Novi Commentarii academiae scientiarum imperialis Petropolitanae
(New memoirs of the imperial academy of sciences in St. Petersburg)
The successor journal to the Commentarii, the Novi
Commentarii was the second journal series of the
St. Petersburg
Academy, and was published in 21 volumes between 1747 and 1778. Its genesis was the
political chaos of the time, which by 1750, had caused significant publication lags in
the Commentarii. By this time, publication of the Commentarii was ten years
behind authorship. In the following year, articles written over the course of six years
were bound together into two final volumes (13 and 14), and publication then passed
to the Novi Commentarii.
Euler published extensively in the Novi Commentarii, ultimately authoring 179
articles for the journal, as shown below:
- Volume 1: published 1750.
- Volume 2: published 1751.
- Volume 3: published 1753.
- Table of contents and summaries of articles
- Figures
- Volume 3 contains nine of Euler's works:
- E188: Methodus aequationes differentiales altiorum graduum integrandi ulterius promota
- E189: De serierum determinatione seu nova methodus inveniendi terminos generales serierum
- E190: Consideratio quarumdam serierum, quae singularibus proprietatibus sunt praeditae
- E191: De partitione numerorum
- E192: Solutio problematis geometrici
- E193: De perturbatione motus planetarum ab eorum figura non sphaerica oriunda
- E194: De machinis in genere
- E195: De motu tautochrono pendulorum compositorum
- E196: Emendatio laternae magicae ac microscopii solaris
- Volume 4: published 1758.
- Title page (no table of contents in this
volume)
- Summaries of articles
- Figures
- Volume 4 contains five of Euler's works:
- E228: De numeris, qui sunt aggregata duorum quadratorum
- E229: De constructione aptissima molarum alatarum
- E230: Elementa doctrinae solidorum
- E231: Demonstratio nonnullarum insignium proprieatatum, quibus solida hedris planis inclusa sunt praedita
- E232: De motu corporum coelestium a viribus quibuscunque perturbato
- Volume 5: published 1760.
- Title page (no table of contents in this
volume)
- Summaries of articles
- Figures
- Volume 5 contains nine of Euler's works:
- E241: Demonstratio theorematis Fermatiani omnem numerum primum formae 4n+1 esse summam duorum quadratorum
- E242: Demonstratio theorematis Fermatiani omnem numerum sive integrum sive fractum esse summam quatuor pauciorumve quadratorum
- E243: Observatio de summis divisorum
- E244: Demonstratio theorematis circa ordinem in summis divisorum observatum
- E245: De methodo Diophanteae analoga in analysi infinitorum
- E246: Subsidium calculi sinuum
- E247: De seriebus divergentibus
- E248: De cochlea Archimedis
- E249: De aptissima figura rotarum dentibus tribuenda
- Volume 6: published 1761.
- Summaries of articles (no table of
contents in this volume)
- Figures
- Volume 6 contains eleven of Euler's works:
- E250: Methodus inveniendi infinitas curvas isoperimetras aliave communi proprietate praeditas
- E251: De integratione aequationis differentialis mdx/V(1-x4)=ndy/V(1-y4)
- E252: Observationes de comparatione arcuum curvarum irrectificibilium
- E253: De problemativus indeterminatis, quae videntur plus quam determinata
- E254: De expressione integralium per factores
- E255: Solutio generalis quorundam problematum Diophanteorum, quae vulgo nonnisi solutiones speciales admittere videntur
- E256: Specimen de usu observationum in mathesi pura
- E257: De frictione corporum rotantium
- E258: Principia motus fluidorum
- E259: De motu et reactione aquae per tubos mobiles transfluentis
- E260: Tentamen theoriae de frictione fluidorum
- Volume 7: published 1761.
- Summaries of articles (no table of contents in this volume)
- Figures
- Volume 7 contains five of Euler's works:
- E261: Specimen alterum methodi novae quantitates transcendentes inter se comparandi; de comparatione arcuum ellipsis
- E262: Theoremata circa residua ex divisione potestatum relicta
- E263: Specimen novae methodi curvarum quadraturas et rectificationes aliasque quantitates transcendentes inter se comparandi
- E264: Demonstratio theorematis et solutio problematis in actis erud. Lipsiensibus propositorum
- E265: De aequationibus differentialibus secundi gradus
- Volume 8: published 1763.
