Lawyers From France

"Just as a maistre Fifi mocks those who hold their noses [in his presence]. because he has handled filth for so long that he can no longer smell his own foulness; so likewise do idolaters make light of those who are offended by a stench they cannot themselves recognize. Hardened by habit, they sit in their own excrement, and yet believe they are surrounded by roses."

"We may also fitly remember that Satan has his miracles, which, though they are deceitful tricks rather than true powers, are such a sort as to mislead the simple-minded and untutored [2 Thes, 2:9-10] ... Idolatry has been nourished by wonderful miracles, yet these are not sufficient to sanction the superstition either of magicians or of idolators."

"The papists abuse this text, not only to the end they may commend feigned miracles, which they say are done at the graves of martyrs, but also that they may try and sell us their relics. Why, say thy, shall not the grave, or garment, or the touching of the bones of Peter have as much power to heal, as his shadow had?"

"No religion is genuine unless it be joined with truth."

"We condemn those who affirm that a man once justified cannot sin. ... As to the special privilege of the Virgin Mary, when they produce the celestial diploma we shall believe what they say."

"It is no small honour that God for our sake has so magnificently adorned the world, in order that we may not only be spectators of this beauteous theatre, but also enjoy the multiplied abundance and variety of good things which are presented to us in it."

"Que donc les nonnains demeurent en leurs convents et en leurs cloistres, et en leurs bourdeaux de Satan: ie di mesmes encores qu’elles ne fussent point putains comme elles sont, comme il y a encores pis de ces abominations de Sodome, faisans des choses si enormes et si abominables que c’est une horreur: encores, di-ie, que toutes ces vilenies-là n'y fussent point, si est-ce que toute la chasteté qu'elles pretendent, n'est rien envers Dieu, au prix de ce qu'il a ordonné, c'est asçavoir que combien que ce soyent choses contemptibles, et qui semblent estre de nulle valeur, qu'une femme ait peine d'adresser son mesnage, de nettoyer les ordures de ses enfans, de tuer les poux et autres choses semblables, que tout cela sera mesprisé, qu’on ne le daignera pas mesmes regarder, ce sont toutesfois sacrifices que Dieu reçoit et qu'il accepte, comme si c'estoyent choses precieuses et honorables."

"We must know and be out of all doubt, that the Pope hath but a devilish Synagogue, and that all his Clergy is but filth & stench, all these varlets that have cast aside the Church of God, are but vermin. Although the Pope, who is Antichrist, be set in God’s sanctuary, (as we have seen before [2 Thes. 2.4]) yet notwithstanding, he is not worthy to be taken and accounted for a minister of the Church, nor all his mates."

"It cannot be denied that God in choosing and destining Mary to be the Mother of his Son, granted her the highest honor."

"Helvidius has shown himself too ignorant, in saying that Mary had several sons, because mention is made in some passages of the brothers of Christ."

"We take nothing from the womb but pure filth [meras sordes]. The seething spring of sin is so deep and abundant that vices are always bubbling up form it to bespatter and stain what is otherwise pure.... We should remember that we are not guilty of one offense only but are buried in innumerable impurities.... all human works, if judged according to their own worth, are nothing but filth and defilement.... they are always spattered and befouled with many stains.... it is certain that there is no one who is not covered with infinite filth."

"Et ne soyons pas semblables à ces fantastiques, qui ont un esprit d'amertume et de contradiction, pour trouver à redire par tout, et pour pervertir l'ordre de nature. Nous en verrons d'aucuns si frénétiques, non pas seulement en la religion, mais pour monstrer par tout qu'ils ont une nature monstrueuse, qu'ils diront que le soleil ne se bouge, et que c'est la terre qui se remue et qu'elle tourne. Quand nous voyons de tels esprits, il faut bien dire que le diable les ait possédez, et que Dieu nous les propose comme des miroirs, pour nous faire demeurer en sa crainte."

"For what accords better and more aptly with faith than to acknowledge ourselves divested of all virtue that we may be clothed by God, devoid of all goodness that we may be filled by him, the slaves of sin that he may give us freedom, blind that he may enlighten, lame that he may cure, and feeble that he may sustain us; to strip ourselves of all ground of glorying that he alone may shine forth glorious, and we be glorified in him?"

"The proper course, therefore, is, in the first instance, to ascertain and examine the doctrine which is said by the Evangelist to precede; then after it has been proved, but not till then, it may receive confirmation from miracles. But the mark of sound doctrine given by our Saviour himself is its tendency to promote the glory not of men, but of God (John 7:18; 8:50). Our Saviour having declared this to be test of doctrine, we are in error if we regard as miraculous, works which are used for any other purpose than to magnify the name of God."

"All the Fathers with one heart execrated, and with one mouth protested against, contaminating the word of God with the subtleties of sophists, and involving it in the brawls of dialecticians. Do they keep within these limits when the sole occupation of their lives is to entwine and entangle the simplicity of Scripture with endless disputes, and worse than sophistical jargon? So much so, that were the Fathers to rise from their graves, and listen to the brawling art which bears the name of speculative theology, there is nothing they would suppose it less to be than a discussion of a religious nature."

