The Eneström Index. In 1913, Swedish mathematician Gustav Eneström completed a comprehensive survey of Euler's works. He counted and enumerated 866 distinct works, including books, journal articles, and some letters he deemed to be especially important. Each of these was assigned a number, from E1 to E866, which is now referred to as the "Eneström number." Most historical scholars today use Eneström numbers to identify Euler's writings quickly.

Euler Translation. Since roughly 80% of Euler's works were published in Latin, translation into modern languages is crucial in order to understand his contributions to science and mathematics. If you are contemplating a particular translation project, please contact Erik Tou (etou@uw.edu) or Chris Goff (cgoff@pacific.edu), using "Euler Translation Notice" as your subject heading.

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Publications from 1786

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E601: De symptomatibus quatuor punctorum, in eodem plano sitorum

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E602: Methodus facilis omnia symptomata linearum curvarum non in eodem plano sitarum investigandi

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E603: De descensu baculi super hypomochlio cylindro fixo delabentis

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E604: De traiectoriis reciprocis tam rectangulis quam obliquangulis

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E605: De miris proprietatibus curvae elasticae sub aequatione y = ∫(xx dx)/√(1–x4)

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E606: Speculationes super formula integrali ∫(xndx)/√(aa–2bx+cxx), ubi simul egregiae observationes circa fractiones continuas occurrunt

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E607: De motu globi circa axem obliquum quemcunque gyrantis et super plano horizontali incedentis

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E608: Accuratior evolutio formularum pro filorum flexibilium aequilibrio et motu inventarum

Publications from 1787

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E609: Considerationes super traiectoriis tam rectangulis quam obliquangulis

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E610: Novae demonstrationes circa divisores numerorum formae xx + nyy

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E611: Investigatio curvarum quae similes sint suis evolutis vel primis vel secundis vel tertiis vel adeo ordinis cuiuscunque

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E612: De motu globi heterogenei super plano horizontali, una cum dilucidationibus necessariis super motu vacillatorio

Publications from 1813

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E613: Dilucidationes in capita postrema calculi mei differentalis de functionibus inexplicabilibus

Publications from 1788

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E614: Commentatio de curvis tractoriis

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E615: De curvis tractoriis compositis

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E616: De transformatione seriei divergentis 1 – mx + m(m+n)x2m(m+n)(m+2n)x3 + etc. in fractionem continuam

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E617: De summatione serierum, in quibus terminorum signa alternantur

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E618: Consideratio motus singularis, qui in filo perfecte flexili locum habere potest

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E619: Enodatio difficultatis super figura terrae a vi centrifuga oriunda

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E620: Methodus facilis inveniendi integrali huius formulae ∫∂x/x∙(xn+p – 2xncos(ζ) + xn-p)/(x2n – 2xncos(θ) + 1) casu, post integrationem ponitur vel x=1 vel x=∞

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E621: De summo usu calculi imaginariorum in analysi

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E622: Specimen singulare analyseos infinitorum indeterminatae

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E623: De lineis rectificabilibus in superficie sphaeroidica quacunque geometrice ducendis

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E624: De superficie coni scaleni, ubi imprimis intentes difficultates, quae in hac investigatione occurrunt, perpenduntur

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E625: De viribus centripetis, ad curvas non in eodem plano sitas describendas, requisitis

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E626: De motu trium corporum se mutuo attrahentium super eadem linea recta

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E627: Solutio problematis mechanici

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E628: Éclaircissemens sur le mémoire de Mr. de La Grange, inséré dans le Ve. volume de Mélanges de Turin, concernant la méthode de prendre le milieu entre les résultats de plusiers observations, etc.

