CARTES (Rene des)
, one of the most eminent philosophers and mathematicians of the 17th century, or indeed of any age whatever. He was descended of an ancient noble family in Touraine in France, being a younger son of a counsellor in the parliament of Rennes, and was born March 31, 1596. His father gave him a liberal education, and the more so as he observed in him the appearance of a promising genius, using to call him the philosopher, on account of his insatiable curiosity in asking the reasons of every thing that he did not understand.
Des Cartes was sent to the Jesuits college at La Fleche in 1604, and put under the tuition of Father Charlet. Here he made a great progress in the learned languages and polite literature; but having passed through his course of philosophy without any great satisfaction to himself, he left the college in 1612, and began to learn military arts, to ride and fence, and other such like exercises. But notwithstanding his inclination to military achievements, the weakness of his constitution not permitting him early to expose himself to the fatigues of war, he was sent to Paris in 1613. Here he formed an acquaintance with several learned persons, who helped to reclaim him from his intention of declining his studies, particularly Father Mersenne, whose conversation revived in him a love for truth, and induced him to retire from the world to pursue his studies without interruption; which he did for two years: but in May 1616, at the repeated solicitations of his relations, he set out for Holland, and entered as a volunteer under the Prince of Orange.
Whilst he lay in garrison at Breda, during the truce between the Spanish and Dutch, an unknown person caused a problem in mathematics, in the Dutch language, to be fixed up in the streets: when Des Cartes, seeing a concourse of people stop to read it, desired one who stood near him to explain it to him in Latin or French. The person promised to satisfy him, upon condition that he would engage to resolve the problem; and Des Cartes agreed to the condition with such an air, that though he little expected such a thing from a young military cadet, he gave him his address, desiring he would bring him the solution. Des Cartes next day visited Beekman, principal of the college of Dort, who was the person that had translated the problem to him. Beekman was surprised at his having resolved it in such a short time; but his wonder was much increased, to find, in the course of conversation, that the young man's knowledge was much superior to his own in those sciences, in which he had employed his whole time for several years. During his stay at Breda, Des Cartes wrote in Latin, a treatise on Music, and laid the foundation of several of his other works.
In 1619, he entered himself a volunteer in the army of the duke of Bavaria. In 1621, he made the campaign in Hungary, under the count de Bucquoy; but the loss of his general, who was killed at a siege that year, determined him to quit the army. He soon after began his travels into the north, and visited Silesia, Poland, Pomerania, the coasts of the Baltic, Brandenburgh, Holstein, East Friesland, West Friesland; in his passage to which last place he was in danger of being murdered. The sailors fancied he was a merchant, who had a large sum of money about him; and perceiving that he was a foreigner who had little acquaintance in the country, and a man of a mild disposition, they resolved to kill him, and throw his body into the sea. They even discoursed of their design before his face, thinking he understood no language but French, in which he always spoke to his servant. Des Cartes suddenly started up; and drawing his sword, spoke to them in their own language, in such a tone as struck terror into them: upon which they behaved very civilly. The year following he went to Paris, where he cleared himself from the imputation of having been received among the Rosicrusians, whom he confidered as a company of visionaries and impostors.
Dropping the study of mathematics, he now applied himself again to ethics and natural philosophy. The same year he took a journey through Switzerland to Italy. Upon his return he settled at Paris; but his studies being interrupted by frequent visits, he went in 1628 to the siege of Rochelle. He returned to Paris in November; but in the following spring he repaired to Amsterdam; and from thence to a place near Franeker in Friesland, where he began his Metaphysical Meditations, and spent some time in Dioptrics; about this time too he wrote his thoughts upon Meteors. After about six months he returned to Amsterdam.
Des Cartes imagined that nothing could more promote the temporal felicity of mankind, than the union of natural philosophy with mathematics. But before he should set himself to relieve men's labours, or multiply the conveniencies of life by mechanics, he thought it necessary to discover some means of securing the hu- | man body from disease and debility: this led him to the study of anatomy and chemistry, in which he employed the winter at Amsterdam.
He now, viz, about 1630 or 1631, took a short tour to England, and made some observations near London on the variation of the compass. In the spring of 1633 he removed to Deventer, where he completed several works that were left unfinished the year before, and resumed his studies in astronomy. In the summer he put the last hand to his “Treatise of the World.” The next year he returned to Amsterdam; but soon after took a journey into Denmark, and the lower parts of Germany. In autumn 1635 he went to Lewarden in Friesland, where he remained till 1637, and wrote his “Treatise of Mechanics.” The same year he published his four treatises concerning Method, Dioptrics, Meteors, and Geometry. About this time he received an invitation to settle in England from Sir Charles Cavendish, brother to the earl of Newcastle, with which he did not appear backward to comply, especially upon being assured that the king was a catholic in his heart: but the breaking out of the civil wars in this country prevented his journey.
