**Carte Blanche**, a sort of white paper signed at the bottom with a person's name, and sometimes also sealed with his seal, giving another person power to superscribe what conditions he pleases. Analogous to this is the French blanc signé, a paper without writing, except a signature at the bottom, given by contending parties to arbitrators or friends, to fill up with the conditions they judge reasonable, in order to end the difference.

**Cartel**, an agreement between two states for the exchange of prisoners of war.

**Cartel** signifies also a letter of defiance or a challenge to decide a controversy either in a tournament or in a single combat. See **Duel**.

**Cartel Ship**, a ship commissioned in time of war to exchange the prisoners of any two hostile powers; also to carry any particular request or proposal from one to another. For this reason the officer who commands her is particularly ordered to carry no cargo, ammunition, or implements of war, except a single gun for the purpose of firing signals.

**Cartes, Rene Des**, or **Descartes, Rene**, was born at La Haye, in Touraine, on the 31st of March 1596, and descended of a noble family, who came originally from Bretagne. In infancy his constitution was extremely delicate, or rather weak, a peculiarity which he shared in common with many other men of genius; and, in fact, it is sometimes in the feeblest body that the intellectual faculties exhibit the greatest vigour. He was educated among the Jesuits, then recently established in the college of La Flèche, and early distinguished himself by an extreme passion for study. It was at this seminary that he became first connected with Mersenne, afterwards a monk of the order of Minims, whose friendship was subsequently approved by its usefulness as well as fidelity to the illustrious object of it. Having completed the usual course of scholastic study, and of what was then as it is still in some parts of the world called philosophy, Descartes at once perceived the worthlessness of the acquisition he had made; but he was keenly alive to the interest and importance of the mathematical sciences, which nature had destined him to renovate. The first thing which he did on leaving college was, as he tells us in his Discourse on Method, to renounce all books, and to labour to efface from his mind every thing uncertain which he had learned, in order henceforward to admit nothing except what appeared to him to be demonstrated by reason and experience; and, in following out this mode of inquiry, he invented that method of sceptical examination which has since become the first principle of all our positive knowledge. At the present day we are unable to appreciate fully the greatness of such an effort, because we are educated in conformity with this very doctrine, which appears to us as natural as it is reasonable. But if we reflect that, at the period when Descartes lived, the Aristotelian philosophy exercised a despotic dominion over all minds, that it reigned supreme in the world as well as in the colleges, that it seemed a necessary support of religion, and that to doubt its truth was then considered as an act of unpardonable temerity, if not a crime, some conception may be formed of that force of mind which enabled a young man of nineteen to discard this intellectual idolatry, and to undertake the reformation of all his opinions. Nor is it less wonderful that at the period in question Descartes seems to have been in possession of his finest geometrical discoveries. This is sufficiently evinced by the history of his life; but the time had not yet arrived for the publication of his new ideas; and he thought that travelling, by extending his knowledge of mankind, would furnish him with favourable opportunities for improving himself in the only true philosophy.

Accordingly, he went abroad, and, conformably with his condition and the manners of his age, engaged in the profession of arms. He served successively as a volunteer in the army of Holland and in that of the Duke of Bavaria; and, in 1620, he was present at the battle of Prague. But although the ardour of youth led him then to take some pleasure in this tumultuous kind of life, he nevertheless knew how to appreciate rightly the bloody game of war; and seeking neither advancement nor fortune, he consented to take part in it only because it was necessary to accompany the men whom he wished to study closely. In the midst of camps he accordingly continued his metaphysical and mathematical speculations, and, as often as an occasion presented itself, put them to the test of experimental application. While he was in garrison at Breda, chance led him one day to a place where he observed on a wall a placard written in Flemish, with a number of persons assembled in a group before it, and containing the enunciation of a geometrical problem, which some unknown person proposed to mathematicians, according to the usage of the time. Not understanding Flemish, Descartes requested one of the spectators to explain the problem. The person to whom he applied was Beckman, principal of the college of Dort, and himself a mathematician, who, finding the problem very difficult, appeared surprised to see a young soldier inquiring about things of this sort, and, in answering him, assumed that air of pedantry and superiority which is common enough among his tribe; but his astonishment was extreme when the young soldier without hesitation promised a solution of the problem, and actually transmitted it to him the following day. For several years Descartes continued to lead this meditative and military life; but at length the reverse of which he was a witness in Hungary disgusted him with the profession of arms, which he therefore renounced, and continued his travels as a private individual. At this period an adventure happened to him which had nearly cost him his life. He had completed his travels through the north of Germany, and was returning to Holland by sea, when the crew of the vessel on board of which he had embarked, observing him to be of a quiet and gentle disposition, took him for a young man without experience, and concluded that it would be an easy matter to kill him, in order to take possession of his property, more especially as he was only attended by a single French domestic. Having come to this resolution, they held council together as to the means of executing their project; and they did not scruple to do so in the presence of their intended victim, under the impression that, being a foreigner, he would not understand them. But in this they were fortunately mistaken. Descartes had understood every word that passed, and when he was fully aware of their design, he started up suddenly, drew his sword, and addressing the ruffians in their own tongue, and in a determined manner, threatened to run them through if they dared to offer him the slightest insult. Intimidated by his boldness, the villains relinquished their purpose, and put him ashore in safety at the place where he wished to land. He then visited in succession Holland, France, Italy, Switzerland, the Tyrol, and ultimately spent some time at Venice and at Rome. Whilst in Italy, he did not visit Galileo, who had just entered upon the career of experimental philosophy; and, what is still more remarkable, he seems never to have entertained a proper sense of the merit of this great man; a circumstance which of itself would be sufficient to prove that Descartes, although admirable as a geometrician, was ignorant of the true method by which alone the physical sciences can be advanced.

