ticians many sincere believers in Jesus Christ; I know several such myself; but I addressed my Analyst to an infidel: and on very good grounds, I supposed that, besides him, there were other deriders of faith, who had nevertheless a profound veneration for fluxions; and I was willing to set forth the inconsistence of such men. If there be no such thing as infidels, who pretend to knowledge in the modern analysis, I own myself misinformed, and shall gladly be found in a mistake; but even in that case, my remarks upon fluxions are not the less true; nor will it follow, that I have no right to examine them on the foot of human science, even though religion were quite unconcerned, and though I had no end to serve but truth. But you are very angry (p. 13 and 14) that I should enter the lists with reasoning infidels, and attack them upon their pretensions to science: and hence you take occasion to shew your spleen against the clergy. I will not take upon me to say, that I know you to be a minute philosopher yourself: but I know, the minute philosophers make just such compliments as you do to our church, and are just as angry as you can be at any who undertake to defend religion by reason. If we resolve all into faith, they laugh at us and our faith and if we attempt to reason, they are angry at us : they pretend we got out of our province, and they recommend to us a blind implicit faith. Such is the inconsistence of our adversaries. But it is to be hoped, there will never be wanting men to deal with them at their own weapons; and to shew, they are by no means those masters of reason which they would fain pass for.

VII. I do not say, as you would represent me, that we have no better reason for our religion than you have for fluxions: but I say, that an infidel, who believes the doctrine of fluxions, acts a very inconsistent part, in pretending to reject the Christian religion, because he cannot believe what he doth not comprehend: or because he cannot assent without evidence; or because he can

not submit his faith to authority. Whether there are such infidels, I submit to the judgment of the reader; for my own part I make no doubt of it, having seen some shrewd signs thereof myself, and having been very credibly informed thereof by others. Nor doth this charge seem the less credible, for your being so sensibly touched and denying it with so much passion. You, indeed, do not stick to affirm, that the persons who informed me are a pack of base, profligate, and impudent liars (p. 27). How far the reader will think fit to adopt your passions I cannot say; but I can truly say, the late celebrated Mr. Addison is one of the persons whom you are pleased to characterize in these modest and mannerly terms. He assured me that the infidelity of a certain noted mathematician, still living, was one principal reason assigned by a witty man of those times for his being an infidel. Not that I imagine geometry disposeth men to infidelity: but that from other causes, such as presumption, ignorance, or vanity, like other men geometricians also become infidels, and that the supposed light and evidence of their science gains credit to their infidelity.

VIII. "You reproach me with calumny, detraction, and artifice (p. 15). You recommend such means as are innocent and just, rather than the criminal method of lessening or detracting from my opponents. (Ibid.) You accuse me of the odium theologicum, the intemperate zeal of divines, that I do stare super vias antiquas," (p. 13); with much more to the same effect. For all which charge I depend on the reader's candour, that he will not take your word, but read and judge for himself. In which case he will be able to discern (though he should be no mathematician) how passionate and unjust your reproaches are, and how possible it is, for a man to cry out against calumny and practise it in the same breath. Considering how impatient all mankind are when their prejudices are looked into, I do not wonder to see you rail and rage at the rate you do. But if your own ima

gination be strongly shocked and moved, you cannot therefore conclude, that a sincere endeavour to free a science, so useful and ornamental to human life, from those subtilties, obscurities, and paradoxes, which render it inaccessible to most men, will be thought a criminal undertaking by such as are in their right mind. Much less can you hope that an illustrious seminary of learned men which hath produced so many free-spirited inquiries after truth, will at once enter into your passions and degenerate into a nest of bigots.

