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 1798

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E701: Formae generales differentialium, quae, etsi nulla substitutione rationales reddi possunt. tamen integrationem per logarithmos et arcus circulares admittunt

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E702: De novo genere quaestionum arithmeticarum pro quibus solvendis certa methodus adhuc desideratur

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E703: Methodus facilis inveniendi series per sinus sosinusve angulorum multiplorum procedentes, quarum usus in universa theoria astronomiae est amplissimus

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E704: Disquisitio ulterior super seriebus secundum multipla cuiusdam anguli progredientibus

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E705: Investigatio quarundam serierum, quae ad rationem peripheriae circuli ad diametrum vero proxime definiendam maxime sunt accommodatae

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E706: De novo genere serierum rationalium et valde convergentium, quibus ratio peripheriae ad diametrum exprimi potest

Publications from 1801

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E707: De insigni usu calculi imaginariorum in calculo integrali

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E708: De formulis speciei mxx+nyy ad numeros primos explorandos idoneis earumque mirabilibus proprietatibus

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E709: De evolutione potestatis polynomialis cuiuscunque (1 + x + x2 + x3 + x4 + etc.)n

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E710: Specimen transformationis singularis serierum

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E711: Methodus nova ac facilis omnium aequationum algebraicarum radices non solum ipsas sed etiam quascumque earum potestates per series concinnas exprimendi

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E712: De corporibus cylindricis incurvatis

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E713: Investigatio trianguli in quo distantiae angulorum ab eius centro gravitatis rationaliter exprimantur

Publications from 1802

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E714: Exempla quarundam memorabilium aequationum differentialium, quas adeo algebraice integrare licet, etiamsi nulla via pateat variabiles a se invicem separandi

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E715: De variis modis numeros praegrandes examinandi, utrum sint primi necne?

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E716: Resolutio formulae diophanteae ab(maa+nbb)=cd(mcc+ndd) per numeros rationales

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E717: Solutio problematis mechanici

Publications from 1805

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E718: Facillima methodus plurimos numeros primos praemagnos inveniendi

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E719: Methodus generalior numeros quosvis satis grandes perscrutandi utrum sint primi necne?

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E720: Observatio singularis circa aequationes differentiales lineares

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E721: De integrationibus difficillimis, quarum integralia tamen aliunde exhiberi possunt

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E722: Disquitiones analyticae super evolutione potestatis trinomialis (1+x+xx)n

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E723: Brief von Euler

Publications from 1806

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E724: Recherches sur quelques intégrations remarquables dans l'analyse des fonctions à deux variables connues sous le nom de différences partielles

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E725: Illustratio paradoxi circa progressionem numerorum idoneorum sive congruorum

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E726: Demonstratio insignis theorematis numerici circa uncias potestatum binomialium

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E727: Accuratior evolutio problematis de linea brevissima in superficie quacunque ducenda

Publications from 1809

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E728: De resolutione fractionum compositarum in simpliciores

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E729: Dilucidationes super Problemate geometrico de quadrisectione trianguli a Iacobo Bernoulli olum tractato

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E730: Solutio completa problematis de quadrisectione trianguli per duas rectas inter se normales

Publications from 1810

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E731: Solutio problematis ob singularia calculi artivicia memorabilis

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E732: Solutio facilior problematis Diophantei circa triangulum, in quo rectae ex angulis latera opposita bisecantes rationaliter exprimantur

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E733: Solutio facilis problematis, quo quaeritur sphaera, quae datas quatuor sphaeras utcunque dispositas contingat

Publications from 1811

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E734: Integratio aequationis differentialis huius dy + yy dx = (A dx)/(a+2bx+cxx)2

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E735: De insigni paradoxo, quod in analysi maximorum et minimorum occurrit

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E736: De summatione serierum in hac forma contentarum a/1 + a2/4 + a3/9 + a4/16 + a5/25 + a6/36 + etc.

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E737: De transformatione functionum duas variabiles involventium dum earum loco aliae binae variabiles introducuntur

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E738: Solutio quaestionis curiosae ex doctrina combinationum

Publications from 1813

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E739: Regula facilis problemata Diophantea per numeros integros expedite resolvendi

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E740: De lineis curvis non in eodem plano sitis, quae maximi minimive proprietate sunt praeditae

Publications from 1818

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E741: Analysis facilis aequationem Riccatianam per fractionem continuam resolvendi

Publications from 1813

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E742: Observationes circa fractiones continuas in hac forma contentas S = n/(1+(n+1)/(2+(n+2)/(3+(n+3)/(4+etc.))))