"To make everything yield to custom would be to do the greatest injustice. Were the judgments of mankind correct, custom would be regulated by the good. But it is often far otherwise in point of fact; for, whatever the many are seen to do, forthwith obtains the force of custom. But human affairs have scarcely ever been so happily constituted as that the better course pleased the greater number. Hence the private vices of the multitude have generally resulted in public error."

"We must not only resist, but boldly attack prevailing evils."

"Be it so that public error must have a place in human society, still, in the kingdom of God, we must look and listen only to his eternal truth, against which no series of years, no custom, no conspiracy, can plead prescription. Thus Isaiah formerly taught the people of God, “Say ye not, A confederacy, to all to whom this people shall say, A confederacy;” i.e. do not unite with the people in an impious consent."

"Depraved custom is just a kind of general pestilence in which men perish not the less that they fall in a crowd."

"The hinges on which the controversy turns are these: first, in their contending that the form of the Church is always visible and apparent; and, secondly, in their placing this form in the see of the Church of Rome and its hierarchy. We, on the contrary, maintain, both that the Church may exist without any apparent form, and, moreover, that the form is not ascertained by that external splendour which they foolishly admire, but by a very different mark, namely, by the pure preaching of the word of God, and the due administration of the sacraments."

"Without knowledge of self there is no knowledge of God. Our wisdom, in so far as it ought to be deemed true and solid Wisdom, consists almost entirely of two parts: the knowledge of God and of ourselves. But as these are connected together by many ties, it is not easy to determine which of the two precedes and gives birth to the other."

"Our feeling of ignorance, vanity, want, weakness, in short, depravity and corruption, reminds us ... that in the Lord, and none but He, dwell the true light of wisdom, solid virtue, exuberant goodness. We are accordingly urged by our own evil things to consider the good things of God; and, indeed, we cannot aspire to Him in earnest until we have begun to be displeased with ourselves. For what man is not disposed to rest in himself? Who, in fact, does not thus rest, so long as he is unknown to himself; that is, so long as he is contented with his own endowments, and unconscious or unmindful of his misery? Every person, therefore, on coming to the knowledge of himself, is not only urged to seek God, but is also led as by the hand to find him."

"Since we are all naturally prone to hypocrisy, any empty semblance of righteousness is quite enough to satisfy us instead of righteousness itself."

"If all are born and live for the express purpose of learning to know God, and if the knowledge of God, in so far as it fails to produce this effect, is fleeting and vain, it is clear that all those who do not direct the whole thoughts and actions of their lives to this end fail to fulfil the law of their being."

"Fermat knew that under reflection light takes the path requiring least time and, convinced that nature does indeed act simply and economically, affirmed in letters of 1657 and 1662 his Principle of Least Time, which states that light always takes the path requiring least time. He had doubted the correctness of the law of refraction of light but when he found in 1661 that he could deduce it from his Principle, he not only resolved his doubts about the law but felt all the more certain that his Principle was correct. ...Huygens, who had at first objected to Fermat's Principle, showed that it does hold for the propagation of light in media with variable indices of refraction. Even Newton's first law of motion, which states that the straight line or shortest distance is the natural motion of a body, showed nature's desire to economize. These examples suggested that there might be a more general principle. The search for such a principle was undertaken by Maupertuis."

"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."

"This great geometrician expresses by the character E the increment of the abscissa; and considering only the first power of this increment, he determines exactly as we do by differential calculus the subtangents of the curves, their points of inflection, the maxima and minima of their ordinates, and in general those of rational functions. We see likewise by his beautiful solution of the problem of the refraction of light inserted in the Collection of the Letters of Descartes that he knows how to extend his methods to irrational functions in freeing them from irrationalities by the elevation of the roots to powers. Fermat should be regarded, then, as the true discoverer of Differential Calculus. Newton has since rendered this calculus more analytical in his Method of Fluxions, and simplified and generalized the processes by his beautiful theorem of the binomial. Finally, about the same time Leibnitz has enriched differential calculus by a notation which, by indicating the passage from the finite to the infinitely small, adds to the advantage of expressing the general results of calculus, that of giving the first approximate values of the differences and of the sums of the quantities; this notation is adapted of itself to the calculus of partial differentials."

"I had a hint of this method [of fluxions] from Fermat's way of drawing tangents, and by applying it to abstract equations, directly and invertedly, I made it general."

"Fermat is... honored with the invention of the differential calculus on account of his method of maxima and minima and of tangents, which, of the prior processes, is in reality the nearest to the algorithm of Leibniz; one could with equal justice, attribute to him the invention of the integral calculus; his treatise De æquationum localium transmutatione, etc., gives indeed the method of integration by parts as well as rules of integration, except the general powers of variables, their sines and powers thereof. However, it must be remarked that one does not find in his writings a single word on the main point, the relation between the two branches of the infinitesimal calculus."

"Cuius rei demonstrationem mirabilem sane detexi hanc marginis exiguitas non caperet."

