ure　negations；　although　they　may　possibly　have　no　existence　outside　of　my　thought；　and　which　are　not　framed　by　me；　although　it　is　within　my　power　either　to　think　or　not　to　think　them；　but　which　possess　natures　which　are　true　and　immutable。　　For　example；　when　I　imagine　a　triangle；　although　there　may　nowhere　in　the　world　be　such　a　figure　outside　my　thought；　or　ever　have　been；　there　is　nevertheless　in　this　figure　a　certain　determinate　nature；　form；　or　essence；　which　is　immutable　and　eternal；　which　I　have　not　invented；　and　which　in　no　wise　depends　on　my　mind；　as　appears　from　the　fact　that　diverse　properties　of　that　triangle　can　be　demonstrated；　viz。　that　its　three　angles　are　equal　to　two　right　angles；　that　the　greatest　side　is　subtended　by　the　greatest　angle；　and　the　like；　which　now；　whether　I　wish　it　or　do　not　wish　it；　I　recognise　very　clearly　as　pertaining　to　it；　although　I　never　thought　of　the　matter　at　all　when　I　imagined　a　triangle　for　the　first　time；　and　which　therefore　cannot　be　said　to　have　been　invented　by　me。　　　　　　Nor　does　the　objection　hold　good　that　possibly　this　idea　of　a　triangle　has　reached　my　mind　through　the　medium　of　my　senses；　since　I　have　sometimes　seen　bodies　triangular　in　shape；　because　I　can　form　in　my　mind　an　infinitude　of　other　figures　regarding　which　we　cannot　have　the　least　conception　of　their　ever　having　been　objects　of　sense；　and　I　can　nevertheless　demonstrate　various　properties　pertaining　to　their　nature　as　well　as　to　that　of　the　triangle；　and　these　must　certainly　all　be　true　since　I　conceive　them　clearly。　Hence　they　are　something；　and　not　pure　negation；　for　it　is　perfectly　clear　that　all　that　is　true　is　something；　and　I　have　already　fully　demonstrated　that　all　that　I　know　clearly　is　true。　　And　even　although　I　had　not　demonstrated　this；　the　nature　of　my　mind　is　such　that　I　could　not　prevent　myself　from　holding　them　to　be　true　so　long　as　I　conceive　them　clearly；　and　I　recollect　that　even　when　I　was　still　strongly　attached　to　the　objects　of　sense；　I　counted　as　the　most　certain　those　truths　which　I　conceived　clearly　as　regards　figures；　numbers；　and　the　other　matters　which　pertain　to　arithmetic　and　geometry；　and；　in　general；　to　pure　and　abstract　mathematics。　　　　　　But　now；　if　just　because　I　can　draw　the　idea　of　something　from　my　thought；　it　follows　that　all　which　I　know　clearly　and　distinctly　as　pertaining　to　this　object　does　really　belong　to　it；　may　I　not　derive　from　this　an　argument　demonstrating　the　existence　of　God？　　It　is　certain　that　I　no　less　find　the　idea　of　God；　that　is　to　say；　the　idea　of　a　supremely　perfect　Being；　in　me；　than　that　of　any　figure　or　number　whatever　it　is；　and　I　do　not　know　any　less　clearly　and　distinctly　that　an　＇actual　and＇　eternal　existence　pertains　to　this　nature　than　I　know　that　all　that　which　I　am　able　to　demonstrate　of　some　figure　or　number　truly　pertains　to　the　nature　of　this　figure　or　number；　and　therefore；　although　all　that　I　concluded　in　the　preceding　Meditations　were　found　to　be　false；　the　existence　of　God　would　pass　with　me　as　at　least　as　certain　as　I　have　ever　held　the　truths　of　mathematics　（which　concern　only　numbers　and　figures）　to　be。　　　　　　This　indeed　is　not　at　first　manifest；　since　it　would　seem　to　present　some　appearance　of　being　a　sophism。　　For　being　accustomed　in　all　other　things　to　make　a　distinction　between　existence　and　essence；　I　easily　persuade　myself　that　the　existence　can　be　separated　from　the　essence　of　God；　and　that　we　can　thus　conceive　God　as　not　actually　existing。　　But；　nevertheless；　when　I　think　of　it　with　more　attention；　I　clearly　see　that　existence　can　no　more　be　separated　from　the　essence　of　God　than　can　its　having　its　three　angles　equal　to　two　right　angles　be　separated　from　the　essence　of　a　＇rectilinear＇　triangle；　or　the　idea　of　a　mountain　from　the　idea　of　a　valley；　and　so　there　is　not　any　less　repugnance　to　our　conceiving　a　God　（that　is；　a　Being　supremely　perfect）　to　whom　existence　is　lacking　（that　is　to　say；　to　whom　a　certain　perfection　is　lacking）；　than　to　conceive　of　a　mountain　which　has　no　valley。　　　　　　But　although　I　cannot　really　conceive　of　a　God　without　existence　any　more　than　a　mountain　without　a　valley；　still　from　the　fact　that　I　conceive　of　a　mountain　with　a　valley；　it　does　not　follow　that　there　is　such　a　mountain　in　the　world；　similarly　although　I　conceive　of　God　as　possessing　existence；　it　would　seem　that　it　does　not　follow　that　there　is　a　God　which　exists；　for　my　thought　does　not　impose　any　necessity　upon　things；　and　just　as　I　may　imagine　a　winged　horse；　although　no　horse　with　wings　exists；　so　I　could　perhaps　attribute　existence　to　God；　although　no　God　existed。　　　　　　