At the end of 1641, Lewis the 13th, of France, invited him to his court, upon very honourable terms; but he could not be persuaded to quit his retirement. This year he published his Meditations concerning the Existence of God, and the Immortality of the Soul. In 1645 he again applied to anatomy; but was a little diverted from this study, by the question concerning the Quadrature of the Circle, which was at that time agitated. During the winter of the same year he composed a small tract against Gassendus's Institutes; and another on the Nature of the Passions. About this time he carried on an epistolary correspondence with the princess Elizabeth, daughter to Frederick the 5th, elector palatine, and king of Bohemia, who had been his pupil in Holland.
A dispute arising between Christina, queen of Sweden, and M. Chanut, the resident of France, concerning the following question; When a man carries love or hatred to excess, which of these two irregularities is the worst? The resident sent the question to Des Cartes, who upon that occasion drew up the dissertation upon Love, that is published in the first volume of his letters, which proved highly satisfactory to the queen. In June 1647 he took a journey to France, where the king settled on him a pension of 3000 livres; but he returned to Holland about the end of September. In November he received a letter from M. Chanut, in queen Christina's name, desiring his opinion of the sovereign good; which he accordingly sent her, with some letters upon the same subject formerly written to the princess Elizabeth, and his treatise on the Passions. The queen was so highly pleased with them, that she wrote him a letter of thanks with her own hand, and invited him to come to Sweden. He arrived at Stockholm in Oct. 1648. The queen engaged him to attend her every morning at five o'clock, to instruct her in his philosophy; and desired him to revise and digest all his unpublished writings, and to draw up from them a complete body of philosophy. She purposed also to fix him in Sweden, by allowing him a revenue of 3000 crowns a year, with an estate which should descend to his heirs and assigns for ever; and to establish an academy, of which he was to be the director. But these designs were frustrated by his death, which happened the 11th of Feb. 1650, in the 54th year of his age. His body was interred at Stockholm: but 17 years after it was removed to Paris, where a magnificent monument was erected to him in the church of Genevieve du Mont.
Dr. Barrow in his Opuscula tells us, that Des Cartes was doubtless a very ingenious man, and a real philosopher, and one who seems to have brought those assistances to that part of philosophy relating to matter and motion, which perhaps no one had done before: namely, a great skill in mathematics; a mind habituated, both by nature and custom, to profound meditation; a judgment exempt from all prejudices and popular errors, and furnished with a good number of certain and select experiments; a great deal of leisure; an entire disengagement, by his own choice, from the reading of useless books, and the avocations of life; with an incomparable acuteness of wit, and an excellent talent of thinking clearly and distinctly, and of expressing his thoughts with the utmost perspicuity.
Dr. Halley, in a paper concerning Optics, communicated to Mr. Wotton, and published by the latter in his “Reflections upon Ancient and Modern Learning,” writes as follows: As to dioptrics, though some of the ancients mention refraction, as a natural effect of transparent media; yet Des Cartes was the first, who in this age has discovered the laws of refraction, and brought dioptrics to a science.
Dr. Keil, in the introduction to his “Examination of Dr. Burnet's Theory of the Earth,” tells us, that Des Cartes was so far from applying geometry and observations to natural philosophy, that his whole system is but one continued blunder on account of his negligence in that point; which he could easily prove, by shewing that his theory of the vortices, upon which his system is founded, is absolutely false, for that Newton has shewn that the periodical times of all bodies, that swim in vortices, must be directly as the squares of their distances from the centre of them: but it is evident from observations, that the planets, in moving round the sun, observe a law quite different from this; for the squares of their periodical times are always as the cubes of their distances: and therefore, since they do not observe that law, which of necessity they must if they swim in a vortex, it is a demonstration that there are no vortices in which the planets are carried round the sun.
“Nature, fays Voltaire, had favoured Des Cartes with a strong and clear imagination, whence he became a very singular person, both in private life, and in his manner of reasoning. This imagination could not be concealed even in his philosophical writings, which are every where adorned with very brilliant ingenious metaphors. Nature had almost made him a poet; and indeed he wrote a piece of poetry for the entertainment of Christina queen of Sweden, which however was suppressed in honour of his memory. He extended the limits of geometry as far beyond the place where he found them, as Newton did after him; and first taught the method of expressing curves by equations. He ap- | plied this geometrical and inventive genius to dioptrics, which when treated by him became a new art; and if he was mistaken in some things, the reason is, that a man who discovers a new tract of land, cannot at once know all the properties of the soil. Those who come after him, and make these lands fruitful, are at least obliged to him for the discovery.” Voltaire acknowledges, that there are innumerable errors in the rest of Des Cartes' works; but adds, that geometry was a guide which he himself had in some measure formed, and which would have safely conducted him through the several paths of natural philosophy: nevertheless he had at last abandoned this guide, and gave entirely into the humour of framing hypotheses; and then philosophy was no more than an ingenious romance, fit only to amuse the ignorant.