- Table of contents
- Summaries of articles:
- Figures
- Volume 8 contains ten of Euler's works:
- E269: De integratione aequationum differentialium
- E270: Solutio problematis de investigatione trium numerorum, quorum tam summa quam productum nec non summa productorum ex binis sint numeri quadrati
- E271: Theoremata arithmetica nova methodo demonstrata
- E272: Supplementum quorundam theorematum arithmeticorum, quae in nonnullis demonstrationibus supponuntur
- E273: Consideratio formularum, quarum integratio per arcus sectionum conicarum absolvi potest
- E274: Constructio aequationis differentio-differentialis Ay du2 + (B+Cu)dudy + (D+Eu+Fuu)ddy = 0, sumto elemento du constante
- E275: Annotationes in locum quendam Cartesii ad circuli quadraturam spectantem
- E276: Dilucidationes de resistentia fluidorum
- E277: Principia theoriae machinarum
- E278: De motu et attrutu lentium dum super catinis poliuntur
- Volume 9: published 1764.
- Table of contents and summaries of articles
- Figures Volume 9 contains ten of Euler's works:
- E279: De resolutione formularum quadricarum indeterminatarum per numeros integros
- E280: De progressionibus arcuum circularium, quorum tangentes secundum certam legem procedunt
- E281: Specimen algorithmi singularis
- E282: De resolutione aequationum cuiusvis gradus
- E283: De numeris primis valde magnis
- E284: De resolutione aequationis dy + ayy dx = bxm dx
- E285: Investigatio functionum ex data differentialium conditione
- E286: De motu vibratorio fili flexilis, corpusculis quotcunque onusti
- E287: De motu vibratorio cordarum inaequaliter crassarum
- E288: Cogitationes de aggeribus construendis
- Volume 10: published 1766.
- Table of contents
- Summaries of articles
- Figures
- Volume 10 contains ten of Euler's works:
- E295: De reductione formularum integralium ad rectificationem ellipsis ac hyperbolae
- E296: Elementa calculi variationum
- E297: Analytica explicatio methodi maximorum et minimorum
- E298: De insigni promotione methodi tangentium inversae
- E299: Dilucidationes de tautochronis in medio resistente
- E300: Demonstratio theorematis Bernoulliani quod ex evolutione curvae cuiuscinque rectangulae in infinitum continuata tandem cycloides naxcantur
- E301: De motu corporis ad duo centra virium fixa attracti
- E302: De motu vibratorio tympanorum
- E303: Tentamen de sono campanarum
- E304: Considerationes de motu corporum coelestium
- Volume 11: published 1767.
- Table of contents
- Summaries of articles
- Figures
- Volume 11 contains ten of Euler's works:
- E322: De usu functionum discontinuarum in analysi
- E323: De usu novi algorithmi in problemate Pelliano solvendo
- E324: Proprietates triangulorum, quorum anguli certam inter se tenent rationem
- E325: Solutio facilis problematum quorundam geometricorum difficillimorum
- E326: Observationes analyticae
- E327: De motu rectilineo trium corporum se mutuo attrahentium
- E328: De motu corporis ad duo centra virium fixa attracti
- E329: De phaenomenis coeli per segmenta sphaerica diaphana spectati
- E330: Supplementum de figura dentium rotarum
- E331: De motu fluidorum a diverso caloris gradu oriundo
- Volume 12: published 1768.
- Table of contents
- Volume 12 contains seven of Euler's works:
- E345: Integratio aequationis dx/V(A+Bx+Cx2+Dx3+Ex4)=dy/V(A+By+Cy2+Dy3+Ey4)
- E346: De arcubus curvarum aeque amplis earumque comparatione
- E347: Evolutio generalior formularum comparationi curvarum inservientium
- E348: Nethodus facilis motus corporum coelestium utcunque perturbatos ad rationem calculi astronomici revocandi
- E349: Disquitio de vera lege refrationis radiorum diversicolorum
- E350: De novo microscopiorum genere ex sex lentibus composito
- E351: De telescopiis quatuor lentibus instructis eorumque perfectione
- Volume 13: published 1769.
