John Buridan and the Theory of Impetus

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1. BOOK VIII, QUESTION 12. It is sought whether a projectile after leaving the hand of the projector is moved by the air, or by what it is moved. It is argued that it is not moved by the air, because the air seems rather to resist, since it is necessary that it be divided. Furthermore, if you say that the projector in the beginning moved the projectile and the ambient air along with it, and then that air, having been moved, moves the projectile further to such and such a distance, the doubt will return as to by what the air is moved after the projectile ceases to move. For there is just as much difficulty regarding this (the air) as there is regarding the stone which is thrown. Aristotle takes the opposite position in the eighth [book] of this work (the Physics) thus: “Projectiles are moved further after the projectors are no longer in contact with them, either by antiperistasis, as some say, or by the fact that the air having been pushed, pushes with a movement swifter than the movement of impulsion by which it (the body) is carried towards its own [natural] place.” He determines the same thing in the seventh and eighth [books] of this work (the Physics) and in the third [book] of the De caelo. 2. This question I judge to be very difficult because Aristotle, as it seems to me, has not solved it well. For he touches on two opinions. The first one, which he calls “antiperistasis,” holds that the projectile swiftly leaves the place in which it was, and nature, not permitting a vacuum, rapidly sends air in behind to fill up the vacuum. The air moved swiftly in this way and impinging upon the projectile impels it along further. This is repeated continually up to a certain distance....But such a solution notwithstanding, it seems to me that this method of proceeding was without value because of many experiences (experientie). The first experience concerns the top (trocus) and the smith’s mill (i.e. wheel – mola fabri) which are moved for a long time and yet do not leave their places. Hence, it is not necessary for the air to follow along to fill up the place of departure of a top of this kind and a smith’s mill. So it cannot be said [that the top and the smith’s mill are moved by the air] in this manner. The second experience is this: A lance having a conical posterior as sharp as its anterior would be moved after projection just as swiftly as it would be without a sharp conical posterior. But surely the air following could not push a sharp end in this way, because the air would be easily divided by the sharpness. MP_C23.qxd 11/23/062:34AMPage191 better thanfallingbackonthestatementthataircontinues tomovethatprojectile.For something whichisthemotiveforce( . . . to sustainorcarrymoveafeathermoreeasilythansomething heavier. shows thistobefalse.Theconsequenceismanifest,forthe airhavingbeenmovedought heavy fartherthansomethingheavier,assumingequalmagnitudes andshapes.Experience we wouldnotperceivethis. you equallyasfast,theairoughttopushimpetuously and withsensiblestrength.[Yet] a greatenoughimpetustomovethestoneswiftly,itseems that ifIweretoimpelairtoward which youwishtoproject.If,therefore,thatairbyreasonof thevelocityofitsmotionis nothing inyourhand,justasfastorfasterthanifyouwereholdinghandastone in amachine. as tohowitwouldsustainastoneofweightonethousandpoundsprojectedinslingor the stalksareblownrathertorearbecauseofresistingambientair. then thatairoughttoblowexteriorstalkstowardthefront.Butcontraryisevident,for And eveniftheshipwereloadedwithgrainorstrawandmovedbyambientair, with theambientairwerewithdrawn,shipwouldnotstopitsmotiononthisaccount. The surroundingairdoesnotmoveit,becauseifitwerecoveredbyaclothandthe moved bytheair. mill doesnotonthisaccountstopbutcontinuestomoveforalongtime.Thereforeitis Because, ifyoucutofftheaironallsidesnearsmith’smillbyacloth( top orsmith’smillisturnedafterthehand[whichsetsthemintomotion]hasbeenremoved. and methodoftheprecedingview.Forthiscannotsolveproblemhow consists ofsucceedingorcontiguousentities. mover butmanyinturn.Hencehealsoconcludesthatthemovementisnotcontinuous [air movesit]intothethirdair,andsoon.Aristotlesays,therefore,thatthereisnotone certain distance.Hencethefirstairmovesprojectileintosecondair,and another partoftheairnexttoit,andthat[part]moves(i.e.,next)upa joined totheprojectorismovedbyandthatairhavingbeenmoves from theplaceofprojectiontowhereprojectilestops,butratherthatair the powerofmovingprojectile.Hedoesnotmeanbythisthatsameairismoved adjacent