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I. WHEN I read your defence of the Britisi mathematicians, I
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II. You express an extreme surprige and concern, that I mouid talie much pains to depreciate one of the nobtest sciences, to disparage v and traduce a set os learned men whose labo urs so greatly conduce to the honour of this istand P. s), to tessen the reputation and authori ty of Sir I ac Ne ton and his followers, by me ing that they a re not such masters of reason as they a re generalty presumed to be; and to depreciate the science they profess, by demonstrating to the worid, that it is not of that clearnesi and certa in ty as is commonly imagined. Alt which, you insist, appears very strange to you and the rest of that ' Dinous Universi ty, who pla in ly see of how great use mathematical learning is to mankind. Hence you take occasion to declaim on theu sesu inest os mathematics in the severat branches, and then to redoubleyour surprige and ama gement P. I9 and go . To ait whicli declamation I reply that it is qui te beside the purpose. For Ι allow, and always have alio ined, iis fuit claim os merit to whateuer is useful and true in themathematics: hut that whicli is not so, the lese it employs men's time and thoughis, the bet ter. Aiad aster ali you have faid or can say, Ι heli evethe unprejudiced reader Will thin k with me, that things obscure are notthere re sacred; and that it is no more a crime, to can vase and detectun und principies or false rea nings in mathematics, than in any other part of learning. III. Yos are, it stems, much at a lose to understand the usefulnest ortendency or prudence of my attempl. I thought I had lassiciently e pla ined this in the Analyst. But sor your further satisfaction stiali here teli you, it is very weli linown, that severat persons who deride Dith and
mysteries in religion, admit the doctrine os fluxions for true and certain. Nom is it be me n that fluxions are reatly most incomprehensi bie myste- sies, and that those, who belle ve them to be clear and scienti fio, do en-teria in an implicii faith in the author of that method; will not this fur-nim a fair argumentum ad hominem against men, Who reject that very
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without them even in science t
ei ther in mathematics, or in any other part of learning ; What a vatis it, or indeed what right hath any one to assi, why at this or that time; in this or that manner; upon this or that moti vel Let the reader judge, is it lassice not, that what I publim is true, and that I have a right topublim such truths, when and how I please in a Dee country. V. I do not say, that mathematicians, as lach, a re infideis; or that geometry is a frien d to infideli ty, which you unt ruty insinuate, as youdo many other things; whence you raise topics for invective : but I saythere are certa in mathematicians, who are known to be se; and that there are Others, Who a re not mathematicians, who are influenced by
a regard for their aut hori ty. Some perhaps, who live in the Universiity, may not be appri sed of this: but the intelligent and observing reader, ho lives in the worid, and is acqua in ted with the humo ur of the times. and the characters of men, is weli a are, there a re too many that deride mysteries, and y et admire fluxions; who yield that Dith to a mere mor
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VI. Τhere are, I mahe no doubi, among the mathematicians many
philosopher yourseis: but I know, the minute philosophers mahe just suci,
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2I3 A Defence of Free- Thinling, Uc. pari, in pretending to reject the christi an religion, hecause he cannot be-lieve what he doth not comprehend; or hecause he cannot assent with out evidence; or hecause he cannot submit his Dith to authori ty. Whether there a re such infideis, I submit to the judgment of the reader; form y own part I mahe no doubt of it, having seen se me stirewd si grasthereos myself, and having been very credibiy informed thereos by others. Nor doth this charge stem the lese credibie, sor your being so sensi blyto uched, and denying it with so much passion. You, indeed, do not sit clito affirm, that the persons Who insor med me a re a paci of bas proflansdand impudent liars P. et f). How far the reader Will thinii fit to adoptyour passions I cannot say; but I can truly sau, the late celebrated MLindison is one of the persons, whom you are pleased to characterire in those modest and mannerly term s. He astu red me that the infideli ty ofa certain noted mathematiCian, stili living, was one principat reason aiasigned by a witly man of those times sor his being an