or，ADefenceofSirIsaacNewtonandtheBritishMathematicians，InaLettertotheAuthoroftheAnalyst。WhereinitisexaminedHowfartheConductofsuchDivinesasintermixtheInterestofReligionwiththeirprivateDisputesandPassions，andallowneitherLearningnorReasontothosetheydifferfrom，isofHonourorServicetoChristianity，oragreeabletotheExampleofourBlessedSaviourandhisApostles。
ByPHILALETHESCANTABRIGIENSIS（JamesJurin）
Nedeusintersit，nisidignusvindicenodusInciderit。TheContentsMathematiciansaccusedofInfidelity，ofpervertingotherpersonstoInfidelity，andoferrorintheirownscience。TitlepagetotheAnalystgiveshopesofaMathematicalDemonstrationoftheChristianReligion。Thisnotattempted。NomorecertaintyinthemodernAnalysis，thanintheChristianReligion。NohonourtoChristianityfromthiscomparison。DesigntolessenthereputationofSirIsaacNewtonandhisfollowersandtheirscience。Mathematicksausefulscience。Nottoomuchstudied。Oughtnottobedepreciated。Reasonforthisdesign。IfMathematiciansareInfidels，itoughtnotinprudencetobepublished。
ObjectionagainstourSaviour。Noroomforthisobjectioninourdays。Thereputationofadversariestoberuined。OdiumTheologicum。NotthepracticeofourSaviourandhisApostles。TheyallowedwisdomandreasontoInfidels。TheChurchofChristinnodanger。ThepropermethodofopposingMathematicians。Aninscriptionforpulpits。ZealoftheClergy。ExamplesetthembytheAuthoroftheAnalyst。Solemnhymnproposedtobesungbythemtohishonour。MathematiciansmistakeninthemethodofFluxions。Maybegoodreasonersnotwithstanding。Adangerousundertaking。Unnecessary。Thebestreasoners，thebestChristians。
DoubtwhetherzealforChristianitywerethemotivetowritingtheAnalyst。Reasonforthatdoubt。ThatAuthor’sformerbehaviourtoMathematicians。Truemotivetothisundertaking。Thetreatmenthehasgiventosomeofthegreatestmen。Hispresumptionandvanity。HisproofofInfidelityagainstMathematicians。AproposaltohangorburnalltheMathematiciansinGreatBritain。WickednessandfollyoftheirAccusers。ExtremecredulityoftheAuthoroftheAnalyst。UnlikelyhoodofInfidelityintheclearestreasoners。ReputationofMathematicksgivesnoauthorityinDivinity，LaworPhysick。
ProvedfromtheexampleofDr。BarrowandSirIsaacNewton。ObjectionsagainstthemethodofFluxions。Fluxionsobscuretowhatreaders。Cleartoothers。DisingenuityoftheAuthoroftheAnalyst。FalsereasoninginFluxions。Firstinstanceoferror。Greattriumphuponthis。Nogreatoccasionforit。Caseproposedforunmathematicalreaders。AFrenchMarquisaccusedofusingtoolittleceremony。Injusticeofthisaccusation。SirIsaacNewtonchargedwithusingtricksandartifices。Blindnessoftheaccuser。Adifficultcase。TwowaysofendingaMathematicaldispute，SirIsaacintheright。Finalcauseofhisproceeding。Ajustreasonforhisproceeding。Velocityofarectanglewhat？Assbetweentwobottlesofhay。WhisperfromaGhost。Momentofarectanglewhat？SirIsaac’sproceedingmoregeometricalthanthatproposedbyhiscensurer。Thecensurer’swantofcaution。Advicetohim。SirIsaac’sforesight，humanity，prudenceandcaution。
Dangerofthosewhounadvisedlyattackhim。Anobjectionprevented。Ascrupleremoved。SecondinstanceoferrorinthemethodofFluxions。Twoinconsistentsuppositions。NodangertoReligionfromsuchreasoners。HorribleblunderchargeduponSirIsaacNewton。Inquiredinto。ProvedtobelongtotheAuthoroftheAnalyst。ArtsandfallaciesimputedtoSirIsaacNewton。Notwanted，norusedbyhim。SirIsaacNewtonsupposednottobesatisfiedwithhisownnotions。
Injusticeofsuchasuppositionwithregardtohim。Ortopreachers。OrtotheAuthoroftheMinutePhilosopher。SirIsaac’swordsmisrepresentedonpurposetodrawafalseinferencefromthem。Truthsupposedtoarisefromthecontrastoftwoerrors。AghostexorcisedwiththePrincipiaMathematica。SirIsaacNewtonproceedsblindfold。Fastasleep。Monstrouslylucky。Thetwoerrorsexaminedinto。Areatmostinfinitelysmall。Noerrorsatall。Amottounluckilychosen。
Abeamlessthanamote。ExcellencyofthemethodofFluxionsowingtothesepretendederrors。Mathematicianswhentheycommitthem，knowwhattheyaredoing。SirIsaacNewtonwasawareofthisobjection，andprovidedagainstit。Mr。Lockechargedwithcontradictinghimself。Intwoinstances。GeneralIdeasnecessarytoScience。DistinctionbetweenabstractandgeneralIdeas。AbstractIdeashowacquired。GeneralIdeashowacquired。ExampleofthemethodofacquiringabstractandgeneralIdeas，takenfromBotany。AnotherexampletakenfromGeometry。GeneralIdeaofaTriangle。Easilyacquiredbyalearner。HowtheAuthoroftheAnalystmayacquireit。NotmoredifficulttoconceivethantheIdeaofanyparticularspeciesofTriangles。OrthantheIdeaofanAngle。MrLockegroslymisrepresented。Firstinstanceofcontradictionexamined。Secondinstance。OneofMr。Locke’strapsforCavillers。Conclusion。ALettertotheAuthoroftheAnalyst。Cambridge，April10，1734。SIR，AsIamoneofthosemanypersonsinthisUniversity，whohaveprofitedbyyourlearnedwritings，andwhogreatlyadmirethedepthofthought，theforceofreason，andtheperspicuityofexpressionthatgenerallyappearsinthem；Icannotbutbeextremelysurprizedandconcerned，thataGentlemanofyourabilitiesshouldhavetakensomuchpainsnotonlytodepreciateoneofthenoblestofallthesciences，buttodisparage，totraduce，andeventodefameasetoflearnedmen，whoselabourssogreatlyconducetothehonourofthisisland，andtothegeneralgoodofmankind。YouwilleasilyseethatIspeakofMathematicks，andtheBritishMathematicians，andofthemannerinwhichyouhavebeenpleasedtotreattheminyourlatepamphlet，intitled，TheAnalyst。Thatdiscourse，itistrue，isseeminglydirectedtoonepersononly；butyouarenotgotthroughyourfirstsection，beforeyouspeakoftoomanymoreofthelikecharacterwithhim；andinthecontentstothatverysection，aswellasinalltherestofyourdiscourse，youtalkofMathematiciansinsogeneralamanner，thatIamafraidyourreaderswillthinkveryfew，ifanyofthoseGentlemenaretobeexceptedoutofthatnumber，againstwhichyoubringsoheavyacharge。