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E743: De serie maxime memorabili, qua potestas binomialis quaecunque exprimi potest

Publications from 1815

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E744: De divisoribus numerorum in forma mxx+nyy contentorum

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E745: De fractionibus continuis Wallisii

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E746: Methodus succincta summas serierum infinitarum per formulas differentiales investigandi

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E747: De seriebus memorabilibus, quibus sinus et cosinus angulorum multiplorum exprimere licet

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E748: Investigatio quadrilateri, in quo singularum angulorum sinus datam inter se teneant rationem, ubi artificia prorsus singularia in Analysi Diophantea occurrunt

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E749: Geometrica et sphaerica quaedam

Publications from 1818

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E750: Commentatio in fractionem continuam, qua illustris La Grange potestates binomiales expressit

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E751: Analysis facilis aequationem Riccatianam per fractionem continuam resolvendi

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E752: De integralibus quibusdam inventu difficillimis

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E753: Solution succincta et elegans problematis, quo quaeruntur tres numeri tales, ut tam summae quam differentiae binorum sint quadrata

Publications from 1820

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E754: Probleme de geometrie resolu par l'analyse de Diophante

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E755: De casibus, quibus formulam x4+mxxyy+y4 ad quadratum reducere licet

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E756: Solutio problematis mechanici non parum curiosi

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E757: De problemate traiectoriarum orthogonalium ad superficies translato

Publications from 1822

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E758: De binis formulis speciei xx+myy et xx+nyy inter se concordibus et discordibus

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E759: Investigatio accuratior circa brachystochronas

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E760: De vera brachystochrona seu linea celerrimi descensus in medio resistente

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E761: De brachystochrona in medio resistente, dum corpus ad centrum virium utunque attrahitur

Publications from 1823

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E762: Lettera inedita di Eulero a Lagrange

Publications from 1824

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E763: De tribus pluribusve numeris inveniendis, quorum summa sit quadratum, quadratorum vero summa biquadratum

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E764: Resolutio facilis quaestionis difficillimae, qua haec formula maxime generalis vvzz(axx+byy)2 + Δxxyy(avv+bzz)2 ad quadratum reduci postulatur

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E765: De problemate curvarum synchronarum, eiusque imprimis inverso

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E766: Methodus nova et generalis problema synchronarum inversum aliaque eiusdem generis resolvendi

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E767: De curvis quarum radii osculi tenent rationem duplicatam distantiae a puncto fixo earumque mirabilibus proprietatibus

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E768: De unciis potestatum binomii earumque interpolatione

Publications from 1826

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E769: Solutio problematis Fermatiani de duobus numeris, quorum summa sit quadratum, quadratorum vero summa biquadratum, ad mentem illustris La Grange adornata

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E770: Enodatio maximi paradoxi, in problemate quodam mechanico occurentis

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E771: Solutio trium problematum difficiliorum ad methodum tangentium inversam pertinentium

Publications from 1830

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E772: De insigni promotione Analysis Diophantaeae

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E773: Solutio problematis difficillimi, quo hae duae formulae aaxx+bbyy et aayy+bbxx quadrata reddi debent

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E774: Investigatio binorum numerorum formae xy(x4y4), quorum productum sive quotus sit quadratum

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E775: De binis numeris, quorum summa sive aucta sive minuta tam unius quam alterius quadrato producat quadrata

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E776: Dilucidationes circa binas summas duorum biquadratorum inter se aequales

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E777: De resolutione huius aequationis 0 = a + bx + cy + dxx + exy + fyy + gxxy + hyy + ixxyy per numeros rationales

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E778: Methodus nova et facilis formulas cubicas et biquadraticas ad quadratum reducendi

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E779: Solutio problematis ad analysin infinitorum indeterminatorum referendi

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E780: De infinitis curvis algebraicis, quarum longitudo indefinita arcui elliptico aequatur

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E781: De infinitis curvis algebraicis, quarum longitudo arcui parabolico aequatur

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E782: De binis curvis algebraicis eadem rectificatione gaudentibus

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E783: De curvis algebraicis, quarum omnes arcus per arcus circulares metiri liceat

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E784: Solutio problematis analytici difficillimi

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E785: Intégration d'une espèce remarqable d'équation différentielle dans l'analyse des fonctions à deux variables

Publications from 1839

E786: Œuvres complètes en français de L. Euler

Publications from 1843

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E787: Solutio problematis in Actis Lipsiensibus A. 1745 propositi

E788: Briefe von L. Euler an Chr. Goldbach 1729-1763

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E789: Einige Zeilen aus einem Brief von L. Euler an Albrecht von Haller vom 4 Juli 1744

Publications from 1847

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E790: Commentatio de matheseos sublimioris utilitate

Publications from 1849

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E791: Commentationes arithmeticae collectae

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E792: Tractatus de numerorum doctrina capita XVI, quae supersunt

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E793: Considerationes circa Analysin Diophanteam

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E794: Theorema arithmeticum eiusque demonstratio

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E795: De quadratis magicis

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E796: Recherches sur le probleme de trois nombres carres tels que la somme de deux quelconques moins le troisieme fasse un nombre carre

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E797: Recherches ulterueures et tres curieuses sur le probleme de quatre nombres positifs et un proportion arithmetique tels que la somme de deux quelconques soit toujours un nombre carre

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E798: De numeris amicibilibus

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E799: Fragmenta commentationis cuiusdam maioris, de invenienda relatione enter latera triangulorum, quorum area rationaliter exprimi possit, et de triangulo in quo rectae ex singulis angulis latera opposita bisecantes sint rationales

Publications from 1851

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E800: Brief von L. Euler an Christoph Jezler vom 4 Mai 1765