Having returned from his travels, and taken a survey of the various occupations of men, Descartes perceived that the only one which suited him was the cultivation of reason; but as his ardent temperament naturally led him into extremes, he conceived a notion that, if he remained in France, he would neither be sufficiently solitary nor sufficiently free for the prosecution of the pursuits in which he was anxious to engage. Accordingly, having sold part of his property, he, in 1629, retired into Holland, which he regarded as a tranquil retreat, peculiarly suitable for peaceful and free meditation; and there applied himself to the study of metaphysics, anatomy, chemistry, and astronomy. He composed a treatise on the System of the World, such as he then conceived it; but on the news of the imprisonment of Galileo, he suppressed this production; and it was probably the dread of similar persecution which caused him, at a later period, to adopt the improbable and absurd notion of the sun and the planets revolving round the earth, as Tycho Brahe had done before him. As yet Descartes had published no mathematical work of any extent; but his genius for the exact sciences, and his immense superiority over the greater part of his contemporaries, were already evinced by the extreme facility with which he resolved, almost in sport, the questions which appeared to them the most difficult. The vivacity of his character involved him in quarrels with some of them; and in these he was sometimes in the right, sometimes in the wrong. He was in the right with Roberval, Cartes, a French mathematician, who, denying his genius, laboured long to represent him as a vile plagiarist of the discoveries of others; but he was in the wrong with regard to Fermat, to whom he did not at first do full justice, and who, though able to maintain a contest on equal terms, was ever desirous to render homage to the genius of Descartes, and to seek his friendship. At length, yielding to the solicitations of his friends, and probably influenced by an honourable desire to shut the mouths of his adversaries, Descartes consented to publish his discoveries. But attaching more value to metaphysical speculations, to which he had then devoted himself, than to the geometrical methods of which he was the inventor, and which had already perhaps lost the charm of novelty, he gave his geometry only as a single chapter of his Treatise on Method, and this chapter was worked up slightly and in haste. Posterity, however, has reversed this judgment, and regarded the geometrical labours of Descartes as affording the best proofs of his genius. Before his time considerable progress had been made in researches purely algebraic, and the resolution of equations of the second, third, and fourth order had already been invented; but the notation employed was still rude, and affected by material relations, which intermixed with algebra, strictly so called, ideas of length, of surface, and of solidity. Algebra, however, is a language the special object as well as the principal advantage of which is to express only the abstract relations of quantities. To extend it, therefore, it is necessary to begin by freeing it from all foreign considerations or elements by which it is limited. Descartes was the first who rendered it this important service; for the metaphysical bent of his mind, which was injurious to him in the sciences of application, proved singularly useful in this particular. According to the ancient limitation of algebra, the successive products of the same quantity were represented in the three first dimensions by a square and a cube in perspective, sometimes by the initial letter of the word "square" or the word "cube" placed above the quantity, and sometimes by the repetition of the letter by means of which the quantity was designated. For this embarrassing mode of notation, which impeded the current of thought, Descartes substituted one clear, simple, general, and, above all, adapted to the purposes of calculation. He placed a cipher above the quantity, and by its different values he indicated the different powers of that quantity. But his greatest discovery consisted in the application of algebra to geometry. He imagined that the nature of each curve might be expressed and defined by a certain relation between two variable lines, of which one represented the absciss and the other the ordinate; and he conceived that, in order to find this relation, it would be sufficient to express in algebraic language one of the characteristic properties of the curve, as, for instance, of the circle, which is a plane curve, all the points of which are equidistant from a given point called the centre. And this discovery had the inestimable advantage, that being once translated into a formula, all that remained to be done was to consider in an abstract manner the resultant equation, in order to deduce from it the other geometrical properties involved in the primary definition.