Thischarge，Sir，consistsofthreeprincipalpoints。OfinfidelitywithregardtotheChristianReligion。OfendeavouringtomakeothersInfidels，andsucceedinginthoseendeavoursbymeansofthedeferencewhichispaidtotheirjudgment，asbeingpresumedtobeofallmenthegreatestmastersofreason。Oferrorandfalsereasoningintheirownscience。This，SiristhechargeyouhavebeenpleasedtobringagainstourMathematicians，andIintendparticularlytoexaminewithwhatreasonandtruthyouhavedoneso。ButbeforeIdothis，Imustbegleavetomakeafewobservationsupontheintentanddesignofyourtreatise，theadvantagetobeexpectedfromit，theprudence，andjusticeandhonourofthisdesign；andafterthattoinquirewhetherthemotivetoyourwritingitwerereallywhatyoupretendandavow。
IfyourdesignweretobeguessedatfromyourTitle-page，whereinyouprofesstoexamine，whethertheobject，principlesandinferencesofthemodernAnalystsaremoredistinctlyconceived，ormoreevidentlydeduced，thanreligiousmysteriesandpointsoffaith，onewouldbeapttoconcludeyourintentwastoshew，thatthemysteriesofReligionmightbeasclearlyconceived，astheobjectandprinciplesofthemodernAnalysis；andthattheseveralpointsofourFaithmightbeasevidentlydeduced，astheinferencesofthatAnalysisarefromitsprinciples；or，inotherwords，thatyouwereabouttogiveusaMathematicaldemonstration，oroneofequalclearnessandcertainty，ofthetruthoftheChristianReligion。This，Isay，fromthewordsofyourTitle-pageonewouldnaturallytaketobeyourdesign：
butitissofarfrombeingso，thatthroughoutyourwholediscourse，thoughaddressedtoanInfidelMathematician，IdonotfindtheleastattempttowardsestablishingtheevidenceofourChristianFaith。
IfindthereforenootherwayofreconcilingyourTitle-pagewiththesubstanceofyourdiscourse，thanbysupposingyoupretendtoprove，thattheobject，principles，andinferencesofthemodernAnalysisarenotmoredistinctlyconceived，normoreevidentlydeduced，thanreligiousMysteriesandpointofFaith，i。e。thatthereisnomoreevidenceandcertaintyinthemodernAnalysis，thanintheChristianReligion。ButhowfaryoudohonourtoChristianity，byenteringintoacomparisonbetweentheevidenceandcertaintyoftheReligiontaughtusbyourSaviourandhisApostles，andtheevidenceandcertaintyofthedoctrineofFluxionsdeliveredbySirIsaacNewtonandhisfollowers，adoctrineinyouropinion，fulloferror，falsereasoning，manifestsophisms，fallaciousandinconsistentwaysofarguing，suchaswouldnotbeallowedofinDivinity，IshallleavetoyourbrethrentheDivinestoconsider。
Nottoinsistthereforetoolonguponthis，IshallnowdismissyourTitle-page，andshallcometoyourdeclaredandavoweddesign，which，itmustbeowned，youhavesteadilypursuedthroughyourwholediscourse；
tolessenthereputationandauthorityofSirIsaacNewtonandhisfollowers，byshewingthattheyarenotsuchgreatmastersofreason，astheyaregenerallypresumedtobe；andtodepreciatethesciencetheyprofess，bydemonstratingtotheworldthatitisnotofthatclearnessandcertainty，asiscommonlyimagined。
Youmustexcuseus，Sir，ifthisdesignappearsaverystrangeonetousoftheUniversity，whoplainlyseeofhowgreatuseMathematicalLearningistomankind，notonlytothosewhomakeitapartoftheirstudies，buttoalltherestoftheworld，whowithoutknowinganythingofMathematicks，doyetdailyandhourlyreapthebenefitoftheinventionsofMathematicalmeninallpartsoflife，especiallyinMechanicalarts，inArchitecture，Civil，Naval，andMilitary，andinNavigation，uponwhichtheprosperityandsecurityofthisNationsomuchdepends。Thoughweseeandknow，thatthestudyofMathematicksflourishesamongus，asmuchasinanypartoftheworld；andthatouryouthhaveasgoodassistanceandopportunitiesforcultivatingthatscience，asareanywheretobemetwith；yetwearefarfromthinkingthattoomanyofourstudentsengageinthispursuit，orspendtoomuchoftheirtimeinit。Believeme，Sir，thegeneralityofyouthhavemoreneedofthespurthanthebridle，whentheyenteruponastudy，thatrequiressolaboriousanattention，andsoconstantanapplication。
Whythen，wouldweask，isthestudyofMathematickstobediscouragedandundervalued？Whatcouldbethereasonormotiveforyourengaginginsuchadesign。
Iperceiveyouranswerisready。MathematiciansareInfidels，andmakeuseoftheirreputationandauthority，asbeingesteemedthegreatestMastersofreason，topervertotherpersonstoinfidelity。Really，Sir，thisassertionofyoursisnewtous，andextremelysurprizesus。
Weseenothingofithere，andcannoteasilybelieveitissoanywhereelse。
Butadmittingitforthepresenttobetrue；haveyouwellconsideredwhetheritbefortheadvantageofChristianity，topublishtotheworld，thatanumeroussetoflearnedmen，andofsuchlearnedmenasaresupposedtoapprehendmoredistinctly，considermoreclosely，infermorejustly，concludemoreaccuratelythanothermen，[Analyst，p。4。]donotbelievethetruthoftheChristianReligion？This，methinks，isanassertionfitterforanAlciphron，oraLysiclestomake，thanforaChristianDivine。TellitnotinGath，publishitnotinthestreetsofAskalon。
