Catholics From France

"The great invention... Descartes gave to the world, the analytical diagram, ...gives at a glance a graphical picture of the law governing a phenomenon, or of the correlation which exists between dependent events, or of the changes which a situation undergoes in the course of time. ...the invention of Descartes not only created the important discipline of analytic geometry, but it gave Newton, Leibnitz, Euler, and the Bernoullis that weapon for the lack of which Archimedes and later Fermat had to leave inarticulate their profound and far-reaching thoughts."

"[B]elievers in the plenum... the Cartesian idea of a space entirely filled with matter—contributed... to what was to become the Newtonian synthesis. Descartes himself achieved the modern formulation of the law of ... working it out by a natural deduction from his theory of the conservation of momentum, his theory that the amount of motion in the universe always remains the same. It was he rather than Galileo who fully grasped this principle of inertia and formulated it in all its clarity. ...The modern doctrine of had been put forward by Descartes and was quickly gaining acceptance, though people like Borelli... still seemed to think that they had to provide a force actually pushing the planets along..."

"Descartes was liable to be misled by too easy an acceptance of data that had been handed down by scholastic writers. ...two grand Aristotelian principles helped to condition the form of the universe as he reconstructed it—first, the view that a vacuum is impossible, and secondly, the view that objects could only influence one another if they actually touched—there could be no such thing as attraction, no such thing as . ...Descartes insisted that every fraction of space should be fully occupied all the time by continuous matter... infinitely divisible. The particles were... packed so tightly that one of them could not move without communicating the commotion to the rest. The matter formed whirlpools in the skies, and it was because the planets were caught each in its own whirlpool that they were carried around... all similarly caught in a larger whirlpool, which had the sun as its centre... Gravity itself was the result of these whirlpools of invisible matter which had the effect of sucking things down towards their centre. ...In the time of Newton the system of Descartes and the theory of vortices or whirlpools proved to be vulnerable to both mathematical and experimental attack."

"Descartes maintained his confidence in the instantaneity of light. ...Yet in his derivation of the law of refraction, Descartes reasoned that light traveled faster in a dense medium than in one less dense. He seems to have had no qualms about comparing infinite magnitudes!"

"CARTESIAN, adj. Relating to Descartes, a famous philosopher, author of the celebrated dictum, Cogito ergo sum -- whereby he was pleased to suppose he demonstrated the reality of human existence. The dictum might be improved, however, thus: Cogito cogito ergo cogito sum -- "I think that I think, therefore I think that I am;" as close an approach to certainty as any philosopher has yet made."

"Descartes devised the notation x, x2, x3, x4,... for powers, and made the final break with the Greek tradition of admitting only the first, second, and third powers ('lengths,' 'areas,' and 'volumes') in geometry. After Descartes, geometers freely used powers higher than the third without a qualm, recognizing that representability as figures in Euclidean space for all of the terms in an equation is irrelevant to the geometrical interpretation of the analysis. The principle of undetermined coefficients was also stated by Descartes. A second outstanding addition to algebra was the famous rule of signs... the first universally applicable criterion for the nature of the roots of an algebraic equation. ...it admirably represents Descartes' flair for generality which made him the mathematician that he was."

"The implications of Descartes' analytic reformulation of geometry are obvious. Not only did the new method make possible a systematic investigation of known curves, but, what is of infinitely greater significance, it potentially created a whole universe of geometric forms beyond conception by the synthetic method. Descartes also saw that his method applies equally as well to surfaces... but he did not develop this. With the extension to surfaces, there was no reason why geometry should stop with equations in three variables; and the generalization to systems of equations in any finite number of variables was readily made in the nineteenth century. Finally, in the twentieth century, the farthest extension possible in this direction led to spaces of a non-denumerable infinity of dimensions. ...The path from Descartes to the creators of higher space is straight and clear; the remarkable thing is that it was not traveled earlier than it was."

"René Descartes is more widely known as a philosopher than as a mathematician, although his philosophy has been controverted while his mathematics has not. ...In accordance with the ideals of his age, when experimental science was first seriously challenging arrogant speculation, Descartes set a greater store by his philosophy than his mathematics. But he fully appreciated the power of his new method in geometry."

"Analytical geometry was invented by Descartes and the first exposition of it was given in 1637: that exposition was both difficult and obscure, and to most of his contemporaries, to whom the method was new, it must have been incomprehensible. Wallis made the method intelligible to all mathematicians."

"I should like you to consider that these functions (including passion, memory, and imagination) follow from the mere arrangement of the machine’s organs every bit as naturally as the movements of a clock or other automaton follow from the arrangement of its counter-weights and wheels."

"I suppose the body to be nothing but a statue or machine made of earth, which God forms with the explicit intention of making it as much as possible like us."

"In order to seek truth, it is necessary once in the course of our life, to doubt, as far as possible, of all things."