Publications from 1789

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E629: Evolutio formulae integralis ∫∂x∙(1/(1–x) + 1/log(x)) a termino x=0 ad x=1 extensae

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E630: Uberior explicatio methodi singularis nuper expositae integralia alias maxime abscondita investigandi

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E631: Analysis facilis et plana ad eas series maxime abstrusas perducens, quibus omnium aequationum algebraicarum non solum radices ipsae sed etiam quaevis earum potestates exprimi possunt

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E632: De innumeris generibus serierum maxime memorabilium, quibus omnium aequationum algebraicarum non solum radices ipsae sed etiam quaecumque earum potestates exprimi possunt

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E633: De binis curvis algebraicis inveniendis, quarum arcus indefinite inter se sint aequales

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E634: De motu oscillatorio tabulae suspensae et a vento agitatae

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E635: Innumera theoremata circa formulas integrales, quorum demonstratio vires analyseos superare videatur

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E636: De multiplicatione angulorum per factores expedienda

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E637: Nova demonstratio, quod evolutio potestatum binomii Newtoniana etiam pro exponentibus fractis valeat

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E638: De innumeris curvis algebraicis, quarum longitudinem per arcus parabolicos metiri licet

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E639: De innumeris curvis algebraicis, quarum longitudinem per arcus parabolicos metiri licet

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E640: Comparatio valorum formulae integralis ∫xp-1∂x/(1–xn)(n-q)/n a termino x=0 usque ad x=1 extensae

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E641: De motu quodam maxime memorabili, satis quidem simplici, at solutu difficillimo

Publications from 1790

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E642: De singulari ratione differentiandi et intagrandi, quae in summis serierum occurrit

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E643: Methodus generalis investigandi radices omnium aequationum per approximationem

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E644: Innumerae aequationum formae ex omnibus ordinibus, quarum resolutio exhiberi potest

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E645: De curvis algebraicis, quarum longitudo exprimitur hac formula integrali ∫(vm-1 ∂v)/√(1–v2n)

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E646: De duabus pluribusve curvis algebraicis in quibus si a terminis fixis aequales arcus abscindantur eorum amplitudines datam inter se teneant rationem

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E647: De methodo tangentium inversa ad theoriam solidorum translata

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E648: Solutio facilis problematis, quo quaeritur circulus, qui datos tres circulos tangat

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E649: De motu oscillatorio penduli circa axem cylindricum plano horizontali incumbentem

Publications from 1793

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E650: De formulis differentialibus quae per duas pluresve quantitates datas multiplicatae fiant integrabiles

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E651: Quatuor theoremata maxime notatu digna in calculo integrali

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E652: De termino generali serierum hypergeometricarum

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E653: De iterata integratione formularum integralium, dum aliquis exponens pro variabili assumitur

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E654: Methodus facilis investigandi radium osculi ex principio maximorum et minimorum petita

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E655: Observationes generales circa series, quarum termini secundum sinus vel cosinus angulorum multiplorum progrediuntur

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E656: De integrationibus maxime memorabilibus ex calculo imaginariorum oriundis

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E657: Supplementum ad dissertationem praecedentem circa integrationem vormulae ∫(zm-1 ∂z)/(1–zn) casu quo ponitur z = v(cos(ϕ) + √(-1)∙sin(ϕ))

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E658: De momentis virium respectu axis cuiuscunque inveniendis; ubi plura insignia symptomata circa binas rectas, non in eodem plano sitas, explicantur

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E659: Methodus facilis omnium virium momenta respectu axis cuiuscunque determinandi

Publications from 1794

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E660: Institutionum calculi integralis volumen quartum, continens supplementa partim inedita partim jam in operibus academiae imperialis scientiarum Petropolitanae impressa.

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E661: Variae considerationes circa series hypergeometricas

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E662: De vero valore formulae integralis ∫∂x∙(log(1/x))n a termino x=0 usque ad terminum x=1 extensae

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E663: Plenior expositio serierum illarum memorabilium, quae ex unciis potestatum binomii formantur

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E664: Exercitatio analytica

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E665: Evolutio problematis cuius solutio analytica est difficillima dum synthetica per se est obvia

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E666: Problema geometricum ob singularia symptomata imprimis memorabile

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E667: De curvis hyperbolicis quae intra suas assymtotas spatium finitum includunt

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E668: De integratione formulae ∫∂x√(1+x4)/(1–x4) aliarumque eiusdem generis per logarithmos et arcus circulares