ThoughtheevidenceandcertaintyofourholyReligionissofirmlyestablished，asnottobeshakenbythearguments，muchlessbythereputationandauthorityofanyunbelieverswhatsoever；yet，Iamafraid，itwouldbeagreatstumblingblocktomenofweakheads，iftheyweremadetobelieve，thatthejustestandclosestreasonersweregenerallyInfidels。Youknow，Sir，itwasashrewdobjection，tho’bynomeansavalidorconclusiveone，thatwasmadeagainstourSaviour。HaveanyoftheHighPriests，orofthePharisees（themenofgreatestlearning，andesteemedthegreatestmastersofreasoninthosedays）believedinhim？Andiftherewereanyroomtorenewthisobjectioninourdays，asconsideringthepietyandzealoftheChristianPriestsofalldegrees，andtheirconstantandsincereattachmenttotheinterestoftheChristianReligionandtonothingelse，surelythereisnot，itwouldindeedbeaperplexingone。
Ifweshouldnowmakeyouafartherconcession，andsupposeitnotonlytobetrue，buttobepublicklyandnotoriouslyknown，thatthebodyofourMathematiciansareInfidelsandenemiestoChristianity，whatthinkyouisthemethodtobetaken？Whatother，youwillsay，buttoruinthereputationofouradversaries？Ifwecannotattackthemintheirlivesandconversations，wemustatleastendeavourtoshewthattheyaredestituteoflearningandreason。Thiswilllessentheirauthorityamongthepeople，willpreventtheirmisleadingunwarypersonsinmattersofthehighestconcernment，[Analyst，p。3。]andwilltakeoffthatbiasanddeferencefortheirjudgment，[p。4。]whichcausesweakmindstosubmittotheirdecisions，wheretheyhavenorighttodecide[Ibid。]。Whyreally，Sir，thismaydoverywell，ifyouaresureofsucceedinginyourattempt。
Atleastitmustbeacknowledged，thatyoudostaresuperviasantiquas。
ThisistheverymethodwhichtheOdiumTheologicum，theintemperatezealofDivineshasalwayspursued，andhaspracticedwithgreatsuccessformanyages。ButImustbegleavetoobserve，thatitisaverydifferentcoursefromwhatwastakenbyJesusChristandhisApostlesonthelikeoccasion。Ithankthee，OFather，Lordofheavenandearth，saysourSaviour，thatthouhasthidthesethingsfromthewiseandprudent，andhastrevealedthemuntobabes。Andafterhisexample，thegreatApostleoftheGentiles，thoughhewasfullysensibleoftheoppositionhemetwithinpreachingtheGospel，fromtheGreekPhilosophers；
yetdidnotthinkitnecessarytoenterthelistswiththeDisciplesofPlatoandtheStoicks，andtoshewthattheydidnotunderstandGeometryorPhilosophy；inordertolessentheirreputation，andtherebytotakeofffromtheweightoftheiroppositiontoChristianity。Hecontentshimselfwithobserving，thatnotmanywise，notmanylearnedarecalled；
throughtheGreeksseekafterwisdom，thoughChristcrucifiedisuntotheGreeksfoolishness，yetthewisdomoftheworldisfoolishnesswithGod。ManymorepassagesmaybefoundinhisEpistlestothesamepurpose。
Yousee，Sir，thatneitherourSaviour，norhisApostles，whowereguidedbyhisHolySpirit，deniedeitherwisdom，orprudence，orlearningtosuchunbelieversaswerereallypossessedofthosequalities：theywellknewtherewasnothingtofear，thattherewasnoinchantmentagainstJacob，nordivinationagainstIsrael，andthatnohumanabilitiesoraccomplishmentswhatsoevercouldbeabletowithstandtheDivineauthority，andtheirresistibleevidenceoftheReligiontheytaughtanddefended。
Itwillbesaidperhaps，thisistoogreatapatternforyoutofollow；
thoughtherewasnofearthattheabilities，thereputationandauthorityofanyadversarieswhatsoevercouldwithstandourSaviourorhisApostles；
yetwhatwasnomatchforthem，maypossiblybetoohardforyou，unlessyoutakepropermeanstopreventit。How，Sir！HasnotourSaviourpromisedtobewithyouuntotheendoftheworld？Hashenotassuredus，thateventhegatesofhellshallnotprevailagainsthisChurch？Afterthisdeclaration，isthereanythingtofear？Cananymeansbenecessary，butsuchashehasrecommendedbyhispracticeandexample？Cancalumny，anddetraction，andartificetolessenthereputationofyouradversaries，bemeansfittobeusedbythefollowersofSt。PaulandofJesusChrist？Ifanyhumanmeansarerequisite，surelytheyshouldbesuchasareinnocentandjust，ratherthanthiscriminalmethodoflesseningordetractingfromyouropponents。
Whatarethese？youwillsay。Whyplainly，Sir，tofightyourenemieswiththeirownweapons，toendeavourtoexcelinthoseartswithwhichtheyopposeyou。St。Paulmadehimselfallthingstoallmen，iftherebyhemightgainsome。IfMathematiciansaresuchdangerousadversariestoChristianity，lettheChurchofEnglandtakecareoftheeducationofherClergy，letherwriteoverherpulpits，asPlatoissaidtohavedoneovertheentrancetohisschoolLetnomanenterintoorders，unlesshebeanableMathematician。Whenthisisdone，Sir，letusseewhatMathematicalInfidelwilldaretobeardaChristianPriest，asgreatamasterofreasonashimself，andarmedbesideswithhisTheologicalaccomplishments，andtheauthorityofhissacredFunction，butaboveallwiththatineffableandincomprehensibleGift，whicheveryoneofyoureceiveatyourordination。
SurelynomanwillthinkthistoolaboriousataskforthezealandpietyoftheChristianClergytoundertake，ifthesalvationofsoulsdependsuponit。Donotweseehowwhollytheydevotethemselvestothisonlyendandpurpose；how，neglectinganddespisingallthegratificationsofsense，alltheallurementsofworldlyinterest，ofhonour，richesandpower，theyalloteveryportionoftheirtimethatcanpossiblybesparedfromthenecessaryexercisesoftheirfunction，tothebetterenablingthemselvestotakecareofthesoulscommittedtotheircharge？Donottheyforthispurpose，withincrediblepainsandindefatigableindustry，ransackandmakethemselvesmastersofallthetreasuresofantiquitysacredandprofane？