But　a　sophism　is　concealed　in　this　objection；　for　from　the　fact　that　I　cannot　conceive　a　mountain　without　a　valley；　it　does　not　follow　that　there　is　any　mountain　or　any　valley　in　existence；　but　only　that　the　mountain　and　the　valley；　whether　they　exist　or　do　not　exist；　cannot　in　any　way　be　separated　one　from　the　other。　　While　from　the　fact　that　I　cannot　conceive　God　without　existence；　it　follows　that　existence　is　inseparable　from　Him；　and　hence　that　He　really　exists；　not　that　my　thought　can　bring　this　to　pass；　or　impose　any　necessity　on　things；　but；　on　the　contrary；　because　the　necessity　which　lies　in　the　thing　itself；　i。e。　the　necessity　of　the　existence　of　God　determines　me　to　think　in　this　way。　For　it　is　not　within　my　power　to　think　of　God　without　existence　（that　is　of　a　supremely　perfect　Being　devoid　of　a　supreme　perfection）　though　it　is　in　my　power　to　imagine　a　horse　either　with　wings　or　without　wings。　　　　　　And　we　must　not　here　object　that　it　is　in　truth　necessary　for　me　to　assert　that　God　exists　after　having　presupposed　that　He　possesses　every　sort　of　perfection；　since　existence　is　one　of　these；　but　that　as　a　matter　of　fact　my　original　supposition　was　not　necessary；　just　as　it　is　not　necessary　to　consider　that　all　quadrilateral　figures　can　be　inscribed　in　the　circle；　for　supposing　I　thought　this；　I　should　be　constrained　to　admit　that　the　rhombus　might　be　inscribed　in　the　circle　since　it　is　a　quadrilateral　figure；　which；　however；　is　manifestly　false。　＇We　must　not；　I　say；　make　any　such　allegations　because＇　although　it　is　not　necessary　that　I　should　at　any　time　entertain　the　notion　of　God；　nevertheless　whenever　it　happens　that　I　think　of　a　first　and　a　sovereign　Being；　and；　so　to　speak；　derive　the　idea　of　Him　from　the　storehouse　of　my　mind；　it　is　necessary　that　I　should　attribute　to　Him　every　sort　of　perfection；　although　I　do　not　get　so　far　as　to　enumerate　them　all；　or　to　apply　my　mind　to　each　one　in　particular。　　And　this　necessity　suffices　to　make　me　conclude　（after　having　recognised　that　existence　is　a　perfection）　that　this　first　and　sovereign　Being　really　exists；　just　as　though　it　is　not　necessary　for　me　ever　to　imagine　any　triangle；　yet；　whenever　I　wish　to　consider　a　rectilinear　figure　composed　only　of　three　angles；　it　is　absolutely　essential　that　I　should　attribute　to　it　all　those　properties　which　serve　to　bring　about　the　conclusion　that　its　three　angles　are　not　greater　than　two　right　angles；　even　although　I　may　not　then　be　considering　this　point　in　particular。　　But　when　I　consider　which　figures　are　capable　of　being　inscribed　in　the　circle；　it　is　in　no　wise　necessary　that　I　should　think　that　all　quadrilateral　figures　are　of　this　number；　on　the　contrary；　I　cannot　even　pretend　that　this　is　the　case；　so　long　as　I　do　not　desire　to　accept　anything　which　I　cannot　conceive　clearly　and　distinctly。　　And　in　consequence　there　is　a　great　difference　between　the　false　suppositions　such　as　this；　and　the　true　ideas　born　within　me；　the　first　and　principal　of　which　is　that　of　God。　　For　really　I　discern　in　many　ways　that　this　idea　is　not　something　factitious；　and　depending　solely　on　my　thought；　but　that　it　is　the　image　of　a　true　and　immutable　nature；　first　of　all；　because　I　cannot　conceive　anything　but　God　himself　to　whose　essence　existence　＇necessarily＇　pertains；　in　the　second　place　because　it　is　not　possible　for　me　to　conceive　two　or　more　Gods　in　this　same　position；　and；　granted　that　there　is　one　such　God　who　now　exists；　I　see　clearly　that　it　is　necessary　that　He　should　have　existed　from　all　eternity；　and　that　He　must　exist　eternally；　and　finally；　because　I　know　an　infinitude　of　other　properties　in　God；　none　of　which　I　can　either　diminish　or　change。　　　　　　For　the　rest；　whatever　proof　or　argument　I　avail　myself　of；　we　must　always　return　to　the　point　that　it　is　only　those　things　which　we　conceive　clearly　and　distinctly　that　have　the　power　of　persuading　me　entirely。　　And　although　amongst　the　matters　which　I　conceive　of　in　this　way；　some　indeed　are　manifestly　obvious　to　all；　while　others　only　manifest　themselves　to　those　who　consider　them　closely　and　examine　them　attentively；　still；　after　they　have　once　been　discovered；　the　latter　are　not　esteemed　as　any　less　certain　than　the　former。　For　example；　in　the　case　of　every　right…angled　triangle；　although　it　does　not　so　manifestly　appear　that　the　square　of　the　base　is　equal　to　the　squares　of　the　two　other　sides　as　that　this　base　is　opposite　to　the　greatest　angle；　still；　when　this　has　once　been　apprehended；　we　are　just　as　certain　of　its　truth　as　of　the　truth　of　the　other。　　And　as　regards　God；　if　my　mind　were　not　pre…occupied　with　prejudices；　and　if　my　thou