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All Works by Eneström Number

The Eneström Index. In 1913, Swedish mathematician Gustaf Eneström completed a comprehensive survey of Euler's works. He 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. If you have completed a translation project, please consider submitting it to the journal Euleriana.

Other Resources. To read more on Euler and his work, check out the Euler Archive's historical information section, as well as Ed Sandifer's How Euler Did It column. Further information on Euler and 18th century science can be found on our Historical and Biographical Resources page.

Publications from 1798 1798

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

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

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

E704: Disquisitio ulterior super seriebus secundum multipla cuiusdam anguli progredientibus

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

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

Publications from 1801 1801

E707: De insigni usu calculi imaginariorum in calculo integrali

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

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

E710: Specimen transformationis singularis serierum

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

E712: De corporibus cylindricis incurvatis

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

Publications from 1802 1802

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

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

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

E717: Solutio problematis mechanici

Publications from 1805 1805

E718: Facillima methodus plurimos numeros primos praemagnos inveniendi

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

E720: Observatio singularis circa aequationes differentiales lineares

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

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

E723: Brief von Euler

Publications from 1806 1806

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

E725: Illustratio paradoxi circa progressionem numerorum idoneorum sive congruorum

E726: Demonstratio insignis theorematis numerici circa uncias potestatum binomialium

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

Publications from 1809 1809

E728: De resolutione fractionum compositarum in simpliciores

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

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

Publications from 1810 1810

E731: Solutio problematis ob singularia calculi artivicia memorabilis

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

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

Publications from 1811 1811

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

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

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

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

E738: Solutio quaestionis curiosae ex doctrina combinationum

Publications from 1813 1813

E739: Regula facilis problemata Diophantea per numeros integros expedite resolvendi

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

Publications from 1818 1818

E741: Analysis facilis aequationem Riccatianam per fractionem continuam resolvendi

Publications from 1813 1813

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

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

Publications from 1815 1815

E744: De divisoribus numerorum in forma mxx+nyy contentorum

E745: De fractionibus continuis Wallisii

E746: Methodus succincta summas serierum infinitarum per formulas differentiales investigandi

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

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

E749: Geometrica et sphaerica quaedam

Publications from 1818 1818

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

E751: Analysis facilis aequationem Riccatianam per fractionem continuam resolvendi

E752: De integralibus quibusdam inventu difficillimis

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

Publications from 1820 1820

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

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

E756: Solutio problematis mechanici non parum curiosi

E757: De problemate traiectoriarum orthogonalium ad superficies translato

Publications from 1822 1822

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

E759: Investigatio accuratior circa brachystochronas

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

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

Publications from 1823 1823

E762: Lettera inedita di Eulero a Lagrange

Publications from 1824 1824

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

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

E765: De problemate curvarum synchronarum, eiusque imprimis inverso

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

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

E768: De unciis potestatum binomii earumque interpolatione

Publications from 1826 1826

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

E770: Enodatio maximi paradoxi, in problemate quodam mechanico occurentis

E771: Solutio trium problematum difficiliorum ad methodum tangentium inversam pertinentium

Publications from 1830 1830

E772: De insigni promotione Analysis Diophantaeae

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

E774: Investigatio binorum numerorum formae xy(x⁴–y⁴), quorum productum sive quotus sit quadratum

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

E776: Dilucidationes circa binas summas duorum biquadratorum inter se aequales

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

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

E779: Solutio problematis ad analysin infinitorum indeterminatorum referendi

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

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

E782: De binis curvis algebraicis eadem rectificatione gaudentibus

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

E784: Solutio problematis analytici difficillimi

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

Publications from 1839 1839

E786: Œuvres complètes en français de L. Euler

Publications from 1843 1843

E787: Solutio problematis in Actis Lipsiensibus A. 1745 propositi

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

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

Publications from 1847 1847

E790: Commentatio de matheseos sublimioris utilitate

Publications from 1849 1849

E791: Commentationes arithmeticae collectae

E792: Tractatus de numerorum doctrina capita XVI, quae supersunt

E793: Considerationes circa Analysin Diophanteam

E794: Theorema arithmeticum eiusque demonstratio

E795: De quadratis magicis

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

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

E798: De numeris amicibilibus

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 1851

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