Descartes, however, did not stop here; but, pursuing his investigations, he made a discovery exactly the inverse of the preceding. Having learned to express and to know the properties of curves by algebraic equations, he no longer

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1 It was during his stay at Breda that Descartes composed his Compendium Musarum, which was not printed till after his death. (Utrecht, 1650, 4to.) A French translation by Father Poisson, of the Oratory, will be found at the end of the Méchanique of Descartes. Paris, 1663, 4to. Cartes, regarded these equations, except as emblems of curves intersected so that the abscisses formed the roots of the equations; and, once in possession of these general methods, he was enabled to enunciate in algebraic language, and to resolve directly, geometrical problems which had baffled all antiquity. This he himself exemplified in the very first question of his geometry; and it is easy to conceive how, possessed of this secret, he was enabled to dispel with the greater part of the questions which puzzled the mathematicians of his age. His geometry, at the time when it appeared, was found exceedingly difficult to read; and he himself tells us that he had not sought to develop the different steps of procedure by which he arrived at his results; but at the present day his methods are the first which are taught to youth, and for this reason they appear to us much more easy. In a word, the treatise on geometry does honour to the genius of Descartes, and forms one of his proudest titles to immortality.

His Discourse on Dioptries also contains many ingenious geometrical applications; but whilst the unequal refrangibility of the different rays of light was unknown, it was impossible that any available progress could be made in this branch of science. Nevertheless it contains another proof of the genius of Descartes in the discovery therein made of the true law of refraction; a discovery which was contested by Huygens after his death, but which, notwithstanding the pretensions of that philosopher, unquestionably belongs to him. The Treatise on Meteors, which is also contained in his Discourse on Method, is much more imperfect than his Dioptries, insomuch as he gives rein to his imagination, and undertakes to explain all meteorological phenomena, including even the formation of lightning. It is, however, distinguished by a discovery; for he has given the true theory of the rainbow, as far as it was possible to do so at a period when the unequal refrangibility of light was altogether unknown. His Principia, or Principles of Philosophy, were first published in 1644, at the age of forty-nine. This work is divided into four parts; the first, devoted to rational philosophy or metaphysics, contains an exposition of the principles of all human knowledge; the second treats of the principles of natural things; and the last two develop his theory of the system of the world, the once celebrated, but, since the time of Newton, for ever exploded theory of vortices. We abstain from making any observations either as to the metaphysical notions or physical theories of Descartes, both of which have been treated of with consummate ability and sufficient amplitude of detail in the Dissertations prefixed to this work. With regard to the former, we shall merely add, that in his celebrated Discourse on the Method of conducting the Reason, and seeking Truth in the Sciences, published in 1637, Descartes had already made known the principal points of his doctrine, and broached the most abstract questions of metaphysics. These, however, he had treated with greater order and fulness in the not less celebrated work which he published in 1641, three years before his Principia, entitled "Meditations concerning the first Philosophy, in which are demonstrated the Existence of God, and the Immortality of the Soul." These Meditations are six in number, forming a book small in itself; but which was considerably enlarged by the objections of several metaphysicians of the time, among whom may be mentioned Arnauld, Gassendi, and Hobbes, and by the answers which Descartes made to these objections. They were originally published in Latin; but, in 1642, the Duke of Luynes translated the Meditations, and Clerselier the Objections and Answers, into French.

The influence which Descartes exercised over his age was very great indeed; his fame spread rapidly, and soon became all but universal. In France, particularly, the novelty of his hypotheses, the grandeur and boldness of his views, and the apparent generality of his methods, swayed more or less the most cultivated minds of the age of Louis XIV. It has been remarked that his partizans were for the most part of the number of those who professed the most independent ideas. Bossuet and Fenelon, Malebranche and the principal members of the congregation of the Oratory, and almost all the writers of the celebrated school of Port-Royal, adopted Cartesianism; and from the same source Pascal derived that spirit of discussion which distinguishes the Provincial Letters. The Jesuits were later in giving in their adherence to the dominant philosophy; and the University admitted it still more reluctantly, and only as it were at the last extremity. But in its transmission the metaphysical doctrine of Descartes experienced the fate which must ever attend all systems of dogmatic philosophy. In adopting it, each modified it according to the bent of his own mind, or the cast of his own character; receiving or rejecting as much of it as suited his convenience, and deducing from it consequences which, in their turn, formed the basis of new systems. Hence the most opposite, not to say contradictory theories, all acknowledged Cartesianism as their common source. From it Malebranche derived his mystical spiritualism, and Berkeley his pure idealism; Spinoza found in it the germ of what has been called his materialism; and the greater part of the schools of philosophy which have succeeded each other in Germany since the time of Descartes, may be considered as originating in the same common source.

