Abbildungen der Seite
PDF
EPUB

and lewdness? There is a reciprocal intoleration between conscience and its effects, on the one side, and luxury, especially philosophical luxury, with its brood of vices, on the other; and who can endure their endless struggles? This, and infinite conceit, have produced a prodigious swarm of very minute philosophers, of whom many cannot so much as read; that flutter like gnats, about religion, biting, stinging, and perishing in their impotent attempts. With these, the appellation of philosopher, at first modestly assumed, as only a lover of knowledge, is now made to stand for a wise, or very knowing man. Under this honorary title they thrust into company with Paschal, Bacon, and Newton; and then, who should speak, who should declaim against religion, but they? In every corner we have a Robin Hood of these insects, who having heard that Newton was infallible in all his opinions, and a staunch Arian, set up for buzzing and biting at the Trinity. But now, as to Newton, though at a prodigious distance I venerate his memory as a most consummate mathematician, I cannot allow him the epithet of infallible, even in natural philosophy and mathematics, his grand fort, much less in matters of religion wherein I am able to prove him most grossly erroneous, and even contradictory, He is, after all, but a borrower from the ancients, as to both his principle of attraction, and his attempt to square the circle. After having fully refuted Des Cartes on the subject of a plenum, a business of but little difficulty, he calls in attraction to account for gravity, as one of his two great organs, whereby the planets and comets are carried round their orbits; and after having, with amazing ability, demonstrated the laws whereby this principle of attraction operates, and shewn, that this power is found in all bodies, which attract one another reciprocally in proportion to their respective quantities of matter and their distances, he dare not call this a property of matter, which perhaps he might have safely done; but sometimes resolves it into the power of God, rightly, in my humble opinion, and why not, as well as the centrifugal or progressive motion of the planets? but, unphilosophically, as other great philosophers maintain, who are for shutting God out of his own works. And sometimes, ashamed to give no account but the power of God for the principle whereon he grounds almost the whole of his philosophy, he insinuates, that attraction may be the effect of a subtile spirit, a sort of equivocation, whereby, if he means any thing, he must mean somewhat of the same, or a similar nature, with

the subtile matter of Des Cartes. All he says in reference to this subtile matter, for which he borrows the appellation of æther, he proposes as purely hypothetical. This fluid of his, he supposes, may surround the sun, and extend itself throughout the solar system; may be exceeding rare near the sun, and grow still denser and denser as its distance from that luminary increases; and endeavours to shew, that all he had ascribed to gravity and attraction, may possibly be thereby accounted for. This, however, he does in a way so futile and unsatisfactory, as, in that instance, to level the great Sir Isaac with the lowest class of thinkers and guessers. On this most important point he goes backward and forward, and wavers in a miserable manner. Here at best he is not absolutely infallible; but still less so in regard to the quadrature of the circle; wherein too he is but a borrower from Archimedes, and others, all prior to the age of Newton. For this (in my humble opinion, not very important purpose, and fitter to employ the talent of a philomath than a Newton) he and Leibnitz, much about the same time, struck out a fluxional method, which they both took for a demonstration. The mathematical disciples of these great men were, at first, of the same opinion, hallooing whatsoever came from them as infallible and perfect, but bitterly contending, some for Newton, and others for Leibnitz, as the first inventor. In England the genius of Newton was cried up as more than human, as somewhat above that of a created being, and still is by the servile crew. His apotheosis however began to be a little doubted of by a few, as soon as they found it had been borrowed, and on trial proved itself defective, and far short of a demonstration. On this, the mathematicians, blushing for their admiration, both of the author and the scheme, fell from the title they had given of a demonstration, to that of an approximation. What, after all! are we put off with an approximation only? We should be glad to know wherein this mathematical, is preferable to our old mechanical approximation. It would be hard upon the excise officers and supernumeraries, to go through a nice fluxion of infinitesimals in gauging a barrel of ale; and upon a surveyor of land, to give the acres, roods, perches, digits, in infinitesimals, and fractions of infinitesimals, in the dimensions of a common field. Query, however, whether there hath been any fluxional approximation really made? Objects, seen at a great distance, under a small angle, appear to be nearer to each other than they are; and then the great mathematician, working in a high cloud of in

finitesimals, and seen by a little mathematician below in a dense fog of logarithms, may have seemed to baloon it nearer to the moon than he did. This disappointment reminds me of two lines in Boileau on the passage of the Rhine. That great poet, intending to give the world an epic on the subject, bids other poets celebrate the glorious exploits of Louis in other fields of action, and claims the arduous passage for himself, I suppose, as the most illustrious of the whole. Accordingly, he sets out with an invocation of Apollo and all the Muses, to aid him in the sublime attempt; but having brought his hero, with a huge army, to the river side, and described the formidable preparations of the allies on the other, he tells us, the generals of Louis, in the midst of no little swagger on his part, represented to him, how far it was beneath the majesty of the grand monarque to take the river, like a common soldier, and their arguments prevailed on a man not over rash in braving dangers of that sort. Then the poet, on a frisky tantrum of sublime, says,

Louis, les animant de feu de son courage,

Se plaint de sa grandeur, qui l'attaque au rivage.
These Louis fir'd, and curs'd his royal rank,
Which fix'd his courage in the hither bank.