"Et cette proposition est généralement vraie en toutes progressions et en tous nombres premiers; de quoi je vous envoierois la démonstration, si je n'appréhendois d'être trop long."

"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."

"The result of my work has been the most extraordinary, the most unforeseen, and the happiest, that ever was; for, after having performed all the equations, multiplications, antitheses, and other operations of my method, and having finally finished the problem, I have found that my principle gives exactly and precisely the same proportion for the s which Monsieur Descartes has established."

"Fermat's Last Theorem is to the effect that no integral values of x, y, z can be found to satisfy the equation xn+yn=zn if n is an integer greater than 2. ...It is possible that Fermat made some... erroneous supposition, though it is perhaps more probable that he discovered a rigorous demonstration. At any rate he asserts definitely that he had a valid proof—demonstratio mirabilis sane—and the fact that no theorem on the subject which he stated he had proved has been subsequently shown to be false must weigh strongly in his favour; the more so because in making the one incorrect statement in his writings (namely, that about binary powers) he added that he could not obtain a satisfactory demonstration of it. … it took more than a century before some of the simpler results which Fermat had enunciated were proved, and thus it is not surprising that a proof of the theorem which he succeeded in establishing only towards the close of his life should involve great difficulties. ...I venture however to add my private suspicion that continued fractions played a not unimportant part in his researches, and as strengthening this conjecture I may note that some of his more recondite results—such as the theorem that a prime of the form 4n+1 is expressible as the sum of two squares— may be established with comparative ease by properties of such fractions."

"Descartes' method of finding tangents and normals... was not a happy inspiration. It was quickly superseded by that of Fermat as amplified by Newton. Fermat's method amounts to obtaining a tangent as the limiting position of a secant, precisely as is done in the calculus today. ...Fermat's method of tangents is the basis of the claim that he anticipated Newton in the invention of the differential calculus."

"Perhaps nowhere does one find a better example of the value of historical knowledge for mathematicians than in the case of Fermat, for it is safe to say that, had he not been intimately acquainted with the geometry of Apollonius and Viéte, he would not have invented analytic geometry."

"Fermat had recourse to the principle of the economy of nature. Heron and Olympiodorus had pointed out in antiquity that, in reflection, light followed the shortest possible path, thus accounting for the equality of angles. During the medieval period Alhazen and Grosseteste had suggested that in refraction some such principle was also operating, but they could not discover the law. Fermat, however, not only knew (through Descartes) the law of refraction, but he also invented a procedure—equivalent to the differential calculus—for maximizing and minimizing a function of a single variable. ...Fermat applied his method ...and discovered, to his delight, that the result led to precisely the law which Descartes had enunciated. But although the law is the same, it will be noted that the hypothesis contradicts that of Descartes. Fermat assumed that the speed of light in water to be less than that in air; Descartes' explanation implied the opposite."

"Since Fermat introduced the conception of infinitely small differences between consecutive values of a function and arrived at the principle for finding the maxima and minima, it was maintained by Lagrange, Laplace, and Fourier, that Fermat may be regarded as the first inventor of the differential calculus. This point is not well taken, as will be seen from the words of Poisson, himself a Frenchman, who rightly says that the differential calculus "consists in a system of rules proper for finding the differentials of all functions, rather than in the use which may be made of these infinitely small variations in the solution of one or two isolated problems.""

"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."

"Fermat applied his method of tangents to many difficult problems. The method has the form of the now-standard method of differential calculus, though it begs entirely the difficult theory of limits."

"I leave to the oppressors of humanity a terrible testament, which I proclaim with the independence befitting one whose career is so nearly ended; it is the awful truth: “Thou shalt die!”"

"I am made to combat crime, not to govern it. The time is not here where good men can serve their patrie with impunity; the defenders of liberty will only be outcasts, as long as the horde of rogues is in control."

"My life? Oh, my life I abandon without a regret! I have seen the Past; and I foresee the Future. What friend of his country would wish to survive the moment when he could no longer serve it — when he could no longer defend innocence against oppression?"

"With this speech, I have signed my own death sentence. I saw today that the league of miscreants is too strong, that I cannot hope to escape. I die without regrets, I leave you my legacy, it will be dear to you and you will defend it."

"Only this is certain, that he remains the most hateful character in the forefront of history since Machiavelli reduced to a code the wickedness of public men."

"He is and will be a lawyer only for the poor."

"We shall distinguish in Robespierre two men, apostle of liberty, and Robespierre the most infamous of tyrants."

"I confess today in good faith that I am angry with myself for having formerly seen in a bad light, within the revolutionary government, Robespierre and Saint-Just. I believe that these two men were better on their own than all the revolutionaries together."

"[Robespierre was] a man without personal ambition, a republican to the fingertips...would to Heaven there were in the Chamber of Deputies today someone to point to those who conspire against our freedom! We were then in the middle of a war, and we did not understand the man. He was a nervous, choleric individual who twitched when he spoke. He was a great man and posterity will not refuse him the title."

"I have the double regret — I should say the double remorse — of having overthrown Robespierre on the 9th of Thermidor and raised Bonaparte on the 13th of Vendemiaire."