- Table of contents
- Volume 13 contains eight of Euler's works:
- E368: De curva hypergeometrica hac aequatione expressa y=1*2*3*…*x
- E369: Quomodo numeri praemagni sint explorandi, utrum sint primi necne
- E370: Nova criteria radices aequationum imaginarias discoscendi
- E371: Considerationes de theoria motus Lunae perficienda et imprimis de eius variatione
- E372: Annotatio quarundam cautelarum in investigatione inaequalitatum quibus corpora coelestia in motu perturbantur observandarum
- E373: Investigatio accuratior phaenomenorum quae in motu terrae diurno a viribus coelestibus produce possunt
- E374: De aequilibrio et motu corporum flexuris elasticis iunctorum
- E375: Sectio prima de statu aequilibrii fluidorum
- Volume 14: published 1770.
- Table of contents
- Volume 14 contains eight of Euler's works:
- E390: Considerationes de traiectoriis orthogonalibus
- E391: De formulis integralibus duplicatis
- E392: Evolutio insignis paradoxi circa aequatlitatem superficierum
- E393: De summis serierum numeros Bernoullianos involventium
- E394: De partitione numerorum in partes tam numero quam specie datas
- E395: De inventione quotumque mediarum proportionalium citra radicum extractionere
- E396: Sectio secunda de principiis motus fluidorum
- E397: Expositio methodorum, cum pro determinanda parallaxi solis ex observato transitu Veneris per solem, tum pro inveniendis longitudinibus locorum super terra, ex observationibus eclipsium solis, una cum calculis et conclusionibus inde deductis
- Volume 15: published 1771.
- Table of contents
- Volume 15 contains seven of Euler's works:
- E405: Solutio problematis, quo duo quaeruntur numeri, quorum productum tam summa quam differentia eorum sive auctum sive minutum fiat quadratum
- E406: Observationes circa radices aequationum
- E407: Problema algebraicum ob affectiones prorsus singulares memorabile
- E408: De curva rectificabili in superficie sphaerica
- E409: Sectio tertia de motu fluidorum lineari potissimum aquae
- E410: Genuina principia doctrinae de statu aequilibrii et motu corporum tam perfecte flesibilium quam elasticorum
- E411: De ictu glandium contra tabulam explosarum
- Volume 16: published 1772.
- Table of contents
- Volume 16 contains seven of Euler's works:
- E419: De solidis quorum superficiem in planum explicare licet
- E420: Methodus nova et facilis calculum variationum tractandi
- E421: Evolutio formulae integralis ∫ xf-1 dx (lx)m/n integratione a valore x=0 ad x=1 extensa
- E422: Problematis cuiusdam geometrici prorsus singularis evolutio
- E423: Considerationes cyclometricae
- E424: Sectio quarta de motu aeris in tubis
- E425: De perturbatione motus terrae ab actione Veneris oriunda
- Volume 17: published 1773.
- Table of contents
- Volume 17 contains eighteen of Euler's works:
- E427: Problematis cuiusdam Diophantei evolutio
- E428: Observationes circa bina biquadrata, quorum summam in duo alia biquadrata resolvere liceat
- E429: De variis integrabilitatis generibus
- E430: Observationes circa aequationem differentialem ydy+Mydx+Ndx=0
- E431: Consideratio aequationis differentio-differentialis (a+bx)ddz+(c+ex)dxdz/x+(f+gx)zdx2/xx=0
- E432: Exercitationes analyticae
- E433: Digressio de traiectoriis tam orthogonalibus quam obliquangulis
- E434: De collisione corporum gyrantium
- E435: De collisione corporum pendulorum, tam obliqua, quam motu gyratorio perturbata
- E436: De vera tautochrona in fluido
- E437: De tautochrona in medio rarissimo, quod resistit in ratione multiplicata quacunque celeritatis
- E438: Dilucidationes de tautochronismo
- E439: De chordis vibrantibus disquisitio ulterior
- E440: Animadversiones in solutionem Bernoullianam de motu chordarum ex duabus partibus diversae crassitiei compositarum Tomo XVI Novorum Commentariorum
- E441: De motu vibratorio chordarum ex partibus quotcunque diversae crassitiei compositarum
- E442: De motu vibratorio chordarum crassitie utcunque variabili praeditarum
- E443: De motu vibratorio laminarum elasticarum, ubi plures novae vibrationum species hactenus non pertractatae evolvuntur
- E444: De motu gravium citissimo super curvis specie datis
- Volume 18: published 1774.