Hencethosenervousandcogentarguments，thatinvinciblepowerofreason，thatresistlessforceofeloquencewhichthundersfromeverypulpit，towithstandthegainsayer，toreclaimthedeluded，toconfirmthewavering，tosilence，confoundandastonishtheobstinate，incorrigibleHeretickandInfidel。Andshallwe，canwesuppose，thatasmallpartoftheirtimeandpainswillnotbeallowedforarmingthemselveswithproperweaponstoencounterourMathematicalunbelievers？You，Sir，havealreadyshownthemhoweasilythisistobedone；sincenotwithstandingyourmanyandgreatavocations，bothathomeandinverydistantregions，youhavenotonlymadeyourselfmasterofthemostprofound，themostobscureandmostdifficultpartsofthatstudy；butbylookingcloserandmoreattentivelyintothemthananybodyhaseverdonebeforeyou，havediscoveredtheirmostsecretdefects，andhaveunravelledtheirmosthiddenandintricatefallacies。AndImakenodoubtbutthatyourgreatexamplewillexcitesuchaspiritofpietyandzeal，andindustryamongyourbrethren，thatintimetocomeevenEuclid，andArchimedes，andAppollonius，iftheyarejudgedtostandinthewayandobstructtheprogressofChristianity，willbeshewntoaboundasmuchwithfalseandfallaciousreasoning，asSirIsaacNewton。
This，Sir，wouldbetheinnocent，thejustandhonourablemethodofencountringtheadversariesofourReligion；rathertomeettheminthefield，thantoseektonailtheircannon，toblowuptheirammunition，andsetfiretotheirmagazines：butifyouchusetheother，assafer，thoughlesscommendable，aseasiertoyourbrethren，thoughmorelaborioustoyourself，Iamcontent；andprovidedyougothroughwiththeundertaking，shallbereadytojoinwiththeReverendDefendersofourfaith，inasolemnchorustoyoureternalhonourandrenown。Unushomonobiscarpendorestituitrem：
Nonponebatenimrumoresantesalutem：
Ergomagisq；magisq；virinuncgloriaclaret。Nowtherefore，Sir，wecometoourmainandprincipalpoint，toexaminebywhatmeans，inordertopreventthedangerthatChristianityisthreatenedwithfromourMathematicalInfidels，youproposetolessentheirreputation，andtoshewthattheyarenotsuchjustandclosereasonersasiscommonlyimagined。Ishallprove，sayyou，thatthemethodofFluxionsinventedbySirIsaacNewton，andimplicitlyreceivedbyallourMathematicians，isbuiltonfalseandprecariousprinciples。
Thiswilldosomething，Imustconfess，inasmuchasitwillshew，thatMathematiciansaremenandliabletoerror。ButiftheyaremistakeninthinkingthemethodofFluxionstobeasoundandjustone，willitfollowfromthis，thatinalltheotherpartsoftheirsciencetheydonotreasonjustlyandaccurately？Youknowverywell，Sir，thatFluxionsareofverylateinvention，andthatthoughtheyareanobleandusefulpartofMathematicks，yetthewholeofMathematicksdoesnotconsistinFluxions。Mathematicianswerealwaysreckonedtobegreatmastersofreason，beforeFluxionswereinvented。AndtheuseofFluxionsdoesbynomeanssupersedethedoctrineofGeometrydeliveredbyEuclid，Apolloniusandsomanyothersofthegreatmastersbothantientandmodern，nottomentionAlgebraandallotherpartsoftheMathematicks，againstwhichyoumakenoobjection；willitnotfollowthatMathematiciansarestilltobeesteemedjustandaccuratereasoners，thoughtheyhavebeenledintosomemistakesinthemethodofFluxions，bytheirimplicitdeferencetothejudgmentoftheGreatAuthorofthatinvention？
Butfarther，ifitshouldappearthatthereisnomistakeinthatmethod，thattheobjectofitisclearlyconceived，thatitsprinciplesareevidentandcertain，thattheinferencesdrawnfromthemarejustlydeduced，thatthewholedoctrineisestablisheduponaclear，justandsolidfoundation，andthisitisyouonlywhohavebeenguiltyofamostinexcusableoversight，inwhichthemeanestMathematicianyoucouldhaveconsulted，wouldhaveimmediatelysetyouright：whatthenwillbecomeofyournobleandwellconcertedprojecttolessenthereputationofMathematiciansfortheserviceofChristianity？
Believeme，Sir，ourholyreligionstandsinnoneedofsuchattemptstoserveit。Nontaliauxilio，necdefensoribusistis。ThebetterreasonerseitherMathematicians，oranyothersortofmenshallbe，themorelikelywilltheybetoembracetruthwhereveritshallbefound，andconsequentlythemorelikelytoreceivethetruthandundoubtedevidenceoftheChristianReligion。
Butpray，Sir，wasitreallyandindeedtheinterestofChristianity，andnothingelse，thatpromptedyoutothisundertaking？Wasthatyouronlymotive？Thereasonofmydoubtis，thatSirIsaacNewton，whobyyourownacknowledgmentwasnotanInfidel，isnomoresparedinyourperformance，nayonthecontraryismoreseverelyhandledthananyofhisfollowers，whomyousupposetobeInfidels。Forbesidesthechargebroughtagainsthimandthemincommon，ofthewantofgoodGeometryandgoodLogic，oferrorandfalsereasoning，youfrequentlyrepresenthimasconsciousofthedefectofhisprinciples，andyetendeavouringtoimposeuponandtomisleadhisfollowersbyshifts，artificeandsubtilty，byambiguousterms，bypuzzling，palliatingandfallaciouswaysofproceeding&；c。thatis，yourepresentthemonlyasweakmen，deceivedandimposedupon；buthimbothasaweakandanillman；asnotonlydeceived，butadeceiverandanimpostor。DidzealforChristianitymoveyoutothis？TotreatinthismannerapersonwhomyouacknowledgetohavebeenabelieveroftheChristianReligion？Iamafraidwemustlookoutforsomeothermotive，andinordertodiscoverit，IshalltakethelibertyofconsideringalittlewhathasbeenyourconductwithregardtoMathematicians，notonlysinceyouhavebeeninformedoftheirbeingInfidels，butfiveandtwentyyearsago，whenitmaybereasonablysupposedyouhadheardandseenlessofthem，thanyouhavelatelydone。