infidet. Not, that I imaginc geometry disposeth men to infidelity : but that hom other causes, such as presumptiora, ignorance, or vani ty, like Other men geometricians also be come in fideis, and that the sui posed light and eviden coof their science gaios credit to their infideli ty. VIII. You reproaeli me with calumny, detraction, and artifice P. I s You recommend such means as a re innocent and just, rather than the criminal method of lessening or detracting from my opponenis sibi θμ You accuse me of the orium theologicum, the intemperate geat os divines, that I do sane super vias antiquas P. I. 3 illi much more to thes a me effeci. For ait whicli charge I depend on the re ader's candour, thathe will not take your Word, but read and jud ge for himself. In whichea se he Mill he able to discern though he mould be no mathematician)hois passionale and unjust your reproaches a re, and how possibie it is, sora man to cry out against calum ny and practi se it in the sanae breath. Considering hore impatient ali man kind. are Wheni their prejudices arelooked
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not there re conclude, that a sincere endeavour to Dee a science, use-
fui and ornamental to human ii se, irom those subtilites, obscurities, and paradoxes whicli render it inaccessibie to most men, will be thought a criminal underi aking by such as are in their right mind. Mucii test canyou hope that an illustrious seminary of learned men, Which hath produced so many Dee- spiri ted inquirers aster truth, will at once enter into our passioris and degenerate into a nest of bigois. IX. I observe upon the inconsistency of certa in infidet analysts. I re marii seme defecis in the principies of the modem analysis. I tal e theliberi y decently to dissent Dom Sir I ac Newton. I propose some hel ps toubridge the tro table os mathematical studies and render them more V tui. What is there in ali this that should mahe you declaim on the u ita inesse of praelicat mathematics t That mould move you lo cry out Spata, inquistion, odium theologicum By what figure of speech, do you extend, what is Laid of the modern analysiis, to mathematics in generat, Or Whatis Laid os mathematical in fideis to ali mathematicians, Or the consul ingata error in science to burning or han ging the authorst But it is nothingneis or strange, that men shouid choose to indulge their pastions, rat herthan quit their opinions horir absurd Qever. Henco the fright fui vision sand tragical uproars of bigo ted men, be the subject of their bigo try whatit wili. A very remarhable instance of this you give P. 27 Where, UP-on my having se id that a deferen ce to certa in mathematical in fideis, as Iwas credibiy insor med, si ad been one motive to infideli ty, you ask withno smali emotion, For God's salie are we in England or in Spain J Is this the langu age of a familiar who is whis pering an inquisitor, Sc 7 And the page besore you exclaim in the solio ing words. v I et us burn
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tragedy of yours is. And is he be as thoroughly satisfied as I am, that the cause of fluxions cannot be defended by reason, he will be as liti lesurprised as I am, to see you helahe yourself to the aris of ali bigoted men, raising terror and calling in the passions to your assistance. Whether those rhetorical Bouri es about the inquisition and the gallies arenot qui te ridiculous, I leave to he determined by the reader. Who will
given the least grounds, for this and a world of such like declamation tAnd whether I have not constantly trealed those celebrated writers, withali proper respeci, though I take the liberty in certain potnis to disserfrom them tXI. As I heartily abhor an inquisition in faith, so I thinii you have noright to erect one in science. At the time of writing your defence youseem to have been overcome with passion : but now you may be sup- posed cool, I destre you to reflect whether it be not wrote in the true spirit os an inquisitor. Whether this becomes a person se exceeding delicate himself upon that potni t And whether your brethren the Analysis will thin k thenaseives honoured or obliged by you, sor having defendediheir doctrino, in the fame manner as any declai ming bigot would defend transubstantiation 8 The same false colours, the fame intemperate salties, and the fame indignation against common senset XII. In a matter of mere science, where authority hath nothing to do,
vitii enuy. Is I see a sophism in the writings os a great author, arid, in