- Table of contents
- Volume 18 contains fourteen of Euler's works:
- E447: Summatio progressionum sin phi2 + sin 2phi2 + … cos phi2 + cos 2phi2 + …
- E448: Nova series infinita maxime convergens perimetrum ellipsis exprimens
- E449: Demonstrationes circa residua ex divisione potestatum per numeros primos resultantia
- E450: Nova ratio quantitates irrationales proxime exprimendi
- E451: Solutio problematis de inveniendo triangulo, in quo rectae ex singulis angulis latera opposita bisecantes sint rationales
- E452: Resolutio aequationis Ax2+2Bxy+Cy2+2Dx+2Ey+F=0 per numeros tam rationales quam integros
- E453: Insignes proprietates serierum sub hoc termino generali contentarum x=1/2(a+b/Vk)(p+qVk)n + 1/2(a-bVk)(p-qVk)n
- E454: De resolutione irrationalium per fractiones continuas, ubi simul nova quaedam et singularis species minimi exponitur
- E455: Determinatio motus oscillatorii in praecedente dissertatione pertracti, ex primus mechanicae principiis petita
- E456: De pressione ponderis in planum cui incumbit
- E457: De harmoniae veris principiis per speculum musicum repraesentatis
- E458: Nova methodus motus planetarum principalium ad tabulas astronomicas reducendi
- E459: Disquitio de lentibus obiectivis triplicatis, quae vel nullam confusionem pariant vel etiam datam confusionem a reliquis lentibus ortam destruere valeant
- E460: De applicatione lentium obiectivarum compositarum ad omnis generis telescopia
- Volume 19: published 1775.
- Table of contents
- Volume 19 contains eleven of Euler's works:
- E462: De valore formulae integralis ∫ (xm-1 ± zm-n-1)/(1±zn) dz casu quo post integrationem ponitur z=1
- E463: De valore formulae integralis ∫ (zλ-ω ± xλ+ω)/(1±z2λ)*(dz/z)(lz)u casu quo post integrationem ponitur z=1
- E464: Nova methodus quantitates integrales determinandi
- E465: Demonstratio theorematis Neutoniani de evolutione potestatum binomii pro casibus, quibus exponentes non sunt numeri integri
- E466: Problema Diophanteum singulare
- E467: De tabula numerorum primorum usque ad millionem et ultra continuanda, in qua simul omnium numerorum non primorum minimi divisores exprimantur
- E468: De oscillationibus minimis penduli quotunque pondusculis onusti
- E469: De motu oscillatorio binarum lancium ex libra suspensarum
- E470: Explicatio motus oscillatorii mirabilis in libra maiore observati
- E471: De motu turbinatorio chordarum musicarum; ubi simul universa theoria aequilibrii quam motus corporum flexibilium simulque etiam elasticorum breviter explicatur
- E472: Commentatio hypothetica de periculo a nimia cometae approponquatione metuendo
- Volume 20: published 1776.
- Table of contents
- Volume 20 contains eleven of Euler's works:
- E474: Solutio quorundam problematum Diophanteorum
- E475: Speculationes analyticae
- E476: Observationes circa novum et singulare progressionum genus
- E477: Meditationes circa singulare serierum genus
- E478: Formulae generales pro translatione quacunque corporum rigidorum
- E479: Nova methodus motum corporum rigidorum degerminandi
- E480: Regula facilis pro diiudicanda firmitate pontis aliusve corporis similis excognita firmitate moduli
- E481: De gemina methodo tam aequilibrium quam motum corporum flexibilium determinandi et utriusque egregio consensu
- E482: De pressione funium tensorum in corpora subiecta eorumque motu a frictione impedito. Ubi praesertim methodus traditur …
- E483: De traiectu citissimo stellae per duos circulos almucantarath datos pro qualibet elevatione poli.
- E484: De circulo maximo fixo in coelo constituendo, ad quem orbitae planetarum et cometarum referantur.