AboutthattimeyoupublishedanEssaytowardsanewTheoryofVision，whereinyouwerepleasedtoinsertagreatmanyseverecensuresuponMathematicians，relatingtotheirignoranceinthefundamentalprinciplesoftheirownscience。HadyouthenheardoftheirbeingInfidels？Ifso，whyweremanyofthosecensuresgreatlymollified，uponfartherconsideration，inaneweditionofthatpiecepublishedthelastyear？Andhowcomesanewchargeofignorancetobebroughtagainstthem，onanotheraccount，atthistime？
Really，Sir，IcannowayascribeallthistoazealforChristianity：
but，ifImaybeallowedtomakeonehypothesis，itwillthenbeeasytoaccountclearlyanddistinctlyforeveryparticularofyourconduct。Itisbrieflythis，thatyouhavetoogreatanopinionofyourself，andtoomeanaoneofallothermen。Hence，notcontentwiththereputationyouhavedeservedlyacquiredofbeingaclearandjustreasoner，youcanneverrest，unlessyouconvincetheworldthatallthose，whohavehithertobeenesteemedthegreatestmastersofreason，areinthisrespectgreatlyinferiortoDr。B——-y。ElsewhytheseattacksuponMathematiciansingeneral？WhyareDr。BarrowandSirIsaacNewtonsingledoutfromamongtheMathematicians；andwhyMr。LockeandLordShaftsburyamongthosewhoareesteemedclearandjustreasoners，thoughnotMathematicians，buttoshewthatDr。B——-yisacloser，ajuster，andmoreaccuratereasonerthananyofthesefourGentlemennottobematchedperhapsbyfourothers，notonlyinGreatBritain，butintheworld？WeretheseGentlemenallunbelievers？Yourselfwillnotcallthemso；andifweexceptone，youwillnotintheleastsuspectthemtobeso。Whythenaretheyallattackedinyourwritings？Icannotpossiblysurmiseanyothercause，butthattheyareallesteemedgreatmastersofreason，andthatyouaredisposedtolessentheirreputationinordertoexaltyourown。
Twoofthemyouhavebeenpleasedtochargewithcontradiction，gross，apparent，glaringcontradiction，suchaswereutterlyunpardonableinamanwhomakestheleastpretencetoreasoning；suchasnobodycouldpossiblysuspectinthosegreatmen，whohadnotamuchgreateropinionofhisownabilitiesthanoftheirs；suchasnomanwhohadtheleastdistrustordiffidenceofhimself，couldeverimaginethemtobeguiltyof。Iwouldsay，Sir，thatyouhadsupposeditpossibleforyourselfevertofallintoanymistake；youwouldcertainly，whenyouimaginedSirIsaacNewtonandMr。Locketohavesomanifestlycontradictedthemselves，havelookedoverthosepassagesoftheirwritingsasecondtime；youwouldhavedonethiscoolly，attentivelyandconsiderately；andhadyoudoneso，youwouldhavefoundyourselfinagross，evidentmistake；andwouldhaveseenthemtobeclearlyandperfectlyconsistentwiththemselves。Imusttakeleavetoadd，thatyournotdoingso，doesevidentlyprovethetruthofthehypothesisIlaiddownbutnow，thatyouhavetoogoodanopinionofyourself，andtoomeanaoneofthosegreatmen。OneoftheseIshallofcoursebeledtovindicateinthepursuitofmydesign；andasyourmistakeabouttheotherhasanearrelationtoGeometry，beforeIclosethisletter，Ishalltakeupalittleofyourtimeinrectifyingthatlikewise。
Havingfinishedmyconsiderationuponthedesign，theusefulness，prudenceandjusticeofyourperformance，andyourmotiveforenteringuponit；
IcomenowtoexamineintothechargeyouhavebroughtagainstourMathematicians。OfinfidelitywithrespecttotheChristianReligion。OfendeavouringtomakeotherInfidels，andsucceedinginthoseendeavours，bymeansofthatdeferencewhichispaidtotheirjudgment，asbeingpresumedtobeofallmenthegreatestmastersofreason。Oferrorandfalsereasoningintheirownscience。Here，Sir，Imustbegleavetoask，whatproofyoucanbringofthetwofirstarticlesofthisaccusation？Ihavecarefullyperusedyourwholediscourse，anddonotfindtheleastfoundationforthem，exceptonlythatyousay，inyourfirstpage，youarenotastrangertotheauthoritythatonenamelessInfidelMathematicianassumesinthingsforeigntohisprofession，nortotheabusethathe，andtoomanymoreofthelikecharacter，areknowntomakeofsuchundueauthority，tothemisleadingofunwarypersonsinmattersofthehighestconcernment，andwhereofhisMathematicalknowledgecanbynomeansqualifyhimtobeacompetentjudge；
andthatinyoursecondpage，youtellus，ThatthisisonewayofmakingInfidels，youarecrediblyinformed。
Howsayyou，Sir，youarenotastrangertoit，itisknown，youarecrediblyinformed？Benehabet，nilplusinterrogo。LetusburnorhangupalltheMathematiciansinGreatBritain，orhalloothemobuponthemtotearthemtopieceseverymother’ssonofthem，TrosRutulusvefuat，LaymenorClergymen，tho’someofthese，bytheirpreaching，theirwritings，theirlivesandconversations，arethoughttodohonourtotheirorder。LetusdigupthebodiesofDr。BarrowandSirIsaacNewton，andburnthemunderthegallows，anddemolishthemonumentserectedtotheirmemories。What，tho’thefirstbeesteemedoneofthegreatestluminariesoftheChristianChurch，andtheotherbeacknowledgedtohavebeenatruebeliever，andtohavegivensomeofthestrongestandclearestproofs，thathaveeverbeenproduced，ofthegoodness，wisdom，andpoweroftheSupremeBeing？Nomatter：theirfollowersareFreethinkers，MinutePhilosophersandInfidels，andlabourtomakeothersso。Dr。B——-yisnotastrangertoit，itisknown，heiscrediblyinformedofit。