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complement to his understanding, suspect he could hardly be qui te fatisfied with his own demonstration : this seis you on declaim ing sor severat pages. It is pompoussy set for th as a criminal method of detractingsrom great men, as a concerted project to testen their reputation, as making them pasi sor impostors. Is I publisia my Dee thoughts, whicli I haveas much right to publim a s any other man, it is imputcd to ram ness and vani ty and the love of opposition. Though perhaps my late publication, of what had been hin ted twenty-five years ago, may aequit me of this charge in the eyes of an impartiat reader. But when I consider the perplexities that beset a man, who underi akes to defend the doctrine os fluxioris, I can easi ly sergive Iour anger. XIII. Two foris of learned men there are: one, who candid ly seel fruth by rational means. These a re ne ver averse to have their principies looked into, and examined by the test os reason. Another sori there is who learn by rote a set os principies and a way of thinking which happen to be in vogue. These bet ray thenaselves by their anger and sur-prile, whene ver their principies a re neely canuassed. But you must notexpect, that your reader Will malle himself a party to your pastions oryour prejudices. I Deely own that Sir Isaac Newton fiath shewed himselfan extraordinary mathematician, a pro und naturalist, a person of the greatest ab ilities and erudition. Thus far I can readi ly go, but I cannot
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A Defence of Fre Thinling, G. defective, and I cannot help thinhing that he was not qui te pleased w thit himself And yet this doth not hinder but the method may be usefui,
considered as an art of inventiora. You, who are a mathematician, mustachnowledge, there have been divers lacti methods admitted in mathematics, whicli are not demonstrative. Such, sor instance, are the inductions of Doctor Mallis in his Arithmetic os Infinites, and lach, what Harrior and, after him, Descartes have wrote concerning the roots of assected aequations. It will not, nevertheless, thence follow that tho methods are uselest; but only, that they are not to be allo ed of a. premises in a strict demonstration. XV. No great name upon ea rili mali ever malae me accept things obscure sor clear, or sophitas sor demonstrations. Nor may you ever liopeto deter me Dom Deely speahing what I Deely thinli, by those arguments ab invidia whicli at every turn you employ against me. You representyourself P. 32 as a man, Ghose highes ambition is in the Aises degree toimitate Sir Isaac Newton. It might, perhaps, have sui ted Miter Withyour appellation os Philalethes, and been altogether as laudabie, is yourhighest ambition had been to discover truth. Very consistently with the character you give of yourself, you speak of it as a sori os crinae P. o to thinli it possibie, you fhould ever se further, or go b ond Sir Isaac Newton. And I am persuaded you speah the sentiments of many more
perly be called a philosopher. XVI. Because I am not guit ty of your mean idolatry, you in 'eighagainst me as a person concei ted of my own abilities: not considering Vo L. II. F f that
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that a person os test abilities may know more on a certain potnt than one of greater; not considering that a purblind cye, in a close and narro Vie , may discern more os a thing, than a much better eye in amore extensive prospect; not considering that this is to fix a ne plus ultra,
to put a stop to ali future inquiries; las ly, not considering that this is in fact, se much as in you lies, converting the republic of letters into an absolute monarchy, that it is even introducing a Lind of philosophic po-pery among a free people.
prehensi ble : that second, third and Durth fluxioris are yet more incomprehensi ble : that it is not possibie to conceive a simple infinitesimal, thatit is yet lese possibie to conceive an infinitesimal os an infinitesimal, and so onward '. What have you to say in ans er to thist Do you attemptio clear Up the notion of a fluxion or a disserence t Nothing like it, you only assure me upon your bare Word) Dom your Own experience, and that os severat others whom y could name, that the doctrine of fluxions may be clearly conceived and distinctly comprehended; and that is I am puggled about it and do not understand it, yet others do.
XVIII. Upon this poliat every reader of common sense may judge asweli as the most pro und mathematician. The simple apprehension ofa thing defined is not made more persect by any subsequent progress in mathematics. What any man evidently knows, he knows as weli as youor Sir Isaac Newton. And every one can know whether the object of this method be as you would have us thinli) clearly conceivable. Tojudge of this, no depili of science is requisite, but only a bare attentionto what passes in his own mind. And the sume is to be underctood of