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 hanged. 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,

duration and space alone, because infinite, are infinitely divisible. But no assignable portion of duration, i. e. time; no assignable portion of space, particularly as occupied by matter, can be infinitely divisible, because, in regard to any part of duration or space, there is respectively a point, a minimum or ultimum, where such divisions become perfectly individual. Perhaps Sir Isaac only supposes, that division may go downward for ever. But there can be no such thing, even in supposition, as lines or angles of this sort. The radii must absolutely destroy either the circle, or the polygon: the circle, if some of them do not go home to it, or pass beyond it in adjusting themselves to the polygon, whether projected within, or without it; or the polygon, if they adjust themselves to the circle. The idea of an infinite too must be lost. It is as ridiculous to say infinitely little in' regard to quantity or dimension, as to say, 'infinitely, few, in regard to number.' Even to this absurdity they make approaches by what they call negative numbers, that is, numbers less than 0 'nought,' a term, whereof, as standing for a nonentity, they cannot possibly have any idea or conception. Yet, setting this, an abstract number on paper to represent things positively existing, they boldly count downward, till they come to a number of nothings,' exceeding any positive number that can be assigned. Now, in good earnest, where is the sense of annumerating nothings;' of adding nothing' to nothing;' of subtracting nothing' from 'nothing;' of multiplying nothings;' and of dividing nothing?' Fractions are an arithmetic of realities, or wholly useless. But whoever attempts an arithmetic of noughts' below units, instead of descending the stairs of science to minutenesses, is only, without knowing it, climbing the ladder of nonsense, for he is forced to have recourse to something, in order to work on nothing, and must lose sight of his negative, of which he hath no idea, and can use only an unmeaning term. This is one of those tricks, made use of by the vanity of philosophers to set common sense a staring. This is a mystery, not of nature, but of men's own making, wherein somewhat imperfectly known, ends in jargon or nonsense. Quantity, downward, dwindles to a point, and loses itself in nothing, long before it can become infinitely small; and number can never sink below unity, for, in truth, there cannot be any such thing as a negative quantity, or a negative number; but infinite must ever be a negative, and consequently can never be the epithet of either quantity or number in finites, upward or down

ward. No aggregate therefore of infinitesimals (could infinitesimals be supposed) can ever produce an answer to quot? or quantum? The talk of such things is nothing better, than artificial nonsense, and the mere dotage of mathematics. Consistently

with common sense, infinite can go only upward, for there is no infinite, but one, that is, God. Space and duration are his attributes. How much is it to be wished, that poor little man, of an understanding so extremely limited, would cease to talk of infinites, which the highest angel of light cannot so much as think of, in the plural, which to speak of as our philosophers, our reasoning worms, have done, is arrogance and blasphemy! I wont say, witchcraft, though there was a time, when mathematicians and magicians were synonymous. It is also much to be wished, that men, but a few inches above us in understanding, would not endeavour, as they do, to ram their idle and conceited speculations down the throats of us poor creatures in the low class of logic and common sense, by giving a dash of infidelity along with their infinitesimals, that we may stare, gape, and transfer our modicum of faith from God to them. The very narrow capacity of man can proceed but a little way in the investigation of knowledge, the most obvious and familiar; far less in deep and abstruse matters; but, excepting as to one particular object, is wholly at a loss when it presumptuously attempts the consideration of infinity. To this it is so totally inadequate, that, on the comparison, it appears humble and modest, when it endeavours to fathom the ocean, and measure the heavens with an inch of line. The ox knows his feeder, the ass his master's crib,' and the horse soon finds his length of tether; but the philosopher cannot discover that he is but a finite creature, that his line of investigation is exceeding short, and that he may attempt infinity, though he is unable to assign the ratio between the diagonal of a square, and one of its sides, or between a circle and its diameter, although he is perfectly sure there are two such ratios. Miserable! But to relieve himself from these difficulties, which to a common workman seem no difficulties at all, he hath recourse to infinity (such is his vanity), and here finds himself distracted, disappointed, lost. He forgets that infinity is a negative, and never can, even by supposition, become a positive, but in God, in whom alone it is essential; and, as if he knew it to be a property of numbers and lines, he seeks, among what he calls the infinitesimals of these, the ratio of a diameter to its circle. He goes out of his depth, and so out

sense.

of mine, to follow him, in this abyss of mud, where both of us are forced to think and speak in the tritical figure, called nonHe finds one infinite less than another, precisely in the same sense and respect, for instance, in the divisibility of matter, not considering that a greater infinite necessarily bounds a less of the same kind, and reduces it to a finite. He drops the distinction between indefinite, which may, and infinite, which may not, be measured or computed. Here he plunges, and throws up such a quantity of mathematical stuff in crabbed terms, and long elaborate calculations, that neither he nor any other mortal can form a competent judgment of the matter. This only we are all sure of, that there can be no calculus of infinites, if he had them to work on, no more than there can be of nothings. It is to me selfevidently plain, that there is an exact proportion between a circle and its diameters; between one side of a square and the diagonal of that square; and that matter, if extension is essential to it, may be infinitely divided, though a flat contradiction, both in ideas and terms, must arise between the number of parts, into which one cubical inch of gold, and two cubical inches of the same metal, may be divided, which must produce one infinite, just twice as numerous as another, a piece of philosophical nonsense, not less gross nor palpable than saying that a thousand and five hundred are exactly equal, and very unequal. These, and such like points, so naturally obvious, and yet so unfathomable to human investigation, seem to be left as mathematical mysteries, to baffle the pride of human understanding, and to expose philosophy to contempt, when it attacks the mysteries of religion, after having left many of its own behind it, attempted indeed, but never solved. It is not altogether my fault, that, in this philosophical instance, I am forced to write nonsense as well as my betters. Be these things, however, as they may, might not one have expected that the almost deified mathematician, who had so many infinites to dispose of, might have allowed one to Christ, and not have limited the Holy One of Israel?' Newton held the Bible to be the word of God himself, consequently how came he not to see that there is but one God; that the universe was made by Christ, and that Christ, in a thousand passages of both Old and New Testament, is asserted to be that one God; nay, that he himself asserts it by Moses, Isaiah, St. John, &c. and denies the being of any other God? What then can we think of Newton as a reasoner, when he disbelieved the infinity, i. e. the divinity, of