"I could give here several other ways of tracing and conceiving a series of curved lines, each curve more complex than any preceding one, but I think the best way to group together all such curves and them classify them in order, is by recognizing the fact that all points of those curves which we may call "geometric," that is, those which admit of precise and exact measurement, must bear a definite relation to all points of a straight line, and that this relation must be expressed by a single equation. If this equation contains no term of higher degree than the rectangle of two unknown quantities, or the square of one, the curve belongs to the first and simplest class, which contains only the circle, the parabola, the hyperbola, and the ellipse; but when the equation contains one or more terms of the third or fourth degree in one or both of the two unknown quantities (for it requires two unknown quantities to express the relation between two points) the curve belongs to the second class; and if the equation contains a term of the fifth or sixth degree in either or both of the unknown quantities the curve belongs to the third class, and so on indefinitely."

"Thus, all unknown quantities can be expressed in terms of a single quantity, whenever the problem can be constructed by means of circles and straight lines, or by conic sections, or even by some other curve of degree not greater than the third or fourth. But I shall not stop to explain this in more detail, because I should deprive you of the pleasure of mastering it yourself, as well as of the advantage of training your mind by working over it, which is in my opinion the principal benefit to be derived from this science. Because, I find nothing here so difficult that it cannot be worked out by anyone at all familiar with ordinary geometry and with algebra, who will consider carefully all that is set forth in this treatise."

"Je pense, donc je suis."

"Le bon sens est la chose du monde la mieux partagée : car chacun pense en être si bien pourvu, que ceux même qui sont les plus difficiles à contenter en toute autre chose, n'ont point coutume d'en désirer plus qu'ils en ont."

"Mais apud me omnia fiunt Mathematicè in Natura"

"No more useful inquiry can be proposed than that which seeks to determine the nature and the scope of human knowledge. ... This investigation should be undertaken once at least in his life by anyone who has the slightest regard for truth, since in pursuing it the true instruments of knowledge and the whole method of inquiry come to light. But nothing seems to me more futile than the conduct of those who boldly dispute about the secrets of nature ... without yet having ever asked even whether human reason is adequate to the solution of these problems."

"The entire method consists in the order and arrangement of the things to which the mind's eye must turn so that we can discover some truth."

"So blind is the curiosity by which mortals are possessed, that they often conduct their minds along unexplored routes, having no reason to hope for success, but merely being willing to risk the experiment of finding whether the truth they seek lies there."

"Me tenant comme je suis, un pied dans un pays et l'autre en un autre, je trouve ma condition très heureuse, en ce qu'elle est libre."

"Mr. Clerselier has written me that you are expecting from him my Meditations... in order to present them to the queen of the land. ...If I had only been as wise as they say the savages persuaded themselves that the monkeys were, I never would have become known as a maker of books: Since it is said that they imagined that the monkeys could indeed speak, if they wanted to, but that they chose not to so lest they be forced to work. And since I had not the same prudence to abstain from writing, I now have neither as much liesure nor as much peace as I would have had if I had kept quiet. But since the mistake has already been made, and since I am now known by an infinity of people at the academy, who look askance at my writings and scour them for means of harming me, I do have great hope of being known to persons of great merit, whose power and virtue could protect me."

"M. Desargues puts me under obligations on account of the pains that it has pleased him to have in me, in that he shows that he is sorry that I do not wish to study more in geometry, but I have resolved to quit only abstract geometry, that is to say, the consideration of questions which serve only to exercise the mind, and this, in order to study another kind of geometry, which has for its object the explanation of the phenomena of nature... You know that all my physics is nothing else than geometry."

"What I have given in the second book on the nature and properties of curved lines, and the method of examining them, is, it seems to me, as far beyond the treatment in the ordinary geometry, as the rhetoric of Cicero is beyond the a, b, c of children."

"No doubt you know that Galileo had been convicted not long ago by the Inquisition, and that his opinion on the movement of the Earth had been condemned as heresy. Now I will tell you that all things I explain in my treatise, among which is also that same opinion about the movement of the Earth, all depend on one another, and are based upon certain evident truths. Nevertheless, I will not for the world stand up against the authority of the Church. ...I have the desire to live in peace and to continue on the road on which I have started."

"I do not fear men-at-arms; my way has been made plain before me. If there be men-at-arms my Lord God will make a way for me to go to my Lord Dauphin. For that am I come."

"Alas! that my body, clean and whole, never been corrupted, today must be consumed and burnt to ashes!"

"About Jesus Christ and the Church, I simply know they're just one thing, and we shouldn't complicate the matter."

"Whatever thing men call great, look for it in Joan of Arc, and there you will find it."

"She is easily and by far the most extraordinary person the human race has ever produced."

"Must then a Christ perish in torment in every age to save those that have no imagination?"

"If Joan had been malicious, selfish, cowardly, or stupid, she would have been one of the most odious persons known to history instead of one of the most attractive."