totheprojectile[simultaneously]withandthatairmovedswiftlyhas fold over( Or, atleast,iftheshipwereloadedwithgrainorstraw,airfollowingandpushingwould very violentlybetweenthatcargoandtheairfollowingit.Experienceshowsthistobefalse. of suchanimpetusthatitcouldpushtheshipalongsostrongly,manwouldbepressed with grainorwoodandamanweresituatedtotherearofcargo.Thenifair only theairfromfrontresisting[him].Again,supposethatsaidshipwereloaded long time.Andyetasailorondeckdoesnotfeelanyairfrombehindpushinghim.Hefeels river, afterthedrawinghasceased,cannotbestoppedquickly,butcontinuestomovefora 4. Thuswecanandoughttosaythatinthestoneorother projectilethereisimpressed Also, itfollowsthatyouwouldthrowafeatherfartherthan astoneandsomethingless Furthermore, youcould,bypushingyourhand,movetheadjacentair,ifthereis Again, theair,regardlessofhowfastitmoves,iseasilydivisible.Hencenotevident Also ashipdrawnswiftlyismovedlongtimeafterthehaulershavestoppedpullingit. But thisopinionandmethodcertainlyseemstomeequallyasimpossiblethe 3. Anotheropinion,whichAristotleseemstoapprove,isthattheprojectormovesair The thirdexperienceisthis:ashipdrawnswiftlyintheriverevenagainstflowof plico ) thestalkswhichwereinrear.Thisisallfalse. virtus motiva ofthatprojectile.Andthisisevidently ) linteamine ,the ), 191

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PHILOSOPHY OF NATURE, PHILOSOPHY OF THE SOUL, METAPHYSICS 192 downward iscontinuallyaccelerated( resisting air. For theimpetusinthatthousandthpartissosmallitovercomeimmediatelyby a stoneofone-halforonepoundweightfartherthanyoucouldthousandthpartit. the largeone,otherthingsbeingequal,thereismoreimpetus to bringrestalargesmith’smillwhichismovingswiftlythansmallone,evidentlybecausein corrupted asthelesserimpetuswouldbecorrupted.Thisalsoisreasonwhyitmoredifficult will bemovedfartherbecausethereisimpressedinitamoreintenseimpetus,whichnotsoquickly heavy ironofthesamevolumeandshapearemovedequallyfastbyaprojector, such animpetusisimmediatelydestroyedbytheresistingair. of thesamequantity more ofthatimpetusandintensely,justasironcanreceivecaliditythanwoodorwater there ismoreofprimematterthaninarareandlightone.Hencedenseheavybodyreceives influence wherebyHeconcursasaco-agentinallthingswhich takeplace;“forthusonthe moved themwithoutHishavingtomoveanymoreexcept bythemethodofgeneral celestial orbsasHepleased,andinmovingthemimpressed inthemimpetuseswhich because itwouldbeansweredthatGod,whenHecreated theworld,movedeachof bodies, itcouldbesaidthatdoesnotappearnecessaryto positintelligencesofthiskind, not feeltheairmovinghim,but[rather]feelsinfront stronglyresistinghim. carry himalongerdistanceinthejump.Whenceperson sorunningandjumpingdoes a wayinordertorunfaster,sothatbyrunninghemightacquire animpetuswhichwould intense. Therefore,themovementevidentlybecomescontinually faster. the motionbecomesfaster;andbyamountitisfaster,soimpetusmore heavy bodyanimpetus.Thisimpetusnow[acting]togetherwithitsgravitymovesit.Therefore, gravity wasmovingit.Therefore,itmovedmoreslowly,butinimpressedthe impetus andmoreintensely Hence bytheamountmorethereisofmatter,thatcanbodyreceive the receptionofallformsandnaturaldispositionsisinmatterbyreasonmatter. fitted tomyhandfartherthanjustasmuchwood,Ianswerthatthecauseofthisis this method. not appeartobetrueandalsobecausealltheappearances( gravity ofthestonewinsoutoveritandmovesdowntoitsnaturalplace. continually becomesslower,andfinallythatimpetusissodiminishedorcorruptedthe in whichtheimpetuswasnaturallypredisposedtomoveit.Thusmovementofstone resisting airandbythegravityofstone,whichinclinesitinadirectioncontrarytothat the projectorceasestomove.Butthatimpetusiscontinuallydecreased( it willimpressinastrongerimpetus circularly. toward whichthemoverwasmovingbody,eitherupordown,laterally, certain motiveforce( motor inmovingabodyimpresses( the airappearsrathertoresist.Therefore,itseemsmethatoughtbesaid 6. Fromthistheoryalsoappearsthecauseofwhynaturalmotionaheavybody Also, sincetheBibledoesnotstatethatappropriateintelligences movethecelestial [The impetusthenalsoexplainswhy]onewhowishestojump alongdistancedropsback 5. ForifanyoneseekswhyIprojectastonefartherthanfeather,andironorlead This method,itappearstome,oughtbesupportedbecausetheothermethodsdo And bytheamountmotormovesthatmovingbodymoreswiftly,same Moreover,afeatherreceivessuchanimpetussoweakly( . i motiva vis (intensius). ofthemovingbody,[whichimpetusacts]indirection ) Itisbythatimpetusthestonemovedafter . o inadenseandheavybody,otherthingsbeingequal, Now continue velocitatur imprimit initacertainimpetus( ) Andforthisreasonyoucouldthrow . .Forfromthebeginningonly ). apparentia And soalsoiflightwoodand areinharmonywith ) remittitur impetus remisse ythe ) by ora ) that ) MP_C23.qxd 11/23/062:34AMPage193 ( from thetwoaforesaidconclusionsandpreceding[statements].Anditisprobable permanentis continue tobesimultaneouswithit. demands aproducer.Buttherecannotbeassignedproducerofthatimpetuswhichwould is notthelocalmotion. fitting toit,aswasstatedelsewhere.Andnowithasjustbeenaffirmedthatimpetus because motionisjustsuchathingandthedefinitionof[assuccessivething] the dispositionnaturaltothem.Inthusreturning,they can impetuouslypushordraw are innatelydisposedtoreturnswiftlyandbythemselves totheircorrectpositionor the earth.Thisisbecausemanythingsarecurvableorintracompressible byviolencewhich than astone,althoughthestonefallsmoreswiftlyand impetuously( example, theballwhichwebouncewithpalminfalling toearthisreflectedhigher that othercausesaptlyconcurwithimpetusforgreater orlongerreflection.For of anobstacle,sothatimpetusbecauseobstacleacts reflexively.Itistrue,however, corrupted, orimpededbyresistanceacontraryinclination. in themovingbodyalongwithmotionbymotor;so withthemotionitisremitted, the irontomagnet.Anditalsoisprobablethatjustas quality (theimpetus)isimpressed in whichitisimpressed,justassaidthataqualityimpressedironbymagnetmoves not resultwhenit produced” ( this reasoning.Foritwassaidelsewherethatmotionisnothingelsethan“theverybeing neither doesthepriorexistwhenposteriorismade.Thisconsequenceobviousfrom the motiondoesnotexistwhenposteriorpartexists,aswaselsewherestated.Hence, “producing something”oughttoexistwhenthesomethingismade,butpriorpartof on uptothecessationofwholemovement.Butthisisnotprobable,because part ofthemotionwhichisrelatedsuccessivelyandthatproducesanotherso they saythatthepriorpartofmotionwhichproducesprojectionanother return. Hencetherewouldbenogaininpositingsuchanimpetus.Butotherscavilwhen some othermotorfromwhichthatmotionwouldarise.Andtheprincipaldifficulty with thatwhichismoved,iftheimpetusweremotion,itwouldbenecessarytoassign Therefore, etc. Therefore, theimpetusproducesthatmotion,andsamethingcannotproduceitself. jectile ismoved,becausethatimpetusmovestheprojectileandmoverproducesmotion. how thesethingstakeplace I mightseekfromthetheologicalmasterswhattheyteachmeinthesemattersasto or repressiveofthatimpetus.ButthisIdonotsayassertively,but[rathertentatively]so celestial bodiesforothermovements.Norwasthereresistancewhichwouldbecorruptive bodies werenotdecreasednorcorruptedafterwards,becausetherewasnoinclinationofthe actions andthepassionsinturn.”AndtheseimpetuseswhichHeimpressedcelestial seventh dayHerestedfromallworkwhichhadexecutedbycommittingtoothersthe verisimile 9. Thethirdconclusionisthatimpetusathingofpermanentnature( Also, sinceapurelysuccessivethingiscontinuallycorruptedandproduced,it 10. Andinthesamewaythataluminantgeneratinglightgenerates lightreflexivelybecause 8. Thesecondconclusionisthatimpetusnotapurelysuccessivething( Also sinceeverymotionarisesfromamotorbeingpresentandexistingsimultaneously 7. Thefirst[conclusion]isthatimpetusnottheverylocalmotioninwhichpro- thatimpetusisaqualitynaturallypresentandpredisposedformovingbody ) ,distinctfromthelocalmotioninwhichprojectileismoved. Thisisevident ), ipsum fieri a been has ) andthe“verybeingcorrupted”( produced ( .... factus est ) butwhenit ipsum corumpi is being produced ( ). Hencemotiondoes impetuosius fit ). res nature res ) to ), 193

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PHILOSOPHY OF NATURE, PHILOSOPHY OF THE SOUL, METAPHYSICS 194 something conjuncttothem,asisevidentinthecaseofbow( discover amoreprobablewayofansweringit.Andthisistheend. direction, nowinanother.Anditcannotbeeasilyandquicklybroughttorest. ( direction andthenagainreturns.Itdoesthismanytimes.Forasimilarreasonbell on accountoftheimpetus,itcrossesbeyondnormalstraightpositionincontrary violently inonedirection,andsoitreturnsswiftlytowarditsnormalstraightposition.But time. Andthistakesplaceasfollows:Asaresultofstriking[thechord]swiftly,itisbent remains alonetimeincertainvibration( From thiselevationitacquirestoitselfanimpetuswhichmovesupwardalongdistance. and immediatelyafterstriking,itreturnsswiftlytoitssphericitybyelevatingitselfupward. the ballthrowntohardgroundiscompressedintoitselfbyimpetusofitsmotion; campana This, then,istheexpositionofquestion.Iwouldbedelightedifsomeone Also, itisthiswaywithacithercordwhich,putunderstrongtensionandpercussion, ), aftertheringerceasestodraw[thechord],ismovedalongtime,ﬁrstinone tremulatio ) fromwhichitssoundcontinuesanotable arcus ). Henceinthisway