IX. I observe upon the inconsistency of certain infidel analysts. I remark some defects in the principles of the modern analysis. I take the liberty decently to dissent from Sir Isaac Newton. I propose some helps to abridge the trouble of mathematical studies, and render them more useful. What is there in all this that should make you declaim on the usefulness of practical mathematics? That should move you to cry out, Spain, inquisition, odium theologicum? By what figure of speech, do you extend what is said of the modern analysis to mathematics in general, or what is said of mathematical infidels to all mathematicians, or the confuting an error in science to burning or hanging the authors? But it is nothing new or strange, that men should choose to indulge their passions, rather than quit their opinions, how absurd soever. Hence the frightful visions and tragical uproars of bigoted men, be the subject of their bigotry what it will. A very remarkable instance of this you give, p. 27, where, upon my having said that a deference to certain mathematical infidels, as I was credibly informed, had been one motive to infidelity, you ask, with no small emotion, " For God's sake are we in England or in Spain? Is "this the language of a familiar who is whispering an inquisitor." &c? And the page before you exclaim in the following words, "Let us burn or hang up all the mathematicians in Great Britain, or halloo the mob upon them to tear them to pieces

every mother's son of them tros rutulusve fuat, laymen or clergyman, &c. Let us dig up the bodies of Dr. Barrow and Sir Isaac Newton, and burn them under the gallows," &c.

X. The reader need not be a mathematician, to see how vain all this tragedy of yours is. And if he be as thoroughly satisfied as I am, that the cause of fluxions cannot be defended by reason, he will be as little surprised as I am, to see you betake yourself to the arts of all bigoted men, raising terror and calling in the passions to your assistance. Whether those rhetorical flourishes about the inquisition and the gallies are not quite ridiculous, I leave to be determined by the reader: who will also judge (though he should not beskilled in geometry) whether I have given the least grounds for this and a world of such-like declamation? And whether I have not constantly treated those celebrated writers with all proper respect, though I take the liberty in certain points to differ from them?

XI. As I heartily abhor an inquisition in faith, so I think you have no right to erect one in science. At the time of writing your defence you seem to have been overcome with passion; but now, you may be supposed cool, I desire you to reflect whether it be not wrote in the true spirit of an inquisitor. Whether this becomes a person so exceeding delicate himself upon that point? And whether your brethren the analysts will think themselves honoured or obliged by you, for having defended their doctrine, in the same manner as any declaiming bigot would defend transubstantiation? The same false colours, the same intemperate sallies, and the same indignation against common sense!

XII. In a matter of mere science, where authority hath nothing to do, you constantly endeavour to overbear me with authorities, and load me with envy. If F see a sophism in the writings of a great author, and, in compliment to his understanding, suspect he could hard

ly be quite satisfied with his own demonstration; this sets you on declaiming for several pages. It is pompously set forth as a criminal method of detracting from great men, as a concerted project to lessen their reputation, as making them pass for impostors. If I publish my free thoughts, which I have as much right to publish as any other man, it is imputed to rashness and vanity and the love of opposition. Though perhaps my late publication, of what had been hinted twenty-five years ago, may acquit me of this charge in the eyes of an impartial reader. But when I consider the perplexities that beset a man who undertakes to defend the doctrine of fluxions, I can easily forgive your anger.

XIII. Two sorts of learned men there are: one who candidly seek truth by rational means. These are never averse to have their principles looked into, and examined by the test of reason. Another sort there is who learn by rote a set of principles and a way of thinking which happen to be in vogue. These betray themselves by their anger and surprise, whenever their principles are freely canvassed. But you must not expect, that your reader will make himself a party to your passions or your prejudices. I freely own that Sir Isaac Newton hath shewed himself an extraordinary mathematician, a profound naturalist, a person of the greatest abilities and erudition. Thus far I can readily go, but I cannot go to the lengths that you do. I shall never say of him as you do, Vestigia pronus adoro (p. 70). This same adoration that you pay to him I will pay only to truth.

XIV. You may, indeed, yourself be an idolater of whom you please: but then you have no right to insult and exclaim at other men, because they do not adore your idol. Great as Sir Isaac Newton was, I think he hath, on more occasions than one, shewed himself not to be infallible. Particularly, his demonstration of the doctrine of fluxions I take to be defective, and I cannot help thinking that he was not quite pleased with it him