ForGod’ssake，Sir，areweinEnglandorinSpain？IsthisthelanguageofaFamiliar，whoiswhisperinganInquisitoragainstasingleHeretick，orofaProtestantDivineagainstagreatnumberofGentlemenprofessingtheProtestantReligion，andinaProtestantCountry？
Thereindeedsuchanaccusationmightbedestructivetothepersonsitfellupon，howinnocentsoever：buthere，thanksbetoGod，andtoourReligiousandCivilLiberties，asnoproofisbroughtagainstus，wehavenomoretoto，buttoaverourinnocence，absolutelytodenythecharge，andplainlytotellyou，thatyourInformers，howcrediblesoeveryoumaythinkthem，arenootherthanapackofbase，profligate，andimpudentLyers。
Thislanguagemayseemtoowarm：butsodetestableandgroundlessadefamationwilljustifytheuseofit。AndImusttellyourself，Sir，thattho’Icanbynomeansthinkyoutohavebeentheauthorandinventorofsohorridacalumny；yetyoucanneverbeacquittedofextremecredulityingivingearandbelieftoit；notofanunpardonableinjusticeinpublishingandpropagatingit，asfarasinyoulay，throughthenation。Surely，ifyouhadnotaverystronginclinationtothinkandspeakillofMathematicians，youcouldnothavedoneeithertheoneortheother。Forisitatalllikelyorprobable，thatanumberofpersons，greatpartofwhoseemploymenthasbeentostudyGeometry，anexcellentLogic，asyouobserve，wherethedefinitionsareclear，wherethePostulatacannotberefuted，northeAxiomsdenied；wherefromthedistinctcontemplationandcomparisonoffigures，theirpropertiesarederived，byaperpetualwell-connectedchainofconsequences，theobjectsbeingstillkeptinview，andtheattentioneverfixeduponthem；wherebythereisacquiredanhabitofreasoning，closeandexactandmethodical：whichhabitstrengthensandsharpensthemind，andbeingtransferredtootherobjects，isofgeneraluseintheinquiringaftertruth；[Analyst，p。5。]isitprobable，orevenpossible，Iwouldsay，thatagreatnumberofpersons，whohaveacquiredthishabitofreasoning，shouldgenerallynotseeandcomprehendtheclear，thecertainandundeniableevidenceoftheChristianReligion？CredatJudaeusApella。
NorcanIfindagrainmoreofprobabilityinthesecondarticleofyouraccusation，thaninthefirst。SupposeaMathematiciantobeanInfidel，andtoendeavourtomakeconvertstoInfidelity，willadeferencebepaidtohisjudgmentinDivinityanymorethaninLaw，orPhysick，oranyotherscienceforeigntohisprofession？WillhisdecisionsagainsttheChristianReligionpassevenuponweakandvulgarminds，becauseheisthoughttoreasonwellinGeometry？Idpopuluscuratscilicet！Dr。BarrowwasagreatandfamousMathematician：tillSirIsaacNewtonshoneout，Quigenushumanumingeniosuperavit，&；omnesPaestrinxit，stellasexortusutiaetheriussol，Dr。BarrowwasesteemedthegreatestGeometricianinEngland：
hewaslikewisealearned，soundandOrthodoxDivine；andyettheArrians，theSocinians，theQuakers，andtheseveralothersectsofDissentersarestillinbeing，thoughthatgreatMasterofreasonbothinMathematicksandDivinitywasofacontraryopiniontothemall。SirIsaacNewtonwasagreaterMathematicianthananyofhiscontemporariesinFrance；
noFrenchmanwilldenyit：andyetIhavenotheardthattheFrenchMathematiciansareconvertedtotheProtestantReligionbyhisauthority，thoughSirIsaacwasknowntobeazealousProtestant。Whenthisgreatmanhadanyillness，hedidnottrusttohisownjudgmentforthecureofit，thoughsogreatamasterofreason，butsentforDr。Mead，andsubmittedhimselfintirelytohisdirections；andIsuppose，uponoccasion，wouldhavepaidthesamedeferencetohisLawyer。ButI
amashamedtoinsistsolonguponathingsoevidentandshallthereforenowcometothatarticleofyourcharge，whichyouseemtohavemuchmoreatheartthantheinterestoftheChristianReligion，namelythatoftheerrorsandfalsereasoningofMathematiciansintheirownscience，orratherinthatonepartoftheirscience，whichiscommonlycalledthemethodofFluxions。
Yourobjectionsagainstthismethodmay，Ithink，allofthembereducedunderthesethreeheads。Obscurityofthisdoctrine。FalsereasoningusedinitbySirIsaacNewton，andimplicitelyreceivedbyhisfollowers。ArtificesandfallaciesusedbySirIsaacNewton，tomakethisfalsereasoningpassuponhisfollowers。Ishalltreatoftheseintheirorder。1。ObscurityofthedoctrineofFluxions。
Itmustbeownedthatthisdoctrine，asitisoneofthemostprofoundpartsofGeometry，andperhapsthegreatestinstancethathaseverbeengivenoftheextentofhumanabilities，isnotwithoutitsdifficulties，andwilldoubtlessseemobscuretoeveryunqualifiedorinattentivereaderofSirIsaacNewton。ButifapersondulyfurnishedwiththenecessarypreviousknowledgeofGeometry，shallperusehiswritingswiththatcareandattentionwhichthedignityandimportanceofthesubjectdeserves；
Idoassureyou，Sir，frommyownexperience，andthatofmanyotherswhomIcouldname，thatthedoctrinemaybeclearlyconceivedanddistinctlycomprehended。Ifyourimaginationisstrainedandpuzzledwithit，ifitappearstoyoutocontainobscureandinconceivablemysteries，inshort，ifyoudonotunderstandit，Itellyouothersdo；andyoumaydosotoo，ifyouwillreadwithdueattention，andwithadesireofcomprehendingit，ratherthananinclinationtocensureit。