The writings of Descartes involved him in controversy, and exposed him to persecution. His disputes with Roberval and Fermat have been already noticed by us when adverting to his geometrical investigations and discoveries. But controversies purely scientific are seldom pursued with exasperation, or calculated to mar the happiness of life; and, in point of fact, if Descartes was misrepresented by Roberval, he was guilty of injustice to Fermat. In the hazy region of metaphysics, however, where it is equally difficult to attain any measure of certainty, and easy to discover pretexts for accusations of error or heresy, the most violent contentions are commonly engendered, and men's passions become excited and envenomed from the very cause which ought to beget charity and forbearance. And so it proved in the case of Descartes. To his metaphysical writings he owed all the disputes which served to disturb the tranquillity of his life; and amongst the clergy he found the bitterest enemies and persecutors. Of the latter, by far the most inveterate was Gisbert Voet, primarius professor of theology in the university of Utrecht; a man whose respectable station and austere manners had secured him a degree of credit much beyond what was due to his ability or learning, and who felt no compunction in accusing of atheism a philosopher who had exhausted all the resources of his genius to discover new demonstrations of the existence of God. But when hatred addresses itself to credulity, it is almost certain to triumph. The fierce theologian of Utrecht attempted in vain to engage Father Mersenne, the intimate and much-loved friend of Descartes, to write publicly against him in defence of the Catholic religion; but though deceived in his expectation of enlisting Mersenne as an auxiliary, he did not relinquish his design; and by continued solicitations and manoeuvres he at length succeeded in "impeaching" a sentence against Descartes, condemning him to pay a very considerable fine, and ordaining his works to be burned. Voet is said to have assisted the executioner in carrying into effect the latter part of the sentence. The theologians of Leyden, imitating the example of those of Utrecht, soon stirred up a new persecution against the philosopher; who, harass- Whilst he was in this mood of mind, Descartes received an invitation from Christina, queen of Sweden, to repair to the court of that country, where he was promised an asylum and protection. Although he had always loved independence, and valued his liberty so highly that, as he said, no prince on earth could induce him to surrender it, yet he accepted this proposal, as indeed he had every reason to do. It was made to him at a moment when he was unhappy; whilst the honour of being sought after by a great queen, and called to her presence and society, was calculated to be useful in enabling him to confound his persecutors. He determined therefore to quit his hermitage at Egmont, in order to repair to Sweden and pass his days in the rigorous climate of that country. On his arrival at court, he was received with the greatest distinction by the queen, and obtained, at his own solicitation, the favour of being exempted from all observance of ceremony, and of only appearing at court when he was specially called. But as the price of this dispensation, the queen stipulated that he would come to converse with her every morning at five o'clock in her library. Descartes, however, who always needed repose, and whose health required great attention, was unable to bear up under the change of life which this matutinal duty imposed on him, especially in so cold a climate, and during the rigour of winter. He was attacked by a disease in the chest, accompanied with delirium, and expired on the 11th February 1650, at the comparatively early age of fifty-four. The queen wished his remains to be interred amongst those of the first families of Sweden; but the ambassador of France interposed, and his corpse was conveyed to Paris for sepulture among his countrymen.

The works of Descartes have been collected under the title of Opera Omnia, Amsterdam, 1690–1701, 9 vols. 4to, or 1713, also 9 vols. The French edition consists of 13 vols. 12mo, containing, 1. Les Principes de la Philosophie, écrits en Latin par Descartes, et traduits en Français par un de ses Amies (Picot), 1724; 2. L'Homme de René Descartes, et la Formation du Fœtus, avec les Rémarsques de Louis de Laforge, 1729; 3. Méditations Métaphysiques, 1724; 4. Les Passions de l'Ame, le Monde, ou Traité de la Lumière, et la Géométrie, &c. 1726; 5. Discours de la Méthode, &c. la Dioptrique et les Météores, la Mécanique et la Musique, 1724; 6. Lettres, 1724–1725; together with Bayle's Recueil de quelques Pièces curieuses concernant la Philosophie de Descartes, 1684. (See Biographie Universelle, art. DESCARTES.)