"...you shall never hold the Kingdom of France from God, the King of Heaven, the son of St. Mary; but King Charles, the true heir, will hold it; for God, the King of Heaven wishes it so...."

"I saw myself in front of an angry mob, facing a firing squad, weeping incomprehensible sorrows and forgiving them! — Like Joan of Arc!"

"Jehanne... If you come from God, I do not fear you … if you come from the Devil, I fear you even less."

"I have always responded to challenges, followed apocalyptical personalities, apostles, Rasputins, Joan of Arcs who hear voices that come from Heaven, illuminated guides of humanity, holders of truth, priests."

"The courage of Joan of Arc was made the subject of a popular lecture not long ago by one of our intelligent citizens."

"Official orators have agreed amongst themselves to leave out one essential point: that to undertake the liberation of the fatherland, Joan had to go directly to the Dauphin Charles, acknowledge the right of his royal blood, and have him crowned and acclaimed on the cathedral square of Reims."

"Children say that people are hanged sometimes for speaking the truth."

"And now I know how Joan of Arc felt Now I know how Joan of Arc felt As the flames rose to her And her started to melt"

"They burned her cruelly to death in the marketplace of Rouen, with eight hundred soldiers round the stake, lest any should attempt to save her. They had put a false accusation on a paper cap, and set it on her head : it was written that she was "Heretic, Relapsed, Apostate, Idolatress." This was her reward for the bravest and best life that was ever lived."

"Joan of Arc was perhaps the most wonderful person who ever lived in the world. The story of her life is so strange that we could scarcely believe it to be true, if all that happened to her had not been told by people in a court of law, and written down by her deadly enemies, while she was still alive."

"Who in the moment of victory remains inaccessible to vanity and hate, who in the midst of popular enthusiasm lives in humility and prayer, who in the universal crush of ambition covets neither profit nor honours."

"Yes, it’s true. It’s true that Joan of Arc was my dream as a little girl. I discovered her toward the age of ten or twelve, when I went to France. I don’t remember where I read about her, but I recall that she immediately took on a definite importance for me. I wanted to sacrifice my life for my country. It seems like foolishness and yet ... what happens when we’re children is engraved forever in our lives."

"Joan was a being so uplifted from the ordinary run of mankind that she finds no equal in a thousand years. She embodied the natural goodness and valour of the human race in unexampled perfection. Unconquerable courage, infinite compassion, the virtue of the simple, the wisdom of the just, shone forth in her. She glorifies as she freed the soil from which she sprang."

"The tide turned and the war began to go against the English. This was due in great part to the influence of a young French peasant girl, Joan of Arc. Inspired by the belief that she had been given a mission by God to deliver France from its invaders and to place the Dauphin on the throne of his fathers, she appeared before him, secured his reluctant consent to allow her to lead some troops, inspired them with her own enthusiasm and confidence, and won a great success by driving away the English who were besieging Orleans. The Dauphin himself was then stirred to greater activity and under the persuasion of the Maid of Orleans, as she came to be called, made his way to Rheims, the ancient coronation city of the French kings, and was there crowned king of France. Joan now felt that she had fulfilled her mission and asked to be allowed to return to her home, but the Dauphin insisted that she should remain with the army. Some time after this she was captured by the English. After a trial which was planned to end in but one way she was burned as a witch in the market place of Rouen. Even one of the persecutors of the innocent French patriot girl wavered and turned away, crying, "God have mercy upon us, we have burned a saint." The movement of success which Joan had begun continued, and although the French frequently wasted their opportunities, yet on the whole the reconquest of their native land went steadily on. The English were driven out of one province after another; their expeditions from England were more poorly equipped and more unsuccessful. Finally the long war came to a close in 1453 by the defeat of an English army near Bordeaux, and the loss of all their territory in France except Calais."

"My Joan is that of a boy who loved parish cinemas and those in the suburbs – the only ones he could afford – between the 1940s and 1950s. For this reason, she will forever have the face of Ingrid Bergman, discovered shortly after 1952 in Fleming's Technicolour blockbuster – admired, moreover, in a cut-up third version – and then seen again, in a completely different interpretation and with a very different intensity, in Roberto Rossellini's 1954 film, which, through the text of Paul Claudel, reinterpreted the allegories of medieval sacred representations. (p. 4"

"Joanni, Joanni wears a golden cross And she looks so beautiful in her armour Joanni, Joanni blows a kiss to God And she never wears a ring on her finger..."

"If I were Joan of Arc I would become governor of Puerto Rico and make my island a state — and then become president of the United States of Banana — and head south to conquer all of Latin America and the Caribbean — and swoop back north to take over Canada. I could do all that — if only I could decide between three options: Wishy, Wishy-Washy, and Washy."

"[O]ne of the great ideas of her whom Villon calls "the good lass of Lorraine" had been the reconciliation of the French people. Thanks to the national movement which her intervention set on foot, the widespread horror at her martyrdom brought her wish to fulfillment. The domination of England was more and more detested."