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 () 'nought,' a term, whereof, as standing for a monentity, 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 readisbelieved the infinity, i. e. the divinity, of

soner, when he

VOL. VI.

C

Christ? How came he to set up his own opinion against the express, the repeated, word of God himself? He could see little, surely, if he could not see the flat contradiction, in this most important case, between God and him. It is an old and just observation, that no man of sense can long continue to be an Arian. Revelation and the Bible must be given up, or the proper and true divinity of Christ must be believed. There is, there can be, no medium. There can be no medium between maintaining, that Christ, who asserts it, is really and truly God, and giving him up as a most impious impostor. Pardon me, blessed Jesu! for writing the horrible words, as I detest them from the depths of my soul. As to the dignity of our Redeemer, whereon depend all the essential principles of our holy religion, and the eternal salvation we hope for through him, we have authority to rest our faith on, infinitely superior to that of Newton, and all the philosophers and mathematicians, of all the Clarkes, Hoadlys, &c. that ever lived. If we must talk of infinites, we have the sole infinitely wise Author of truth to depend on for information concerning the respect we ought to pay to the Redeemer of mankind. When St. Stephen gave his life for Christ, whom he then saw at his Father's right hand, on the throne of heaven, he left this world on principles very different from those of fluxions and infinitesimals. Yet no man since hath thought or died on better reasons than he did. The true and real divinity of our blessed Saviour are so amply, so clearly set forth by the Fountain of Truth in his holy Scriptures, that there is no room left for the reason of him, who believes in those Scriptures, to doubt or balance on the important subject. But were this point less thoroughly enforced therein on reason and faith, a very short comparison of the difficulties on both sides, for some there seem to be, must result in a full and final decision. On the Arian side, reason, or somewhat which the vanity of a man takes for reason in himself, objects to a personal distinction in God, that infinite being, so perfectly one. Again, although there is not a single passage which denies the divinity of Christ throughout the whole Scriptures, there are some which indirectly, yet strongly, seem to militate against it. But is any man so perfectly acquainted with the infinitely incomprehensible Being, as to be sure there is no distinction in that Being analogous to the personal distinction of one man from another? And may not the passages of Scripture, which, at first sight, seem to favour the Arian opinion, be interpreted fairly of

Christ, as a son, and a man? Nay, must they not be so interpreted, since, in the first place, those Scriptures every where absolutely deny the being of any God but one? Since those Scriptures so often affirm Christ to be God? since, although in those Scriptures Christ so often speaks of himself as Son and messenger of his Father, there is not to be found a single intimation that he is an inferior God, or a creature only, deputed by his Father to create, and then to redeem the world? It is easy to see on which of these sides right reason must decide, if the word of God is allowed to speak to reason, or if reason, so instructed, is permitted to speak to our faith. No, philosophy sets itself above faith; and, in this instance, the philosophy even of Newton is so far below reason, as to terminate in downright absurdity of contradiction, probably to teach us feebler thinkers, not any longer to idolize our wretched understanding. Let Newton, therefore, say what he will, I repeat, without controversy, great is the mystery of godliness, God was manifested in the flesh, justified in the spirit, seen of angels, preached unto the Gentiles, believed on in the world, received up into glory. By him (Christ) were all things created, that are in heaven, and that are in earth, visible and invisible, whether they be thrones, or dominions, or principalities, or powers, all things were created by him, and for him. And he is before all things, and by him all things consist.' Between these plain passages, and the assent of a plain man, who believes the Scriptures, is a ratio so easily demonstrated, that Newton and Clarke, both believing in the Scriptures, must have perceived it, had they not been more taken up with the ratio of a right line to a circle, as a matter of greater consequence to their mathematical characters; for, I cannot think, they intended directly to give the lie to God's word. Inquisitiveness, or a too ardent thirst of knowledge, was among the first faults of mankind; and though it is found by experience, that he who increaseth knowledge increaseth sorrow,' at least in a thousand instances; yet our philosophers and mathematicians still go on to prove themselves the children of Eve. Ignorance is frequently better than knowledge. To consult with a soothsayer about futurity is double folly, both because the soothsayer knows nothing of the matter, and it were better for the consulter not to foresee either the good or evil he is to meet with. God, in his mercy, hides the latter, and in his wisdom the former, from us. If a man knows not how to square a circle, he may do well enough without it; nay, may do much better without