On which the parody of Prior is remarkable,

And Boileau summon'd all the tuneful nine,

To sing how Louis did-not pass the Rhine.

It is to me astonishing, that the grand monarch of mathematics did not better consider two things; in the first place, the insignificance of a quadrature to every purpose, but his own glory; and in the next place, how impossible it was for him to succeed, even as to that, by the method he took. Surveyors, carpenters, gaugers, &c. going on merely mechanical principles, do well enough without squaring circles. They suppose, which is true, that the diameter of a circle is nearly equal to one-third part of the circumference; and stand in need of no other approximation. If it is self-evident, that the circle and its diameter reciprocally define each other, how is it possible to prove it? Is not this enough for use and practice? And why then insufficient for science? And perhaps, after all, the mathematicians had better go back to mechanics, from whence all the science of lines and surfaces did certainly originate, that by trying up, as the carpenters call it, they may learn of the homely mother what they can never be taught by the Lady Geometry, as she is now tricked

out in fringes, furbelows, gauzes; oiled with fluxions, and powdered with polygons, infinitesimals, nonsense; and habituating herself to prattle in an affected cant of hard words, so mysterious, that it is the work of half a life to understand it. Why should knowledge affect to be mysterious? Possibly, if in imitation of her great grandmother, Truth, she went naked, we should admire her the more. No sooner are the terms, diagonal, and square, known to any one, than his assent to an exact commeasurement between them respectively, is forced. The same is true of a diameter and its circle, although it is still said by mathematical men, that there can be no exact ratio or proportion found between a right line and a circle. As to the latter, the diameter is found, suppose mechanically to be nearly one-third of the circumference; why nearly and not exactly, is hard to say (and not worth the saying), for twenty-two miles (in this case, measurement alone is to be considered) may be exactly divided by three into seven miles, and four-twelfths of a mile. If a greater degree of exactness is sought for, it is probably more than mathematical demonstration is adequate to. If a man cannot find the ratio between the water in his tea-kettle, and in the ocean, is he never to take his breakfast? If a mathematician knows not the different distances between his chair and the farther corner of his study; and between that chair and the parish church, by actual measurement, is he never to go to church till he finds the ratios of those distances mathematically without the help of a rule, chain, or string? Every mortal who knows any thing of a square and its diagonal, knows, that said diagonal, and any side of its square are accurately commensurable; and if no man can find out how to demonstrate their commensurability, what matters it? Yet among the ablest mathematicians, a flat contradiction arises on the subject of a square and its diagonal. The latter cuts the former into two right angled triangles, exactly equal. Now the square of the diagonal is found by them to be equal to the squares of two sides of the former, though the length of every right line is exactly commensurable with the square of that line. Are there not then two ratios, and yet no ratio, between the diagonal of a square, and one of its sides? Is there not intuitively evident an exact proportion between the diagonal of a square and every one of its sides? And to lead to the knowledge of that proportion, is there not another between the square of that diagonal and the square of any side in the original square? Every mortal, that knows what a circle is,

and its diameter, knows, they are accurately commensurable; but if no man can demonstrate that commensurability, what loss is this to mankind? These two are mysteries of nature, wherein somewhat is perfectly known, and somewhat utterly unfathomable, left perhaps to baffle the understandings of such as will not receive the plain doctrines of religion, on the word of God, because they cannot account for the depths, wherein those doctrines terminate. He who knows, the whole is greater than any of its parts, but how much greater, in regard to any particular whole and part, can never find but by weight or measure of that whole, and a given part. To look for any thing farther, or by any other mode of inquiring, is but to vaunt the force of his genius in having found out what nobody else could. If nothing is to be taken for a truth, that is not mathematically proved, a jury must not find a culprit guilty on ocular evidence, if he who gives it cannot mathematically prove that his eyesight may be depended on. He is no mathematician, but he can see as well as the best of them, and the prisoner at the bar must be banged. If the square of a circle cannot be mechanically found, it will be in vain to attempt it by a polygon and fluxions, whereby the essential difference of a right line and a circle must be confounded and sunk, as no difference at all, and the angles of the polygon must cease to be angles. Making the lines of the polygon infinitely short, and the angles infinitely obtuse, will never hinder them to be still right lines and angles, nor bend them into a curve of any sort. An angular circle, whether mathematical or not, is indubitably nonsensical. It may be wished, that the venders of infinitesimals would also furnish us professedly, with a system of unintelligibles, alias transcendentals, alias nonsensicals. These two latter terms of art would not be so apt to frighten the ladies, and young beginners, as polygons and infinitesimals. If in some degree, I mistake the great Sir Isaac, the much abler interpreters of him, through whom I see him, are to blame. Some of them have (and I hope fairly) stripped his opinions and reasonings of their mathematically mysterious dress, so as to bring them down to the test of common sense. Among these I get into some acquaintance with him; and take not half the liberty with him that he hath taken with the Holy Ghost, speaking in terms intelligible to all men. As to those very minute things, which he calls infinitesimal, that is infinitely divisible, or divided, common sense absolutely denies, there are any such. To human apprehension,

« ZurückWeiter »