It has been pretty generally acknowledged, that he borrowed his improvements in Algebra from Harriot's Artis Analyticæ Praxis; which is highly probable, as he was in England about the time when Harriot's book was published, and as he follows the manner of Harriot, except in the method of noting the powers. Upon this head the following anecdote is told by Dr. Pell, in Wallis's Algebra, pa. 198. Sir Charles Cavendish, then resident at Paris, discoursing there with M. Roberval, concerning Des Cartes's Geometry, then lately published: I admire, said Roberval, that method in Des Cartes, of placing all the terms of the equation on one side, making the whole equal to nothing, and how he lighted upon it. The reason why you admire it, said Sir Charles, is because you are a Frenchman; for if you were an Englishman, you would not admire it. Why so? asked Roberval. Because, replied Sir Charles, we in England know whence he had it; namely from Harriot's Algebra. What book is that? says Roberval, I never saw it. Next time you come to my chamber, saith Sir Charles, I will shew it to you. Which a while after he did; and upon perusal of it, Roberval exclaimed with admiration, Il l'a vu! il l'a vu! He had seen it! he had seen it! finding all that in Harriot which he had before admired in Des Cartes, and not doubting but that Des Cartes had it from thence. See also Montucla's History of Mathematics.
The real improvements of Des Cartes in Algebra and Geometry, I have particularly treated of under the article Algebra; and his philosophical doctrines are displayed in the article Cartesian Philosophy, here following. He was never married, but had one natural daughter, who died when she was but five years old. There have been several editions of his works, and commentaries upon them; particularly those of Schooten on his Geometry.
CARTESIAN Philosophy, or Cartesianism, the system of philosophy advanced by Des Cartes, and maintained by his followers, the Cartesians.
The Cartesian philosophy is founded on two great principles, the one metaphysical, the other physical. The metaphysical one is this: I think, therefore I am, or I exist: the physical principle is, that nothing exists but substances. Substance he makes of two kinds; the one a substance that thinks, the other a substance extended: so that actual thought and actual extension make the essence of substance.
The essence of matter being thus fixed in extension, Des Cartes concludes that there is no vacuum, nor any possibility of it in nature; but that the universe is absolutely full: by this principle, mere space is quite excluded; for extension being implied in the idea of space, matter is so too.
Des Cartes defines motion to be the translation of a body from the neighbourhood of others that are in contact with it, and considered as at rest, to the neighbourhood of other bodies: by which he destroys the distinction between motion that is absolute or real, and that which is relative or apparent. He maintains that the same quantity of motion is always preserved in the universe, because God must be supposed to act in the most constant and immutable manner. And hence also he deduces his three laws of motion. See Motion.
Upon these principles Des Cartes explains mechanically how the world was formed, and how the present phenomena of nature came to arise. He supposes that God created matter of an indefinite extension, which he separated into small square portions or masses, full of angles <*> that he impressed too motions on this matter; the one, by which each part revolved about its own centre; and another, by which an assemblage, or system of them, turned round a common centre. From whence arose as many different vortices, or eddies, as there were different masses of matter, thus moving about common centres.
The consequence of these motions in each vortex, according to Des Cartes, is as follows: The parts of matter could not thus move and revolve amongst one another, without having their angles gradually broken; and this continual friction of parts and angles must produce three elements: the first of these, an infinitely fine dust, formed of the angles broken off; the second, the spheres remaining, after all the angular parts are thus removed; and those particles not yet rendered smooth and spherical, but still retaining some of their angles, and hamous parts, from the third element.
Now the first or subtilest element, according to the laws of motion, must occupy the centre of each system, or vortex, by reason of the smallness of its parts: and this is the matter which constitutes the sun, and the fixed stars above, and the fire below. The second element, made up of spheres, forms the atmosphere, and all the matter between the earth and the fixed stars; in such sort, that the largest spheres are always next the circumserence of the vortex, and the smallest next its centre. The third element, formed of the irregular particles, is the matter that composes the earth, and all terrestrial bodies, together with comets, spots in the sun, &c.
He accounts for the gravity of terrestrial bodies from the centrifugal force of the ether revolving round the earth: and upon the same general principles he pretends to explain the phenomena of the magnet, and to account for all the other operations in nature.