Youwillsay，perhaps，youhavealreadydonethis，andfindtheclearconceptionofittobeimpossible，andappealtothetrialofeverythinkingreader。Pray，Sir，whoarethesethinkingreadersyouappealto？AretheyGeometricians，orpersonswhollyignorantofGeometry？Iftheformer，Ileaveittothem：ifthelatter，Iask，howwellaretheyqualifiedtojudgeofthemethodofFluxions？I，youwillsay，haverepresentedthatmethodtothem，andfromwhatIhavelaidbeforethem，theymayeasilyjudgeofit。Buthaveyoufairly，andtruly，andfullyrepresentedit？
HavenotyouverymuchabridgedwhatSirIsaacNewton，forthemoreeasyandclearcomprehensionofhisdoctrine，hasdeliveredmoreatlargeinthoseparts[Introd。adQuadr。Curv。&；Princ。Phil。Math。lib。2。
lemm。2。]ofhisworksfromwhichyouraccountofFluxionsistaken？Haveyougivenanyaccountofanotherpart[Princ。Phil。Math。lib。1。Sect。
1。]ofhiswritings，wherethefoundationofthismethodisgeometricallydemonstrated，andlargelyexplained，anddifficultiesandobjectionsagainstitareclearlysolved？Haveyounotalteredhisexpressionsinsuchamanner，astomisleadandconfoundyourreaders，insteadofinformingthem？WheredoyoufindSirIsaacNewtonusingsuchexpressionsasthevelocitiesofthevelocities，thesecond，thirdandfourthvelocities，theincipientcelerityofanincipientcelerity，thenascentaugmentofanascentaugment？Isthisthetrueandgenuinemeaningofthewords，fluxionummutationesmagisautminusceleres？Believeme，Sir，itisveryeasybysuchpiousartsasthese，tomakeanydoctrineappearabsurdeventoathinkingreader；unlessinsteadoftrustingtotherepresentationofanadversary，hewilltakepainstoconsulttheAuthorthatiscensured。ThisthereforeIshalladvisebothyourthinkingreaderandyourselftodo，andshallbetakemyselftotheconsiderationofthenextheadofyourobjections。
2。FalsereasoningusedinthemethodofFluxionsbySirIsaacNewton，andimplicitelyreceivedbyhisfollowers。
Ofthisyouproducetwoinstances，bothrelatingtoapointwhichyoujustlycallfundamental，namelytheruleforfindingtheFluxionofarectangleoftwoflowingquantities；oneofwhichinstancesistakenfromthePrincipiaPhilos。andtheotherfromthebookofQuadratures。
Theobjection[Analyst。p。16，17。]youmaketothefirstoftheseis，thattheAuthor，inordertofindthemomentorincrementoftherectangleAB，doesnottakethesidesAa，andBb，asincreasedbytheirwholemoments，aandb，whichyousayisthedirectandtruemethod；
butinsteadthereofusestheillegitimateandindirectmethodofsupposingthesidesAandBtobedeficientorlessbyonehalfoftheirmoments，as，and，andthenfindingwhattheincrementoftherectanglewillbe，whenthosesidescometobeincreasedbytheothertwohalvesoftheirmoments，as，and。
BytheformermethodtheincrementoftherectangleABwouldcomeoutaBbAab；bythelatteritisaBbA；andthedifferencebetweenthesetwoistherectangleab。
HereyouarepleasedexceedinglytoinsultandtriumphoverthegreatAuthorofthismethodandallhisfollowers，asbeingverymuchatalosshowtogetridofthissamerectangleab。Why，Sir，supposetheycannotingeometricalrigourgetridofit，butthatitmustcontinuetobeapartoftheincrementoftherectangleAB；andyetMathematiciansrejectit，andinsteadoftherigorousgeometricalincrementaBbAab，theyuseonlyaBbA：pray，whatisityouwouldinferfromthis？Willitfollowthattheydonotproceedscientifically，thattheyareatalosshowtoconductthemselves，thattheydon’tseetheirwaydistinctly，thattheyproceedblindfold？Willyousaythattheydonotexactlyseetheconsequenceofthisomission，throughtheirwholeproceeding，anddonotcertainlyandclearlyknowhowfartheirconclusionwillbeaffectedbyit？Donottheyknowthatinestimatinganyfinitequantityhowgreatsoever，proposedtobefoundbythemethodofFluxions，aglobe，suppose，asbigasthatoftheearth，or，ifyouplease，ofthesun，orofthewholeplanetarysystem，oreventheorbofthefixedstars；donottheyknow，Isay，andaretheynotableclearlyandinvinciblytodemonstratethat，insoimmenseamagnitude，thisomissionshallnotcausethemtodeviatefromthetruthsomuchasasinglepin’shead，naynotthethousandth，notthemillionthpartofapin’shead？Howthencanitbesaidthattheyproceedwithoutclearnessandwithoutscience，anddon’tknowwhattheyaredoing，norwhitherthismethodiscarryingthem？
Ishallherebegleave，forthesakeofreaderslessmathematicallyqualified，toputaveryeasyandfamiliarcase。SupposetwoArithmeticianstobedisputingwhethervulgarfractionsaretobepreferredtodecimal；
woulditbefairinhimwhoisforexpressingthethirdpartofafarthingbythevulgarfraction1/3，toaffirmthathisantagonistproceededblindfold，andwithoutknowingwhathedid，whenhepretendedtoexpressitby0。33333
&；c。becausethisexpressiondidnotgivetherigorous，exactvalueofonethirdofafarthing？Mightnottheotherreplythat，ifthisexpressionwasnotrigorouslyexact，yetitcouldnotbesaidheproceededblindfold，orwithoutclearnessandwithoutscienceinusingit，becausebyaddingmorefigureshecouldapproachasnearashepleased，andwhereverhethoughtfittostop，hecouldclearlyanddistinctlyfindanddemonstratehowmuchhefellshortoftherigorousandexactvalue？Mightnothefurthersaythatasthe&；c。impliedallthepossiblerepetitionsofthefigure3，eventoinfinity，thereforehisexpressiondidnotdifferbyanytheleastassignablequantityfromtheothervalue，1/3；andthatasheknewandclearlyconceivedthatitdidso，hecouldnotjustlybesaidtobeinanyerror，muchlesstoactinthedark，whenheusedthatexpression？