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E669: Memorabile genus formularum differentialium maxime irrationalium quas tamen ad rationalitatem perducere licet

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E670: De resolutione formulae integralis ∫xm-1∂x(Δ+xn)λ in seriem semper convergentem, ubi simul plura insignia artificia circa serierum summationem explicantur

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E671: De formulis differentialibus angularibus maxime irrationalibus, quas tamen per logarithmos et arcus circulares integrare licet

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E672: Theorema maxime memoragile circa formulam integralem ∫ cos(λϕ)/(1+aa–2acos(ϕ))n+1

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E673: Disquisitio coniecturalis super formula integrali ∫∂ϕ cos(iϕ)/(α+βcos(ϕ))n

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E674: Demonstratio theorematis insignis per coniecturam eruti circa intagrationem formulae ∫ ∂ϕ cos(iϕ)/(1+aa–2acos(ϕ))n+1

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E675: De valoribus integralium a termino variabilis x=0 usque ad x=∞ extensorum

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E676: Methodus succinctior comparationes quantitatum transcendentium in forma ∫ P ∂z/√(A+2Bz+Czz+2Dz3+Ez4) contentarum inveniendi

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E677: Methodus singularis resolvendi aequationes differentiales secundi gradus

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E678: Methodus nova investigandi omnes casus quibus hance aequationem differentialem ∂∂y(1–axx) – bx ∂x ∂ycy ∂x2 = 0 resolvere licet

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E679: De formulis integralibus implicatis earumque evolutione et transformatione

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E680: De aequationibus differentialibus cuiuscunque gradus quae denuo differentiatae integrari possunt

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E681: Specimen aequationum differentialium indefiniti gradus earumque integrationis

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E682: Von dem Drucke eines mit einem Gewuchte beschwerten Tisches auf einer Flache. Aus den Papieren des sel. Leonhard Euler gozogen von Jakob Bernoulli

Publications from 1795

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E683: De singulari genere quaestionum Diophantearum et methodo maxime recondita eas resolvendi

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E684: De radicibus aequationis infinitae 0 = 1 – xx/(n(n+1)) + x4/(n(n+1)(n+2)(n+3)) – x6/(n.....(n+5)) + etc.

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E685: Exercitatio analytica, ubi imprimis seriei maxime generalis summatio traditur

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E686: Dilucidationes super formulis, quibus sinus et cosinus angulorum multiplorum exprimi solent, ubi simul ingentes difficultates diluuntur

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E687: De insignibus proprietatibus formularum integralium praeter binas variabiles etiam earum differentialia cuiuscunque ordinis involventium

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E688: Specimen integrationis abstrusissimae hac formula ∫∂x/((1+x)∙(2xx–1)1/4) contentae

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E689: Integratio formulae differentialis maxime irrationalis, quam tamen per logarithmos et arcus circulares expedire licet

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E690: Evolutio formulae integralis ∫∂z(3+zz)/((1+zz)∙(1+6zz+z4)1/4) per logarithmos et arcus circulares

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E691: Problema geometricum quo inter omnes ellipses quae per data quatuor puncta traduci possunt ea quaeritur quae habet aream minimam

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E692: Solutio problematis maxime curiosi quo inter omnes ellipses quae circa datum triangulum circumscribi possunt ea quaeritur cuius area sit omnium minima

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E693: De centro simulitudinis

Publications from 1797

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E694: Ulterior disquitio de formulis integralibus imaginariis

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E695: Integratio succincta formulae integralis maxime memorabilis ∫∂z/((3±zz)∙(1±3zz)1/3)

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E696: De casubus quibus hanc formulam x4 + kxxyy + y4 ad quadratum reducere licet

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E697: Investigatio superficierum quarum normales ad datum planum productae sint omnes inter se aequales

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E698: Variae speculationes super area triangulorum sphaericorum

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E699: Utrum hic numerus 100009 sit primus necne inquiritur

Publications from 1798

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E700: De formulis differentialibus secundi gradus quae integrationem admittunt