calvin's love for the classic poets, and the clear concise style of his own writing stand in welcome contrast to his lack of artistic sensitivity toward the other art media. I would not consider his encouragement of the congregational singing of the Psalms as showing a love of music as such, but only a realization of the power of music to help in bringing the word to the hearts of the people."

- John Calvin

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"It's been quite a journey this decade, and we held together through some stormy seas. And at the end, together, we are reaching our destination. The fact is, from Grenada to the Washington and Moscow summits, from the recession of '81 to '82, to the expansion that began in late '82 and continues to this day, we've made a difference. The way I see it, there were two great triumphs, two things that I'm proudest of. One is the economic recovery, in which the people of America created—and filled—19 million new jobs. The other is the recovery of our morale. America is respected again in the world and looked to for leadership. Something that happened to me a few years ago reflects some of this. It was back in 1981, and I was attending my first big economic summit, which was held that year in Canada. The meeting place rotates among the member countries. The opening meeting was a formal dinner of the heads of government of the seven industrialized nations. Now, I sat there like the new kid in school and listened, and it was all Francois this and Helmut that. They dropped titles and spoke to one another on a first-name basis. Well, at one point I sort of leaned in and said, "My name's Ron." Well, in that same year, we began the actions we felt would ignite an economic comeback—cut taxes and regulation, started to cut spending. And soon the recovery began. Two years later, another economic summit with pretty much the same cast. At the big opening meeting we all got together, and all of a sudden, just for a moment, I saw that everyone was just sitting there looking at me. And then one of them broke the silence. "Tell us about the American miracle," he said."

- François Mitterrand

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"Of course, peace might have come to Europe without the Union. Maybe. We will never know. But it would never have been of the same quality. A lasting peace, not a frosty cease-fire. To me, what makes it so special, is reconciliation. In politics as in life, reconciliation is the most difficult thing. It goes beyond forgiving and forgetting, or simply turning the page. To think of what France and Germany had gone through …, and then take this step … Signing a Treaty of Friendship … Each time I hear these words – Freundschaft, Amitié –, I am moved. They are private words, not for treaties between nations. But the will to not let history repeat itself, to do something radically new, was so strong that new words had to be found. For people Europe was a promise, Europe equalled hope. When Konrad Adenauer came to Paris to conclude the Coal and Steel Treaty, in 1951, one evening he found a gift waiting at his hotel. It was a war medal, une Croix de Guerre, that had belonged to a French soldier. His daughter, a young student, had left it with a little note for the Chancellor, as a gesture of reconciliation and hope. I can see many other stirring images before me. Leaders of six States assembled to open a new future, in Rome, città eterna … Willy Brandt kneeling down in Warsaw. The dockers of Gdansk, at the gates of their shipyard. Mitterrand and Kohl hand in hand. Two million people linking Tallinn to Riga to Vilnius in a human chain, in 1989. These moments healed Europe."

- François Mitterrand

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"— 'India is the world’s cradle : thence it is that the common mother in sending forth her children, even to the utmost west has, in unfading testimony of our origin bequeathed us the legacy of her language, her laws, her 'Morale,' her literature and her religion-Traversing Persia, Arabia, Egypt and even forcing their way to the cold and cloudy north far from the sunny soil of their birth, in vain they may forget their point of departure, their skin may remain brown or become white from contact with snows of the west, of the civilizations founded by them splendid kingdoms may fall and leave no trace behind but some few ruins of sculptured columns, new people may arise from the ashes of the first; new cities may flourish on the site of the old but time and ruin united fail to obliterate the ever legible stamp of origin. The legislator Manu; whose authenticity is incontestible, dates back more than three thousand years before Christian era; the Brahmans assign him a still more ancient epoch. What instruction for us, and what testimony almost material, in favour of the oriental chronology, which, less ridiculous than ours (based on Biblical traditions) adopts, for the formation of this world, an a speech more in harmony with science. We shall presently see Egypt, Judea, Greece, Rome, all antiquity, in fact, copies Brahminical society in its castes, its theories, its religious opinion, and adopts its Brahmins, its priests, its levites as they had already adopted the language, legislation and philosophy of the ancient Vedic Society whence their ancestors had departed through the world to dessiminate the grand ideas of primitive revelation."

- Louis Jacolliot

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""To study India," he says, "is to trace humanity to its sources." "In the same way as modern society jostles antiquity at each step," he adds, "as our poets have copied Homer and Virgil, Sophocles and Euripides, Plautus and Terence; as our philosophers have drawn inspiration from Socrates, Pythagoras, Plato, and Aristotle; as our historians take Titus Livius, Sallust, or Tacitus, as models; our orators, Demosthenes or Cicero; our physicians study Hippocrates, and our codes transcribe Justinian--so had antiquity's self also an antiquity to study, to imitate, and to copy. What more simple and more logical? Do not peoples precede and succeed each other? Does the knowledge, painfully acquired by one nation, confine itself to its own territory, and die with the generation that produced it? Can there be any absurdity in the suggestion that the India of 6,000 years ago, brilliant, civilized, overflowing with population, impressed upon Egypt, Persia, Judea, Greece, and Rome, a stamp as ineffaceable, impressions as profound, as these last have impressed upon us? "It is time to disabuse ourselves of those prejudices which represent the ancients as having almost spontaneously-elaborated ideas, philosophic, religious, and moral, the most lofty--those prejudices that in their naive admiration explain all in the domain of science, arts, and letters, by the intuition of some few great men, and in the realm of religion by revelation." *"

- Louis Jacolliot

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