Havingobservedthatthisomission，orerrorasyouarepleasedtocallit，inrejectingtherectangleab，isatmostsuchanoneascancausenoassignabledifference，howsmallsoever，intheconclusionsdrawnfromthemethodofFluxions；andthatMathematiciansincommittingthiserror，doneverthelessproceedscientificallyandwiththeireyesopen，ashavingaclearanddistinctviewnotonlyoftheoriginalerror，butoftheeffectofitbothineverysteptheytake，andinalltheconclusionstheydrawfromthismethod；Ishallnowforyourfarthersatisfactionproceedtoexamine，whetherinrealityitbeanyerroratall；andwhetheraBbAbenotinstrict，geometricalrigourthetruefluxion，moment，orincrementoftherectangleAB。AndasyousaytheforeignMathematiciansaresupposedbysome，evenofourown，toproceedinamanner，lessaccurateperhapsandgeometrical，yetmoreintelligible，thanthatofSirIsaacNewton；IshallfirstconsiderwhatcoursetheytakeinrejectingtherectangleabandshallthenproceedtoSirIsaacNewton’swayofexcludingit。
ThefamousMarquisdel’Hospital，whomItheratherfollowbecauseheisthoughttohavewrittenuponthissubjectwithgreaterperspicuitythananyotherforeignMathematician，asalsobecauseyouexpresslyquotehim，afterhehasfoundthefluxionoftherectanglexycomposedofthetwovariablequantitiesxandy，tobeydxxdydxdy；[Analysedesinfinimentspetits，Prop。2。]
doesafterwardsrejecttherectangledxdy，andtherebyleaveonlyydxxdyforthefluxionofxy。Uponwhichyouobserve，astothemethodofgettingridofthisquantitydxdy，equivalenttotherectangleabofSirIsaacNewton，thatitisdonewithouttheleastceremony。[Analyst，p。28。]Isthistrue？
DoesnottheMarquis，inthisverypropositionquotedbyyou，[ibid。p。
26。]andattheveryinstantthatherejectsthatquantity，givethisreasonforit，thatitisinfinitelysmallwithrespecttotheothertermsxdyandydx？Doeshenotimmediatelyaftergiveademonstrationofitsbeingso？Anddoeshenot，toshewthathehasarighttorejectituponthatreason，plainlyandexpresslyreferhisreadertohisfirstpostulatumorsupposition？Doesnotheinthatpostulatumexpresslyrequireitshouldbeallowedhim，thataquantity，whichisaugmentedordiminishedbyanotherquantityinfinitelylessthanthefirst，maybeconsideredasifitcontinuedthesame，i。e。hadreceivednosuchaugmentationordiminution？Isnotthisplainlythecaseofthequantityxdyydx，augmentedordiminishedbythequantitydxdy？HaveyouthendonefairlyandjustlybythisGreatMan，inconcealingallthisfromyourthinkingreaderstowhosejudgmentyoureferyourself，andintellingthemthatthisquantityisrejectedwithouttheleastceremony？
Youwilltellmeperhaps，thatyoudonotallowofthispostulatum。
WhythenyoumustnotreadtheMarquisdel’Hospital’sbook。Thepostulatumisplacedattheverybeginningofit，asanexpressdeclarationtohisreaders，thatunlessthatbeallowedhim，hewillnotundertaketodemonstratewhatfollows。Ifyouadmithispostulatum，youwillfindhimproceedclearlyandevidentlyandlikeaMathematicianinrejectingthequantitydxdy：ifnot，youhavenorighttoattackhispropositionfoundeduponthatpostulatum，butonlytogiveyourreasonsagainstthepostulatumitself。Andthusmuchinvindicationofmyfirstmaster，thatgreatandclear-headedGeometriciantheMarquisdel’Hospital，whoseonlymisfortuneitwastohavemetwithmuddywaters，andnottohavedrunkofthefountainitself。
IcomenowtoconsiderwhatcourseSirIsaacNewtonhimselfhastakentoavoidthisformidablerectangleab，thisfatalrock，thisBishopandhisClerks，thatthreatensdestructiontohimandallhisfollowers。Andhere，Sir，inordertogiveyourreasoningitsfullforce，Ishalltranscribethegreatestpartoftheninthsectionofyourdiscourse，afterwhichIshalldothesamejusticetoSirIsaacNewton，bygivinghisdemonstrationinhisownwords。Yourninthsectionbeginsthus。``Havingconsideredtheobject，IproceedtoconsidertheprincipleofthisnewAnalysisbyMomentums，Fluxions，orInfinitesimals；whereinifitshallappearthatyourcapitalpoints，uponwhichtherestaresupposedtodepend，includeerrorandfalsereasoning；itwillthenfollowthatyou，whoareatalosstoconductyourselves，cannotwithanydecencysetupforguidestoothermen。ThemainpointinthemethodofFluxionsistoobtainthefluxionormomentumoftherectangleorproductoftwoindeterminatequantities。InasmuchasfromthencearederivedrulesforobtainingtheFluxionsofallotherproductsandpowers；bethecoefficientsortheindexeswhattheywill，integersorfractions，rationalorsurd。
Nowthisfundamentalpointonewouldthinkshouldbeveryclearlymadeout，consideringhowmuchisbuiltuponit，andthatitsinfluenceextendsthroughoutthewholeAnalysis。Butletthereaderjudge。Thisisgivenfordemonstration。[Philos。Nat。Princ。Math。Lib。II。Lemma。2。]SupposetheproductorrectangleABincreasedbycontinualmotion：andthatthemomentaneousincrementsofthesidesAandBareaandb。WhenthesidesAandBweredeficient，orlesserbyonehalfoftheirmoments，therectanglewas，i。e。，。AndassoonasthesidesAandBareincreasedbytheothertwohalvesoftheirmoments，therectanglebecomes，or。Fromthelatterrectanglesubducttheformer，andtheremainingdifferencewillbeaBbA。ThereforetheincrementoftherectanglegeneratedbytheintireincrementsaandbisaBbA。Q。E。D。ButitisplainthatthedirectandtruemethodtoobtainthemomentorincrementoftherectangleAB，istotakethesidesasincreasedbytheirwholeincrements，andsomultiplythemtogether，AabyBb，theproductwhereofABaBbAabistheaugmentedrectangle；whenceifwesubductAB，theremainderaBbAabwillbethetrueincrementoftherectangle，exceedingthatwhichwasobtainedbytheformerillegitimateandindirectmethodbythequantityab。