[613] Tant s’en faut que les choses que j’ai écrites puissent être aisément tirées de Viéte, qu’au contraire ce qui est cause que mon traité est difficile à entendre, c’est que j’ai tâché à n’y rien mettre que ce que j’ai crû n’avoir point été su ni par lui ni par aucun autre; comme on peut voir si on confére ce que j’ai écrit du nombre des racines qui sont en chaque équation, dans la page 372, qui est l’endroit où je commence à donner les règles de mon algèbre, avec ce que Viéte en a écrit tout à la fin de son livre, De Emendatione Æquationum; car on verra que je le determine généralement en toutes équations, au lieu que lui n’en aiant donné que quelques exemples particuliers, dont il fait toutefois si grand état qu’il a voulu conclure son livre par là, il a montre qu’il ne le pouvoit déterminer en général. Et ainsi j’ai commencé où il avoit achevé, ce que j’ai fait toutefois sans y penser; car j’ai plus feuilleté Viéte depuis que j’ai reçu votre dernière que je n’avois jamais fait auparavant, l’ayant trouvé ici par hasard entre les mains d’un de mes amis; et entre nous, je ne trouve pas qu’il en ait tant su que je pensois, non obstant qu’il fût fort habile. This is in a letter to Mersenne in 1637. Œuvres de Descartes, vol. vi., p. 300.
The charge of plagiarism from Harriott was brought against Descartes in his lifetime: Roberval, when an English gentleman showed him the Artis Analyticæ Praxis, exclaimed eagerly, Il l’a vu! il l’a vu! It is also a very suspicious circumstance, if true, as it appears to be, that Descartes was in England the year (1631) that Harriott’s work appeared. Carcavi, a friend of Roberval, in a letter to Descartes in 1649, plainly intimates to him that he has only copied Harriott as to the nature of equations Œvres des Descartes, vol. x., p. 373. To this accusation Descartes made no reply. See Biographia Britannica, art. Harriott. The Biographie Universelle unfairly suppresses all mention of this, and labours to depreciate Harriott.
See Leibnitz’s catalogue of the supposed thefts of Descartes in Vol. III., p. 267, of this work.
Fermat. 22. The geometer next in genius to Descartes, and perhaps nearer to him than to any third, was Fermat, a man of various acquirements, of high rank in the parliament of Toulouse, and of a mind incapable of envy, forgiving of detraction, and delighting in truth, with almost too much indifference to praise. The works of Fermat were not published till long after his death in 1665; but his frequent discussions with Descartes, by the intervention of their common correspondent Mersenne, render this place more appropriate for the introduction of his name. In these controversies Descartes never behaved to Fermat with the respect due to his talents; in fact, no one was ever more jealous of his own pre-eminence, or more unwilling to acknowledge the claims of those who scrupled to follow him implicitly, and who might in any manner be thought rivals of his fame. Yet it is this unhappy temper of Descartes which ought to render us more unwilling to credit the suspicions of his designed plagiarism from the discoveries of others; since this, combined with his unwillingness to acknowledge their merits, and affected ignorance of their writings, would form a character we should not readily ascribe to a man of great genius, and whose own writings give many apparent indications of sincerity and virtue. But in fact there was in this age a great probability of simultaneous invention in science, from developing principles that had been partially brought to light. Thus Roberval discovered the same method of indivisibles as Cavalieri, and Descartes must equally have been led to this theory of tangents by that of Kepler. Fermat also, who was in possession of his principal discoveries before the geometry of Descartes saw the light, derived from Kepler his own celebrated method, de maximis et minimis; a method of discovering the greatest or least value of a variable quantity, such as the ordinate of a curve. It depends on the same principle as that of Kepler. From this he deduced a rule for drawing tangents to curves different from that of Descartes. This led to a controversy between the two geometers, carried on by Descartes, who yet is deemed to have been in the wrong, with his usual quickness of resentment. Several other discoveries, both in pure algebra and geometry, illustrate the name of Fermat.[614]
[614] A good article on Fermat, by M. Maurice, will be found in the Biographie Universelle.
Algebraic geometry not successful at first. 23. The new geometry of Descartes was not received with the universal admiration it deserved. Besides its conciseness and the inroad it made on old prejudices as to geometrical methods, the general boldness of the author’s speculations in physical and metaphysical philosophy, as well as his indiscreet temper, disinclined many who ought to have appreciated it; and it was in his own country, where he had ceased to reside, that Descartes had the fewest admirers. Roberval made some objections to his rival’s algebra, but with little success. A commentary on the treatise of Descartes by Schooten, professor of Geometry at Leyden, first appeared in 1649.
Astronomy.—Kepler. 24. Among those who devoted themselves ardently and successfully to astronomical observations at the end of the sixteenth century, was John Kepler, a native of Wirtemburg, who had already shown that he was likely to inherit the mantle of Tycho Brahe. He published some astronomical treatises of comparatively small importance in the first years of the present period. But in 1609 he made an epoch in that science by his Astronomia Nova αιτιολογητος, or Commentaries on the Planet Mars. It had been always assumed that the heavenly bodies revolve in circular orbits round their centre, whether this were taken to be the sun or the earth. There was, however, an apparent eccentricity or deviation from this circular motion, which it had been very difficult to explain, and for this Ptolemy had devised his complex system of epicycles. No planet showed more of this eccentricity than Mars; and it was to Mars that Kepler turned his attention. After many laborious researches he was brought by degrees to the great discovery, that the motion of the planets, among which, having adopted the Copernican system, he reckoned the earth, is not performed in circular but in elliptical orbits, the sun not occupying the centre but one of the foci of the curve; and, secondly, that it is performed with such a varying velocity, that the areas described by the radius vector, or line which joins this focus to the revolving planet, are always proportional to the times. A planet, therefore, moves less rapidly as it becomes more distant from the sun. These are the first and second of the three great laws of Kepler. The third was not discovered by him till some years afterwards. He tells us himself that on the 8th May, 1618, after long toil in investigating the proportion of the periodic times of the planetary movements to their orbits, an idea struck his mind, which, chancing to make a mistake in the calculation, he soon rejected. But a week after, returning to the subject, he entirely established his grand discovery, that the squares of the times of revolution are as the cubes of the mean distances of the planets. This was first made known to the world in his Mysterium Cosmo graphicum, published in 1619; a work mingled up with many strange effusions of a mind far more eccentric than any of the planets with which it was engaged. In the Epitome Astronomiæ Copernicanæ, printed the same year, he endeavours to deduce this law from his theory of centrifugal forces. He had a very good insight into the principles of universal gravitation, as an attribute of matter; but several of his assumptions as to the laws of motion are not consonant to truth. There seems indeed to have been a considerable degree of good fortune in the discoveries of Kepler; yet, this may be deemed the reward of his indefatigable laboriousness, and of the ingenuousness with which he renounced any hypothesis that he could not reconcile with his advancing knowledge of the phenomena.
Conjectures as to comets. 25. The appearance of three comets in 1619 called once more the astronomers of Europe to speculate on the nature of those anomalous bodies. They still passed for harbingers of worldly catastrophies; and those who feared them least could not interpret their apparent irregularity. Galileo, though Tycho Brahe had formed a juster notion, unfortunately took them for atmospheric meteors. Kepler, though he brought them from the far regions of space, did not suspect the nature of their orbits, and thought that, moving in straight lines, they were finally dispersed and came to nothing. But a Jesuit, Grassi, in a treatise, De Tribus Cometis, Rome, 1618, had the honour of explaining what had baffled Galileo, and first held them to be planets moving in vast ellipses round the sun.[615]
[615] The Biographie Universelle, art. Grassi, ascribes this opinion to Tycho.
Galileo’s discovery of Jupiter’s satellites. 26. But long before this time the name of Galileo had become immortal by discoveries which, though they would certainly have soon been made by some other, perhaps far inferior, observer, were happily reserved for the most philosophical genius of the age. Galileo assures us that, having heard of the invention of an instrument in Holland which enlarged the size of distant objects, but knowing nothing of its construction, he began to study the theory of refractions till he found by experiment, that by means of a convex and concave glass in a tube, he could magnify an object threefold. He was thus encouraged to make another which magnified thirty times; and this he exhibited in the autumn of 1609 to the inhabitants of Venice. Having made a present of his first telescope to the senate, who rewarded him with a pension, he soon constructed another; and in one of the first nights of January, 1610, directing it towards the moon, was astonished to see her surface and edges covered with inequalities. These he considered to be mountains, and judged by a sort of measurement that some of them must exceed those of the earth. His next observation was of the milky way; and this he found to derive its nebulous lustre from myriads of stars not distinguishable through their remoteness, by the unassisted sight of man. The nebulæ in the constellation Orion he perceived to be of the same character. Before his delight at these discoveries could have subsided, he turned his telescope to Jupiter, and was surprised to remark three small stars, which, in a second night’s observation, had changed there places. In the course of a few weeks, he was able to determine by their revolutions, which are very rapid, that these are secondary planets, the moons or satellites of Jupiter; and he had added a fourth to their number. These marvellous revelations of nature he hastened to announce in a work, aptly entitled Sidereus Nuncius, published in March, 1610. In an age when the fascinating science of astronomy had already so much excited the minds of philosophers, it may be guessed with what eagerness this intelligence from the heavens was circulated. A few, as usual, through envy or prejudice, affected to contemn it. But wisdom was justified of her children. Kepler, in his Narratio de observatis a se Quatuor Jovis Satellitibus, 1610, confirmed the discoveries of Galileo. Peiresc, an inferior name, no doubt, but deserving of every praise for his zeal in the cause of knowledge, having with difficulty procured a good telescope, saw the four satellites in November, 1610, and is said by Gassendi to have conceived at that time the ingenious idea that their occultations might be used to ascertain the longitude.[616]