Enestrom Numbers 500-599

Original Titles
English Titles

500On the value of the integral formula ∫ ((xa-1 dx)/lx)(1-xb)(1-xe)/(1-xn) bounded at x = 0 and extended to x = 1
501Considerations about brachistochrones
502On the effects of refraction during terrestrial observations
503De motu oscillatorio penduli cuiuscunque, dum arcus datae amplitudinis absolvit
504On the Theory of the Moon which is to be carried to a higher level of perfection
505De corporibus regularibus per doctrinam sphaericam determinatis; ubi simul nova methodus globos sive coelestes sive terrestres charta obducendi traditur
506(Elucidations about a most elegant method, which the illustrious la Grange used in the integration of the differential equation dx/√X = dy/√Y
507On the infinity of infinities of orders of the infinitely large and infinitely small
508The determination of the loads which columns are strong enough to bear
509An examination of an outstanding paradox occurring in the theory of columns
510De altitudine columnarum sub proprio pondere corruentium
511Thoughts concerning the Earth's motional inequalities caused by Venus' action, accompanied with a table of the corrections of Earth's position
512Investigatio perturbationum quae in motu terrae ab actione Veneris producunter: cum tabula perturbationum istarum
513On triangular curves
514On the measure of solid angles
515De casibus quibusdam maxime memorabilibus in analysi indeterminata, ubi imprimis insignis usus calculi angulorum in analysi Diophantea ostenditur
516De motu oscillatorio duorum corporum ex filo super trochleas traducto suspensorum
517On a certain problem in mechanics, obvious enough, but with a most difficult solution
518Solutio gemina problematis, quo motus corporis, filo alicubi alligati, super plano horizontali quaeritur
519New method to determine the motion of planets
520Essay of the theory of resistance that a prow of a ship experiences throughout its motion
521Analytical theories. Extracts of different letters of Mr. Euler to Mr. le Marquis de Condorcet
522On the formation of continuous fractions
523On three square numbers, of which the sum and the sum of products two apiece will be a square
524A universal spherical trigonometry, derived briefly and from first principles
525De motu oscillatorio mixto plurium pendulorum ex eodem corpore mobili suspensorum
526Investigatio motuum, quibus laminae et virgae elasticae contremiscunt
527A conjecture about the nature of air, by which are to be explained the phenomenon which have been observed in the atmosphere
528An annotation to the preceding dissertation
529A theory of parallaxes, accommodating the spheroid shape of the Earth
530Investigations on a new type of magic square
531Brief analytical works, volume 1
532On the remarkable properties of a series of Lambert and others
533On the oscillating motion derived from a tense hanging thread
534Elucidations about several rather difficult cases of equilibrium
535Determinatio omnium motuum, quos chorda tensa et uniformiter crassa recipere potest
536On the properties of triangles in mechanics
537On the figure of elastic curves against the objections of the illustrious d'Alembert
538Necessary cautions in the determination of the motion of planets which are to be observed
539A supplement to the calculation of integrals for the calculation of irrational formulas
540A new method for resolving all rational fractions into simpler fractions
541The expansion of the infinite product (1-x)(1-xx)(1-x3)(1-x4)(1-x5) etc. into a single series
542On the remarkable properties of the pentagonal numbers
543Problematis cuiusdam Pappi Alexandrini constructio
544De motu libero plurium corporum filis colligatorum super plano horizontali
545De vi fluminis ad naves sursum trahendas applicanda
546De statu aequilibrii maris a viribus solis et lunae sollicitati.
547Simple determination of the orbit of a comet, when it is possible to observe its transit across the ecliptic twice
548De variis motuum generibus, qui in satellitibus planetarum locum habere possunt.
549De motibus maxime irregularibus, qui in systemate mundano locum habere possent, una cum methodo hujusmodi motus per temporis spatium quantumvis magnum prosequendi.
550On series in which the product of two consecutive terms make a given progression
551Various methods for inquiring into the innate characters of series
552Observations about the division of squares by prime numbers
553Analytical observations
554A more exact disquisition about the residues remaining from the division of squares and of higher powers by prime numbers
555An examination of the use of interpolating methods in the doctrine of series
556On the criteria of whether equation fxx + gyy = hxx admits a resolution or not
557De quibusdam eximiis proprietatibus circa divisores potestatum occurrentibus
558Proposita quacunque protressione ab unitate incipiente, quaeritur quot eius terminos a dminimum addi oporteat, ut omnes numeri producantur
559New assistance for solving the formula axx + 1 = yy
560Miscellaneous analyses
561Various observations about angles proceeding in geometric progression
562On how sines and cosines of multiplied angles may be expressed by products
563On the smallest ellipse which is to circumsrcibe a given rectilinear parallelogram
564Speculations about certain outstanding properties of numbers
565On highly transcendental quantities, which may not be expressed in any way by integral formulas
566De inductione ad plenam certitudinem evehenda
567Dilucidationes de motu chordarum inaequaliter crassarum
568De motu penduli circa axem cylindricum, fulcro datae figurae incumbentem, mobilis. Remota frictione
569De motu penduli circa axem cylindricum, fulcro datae figurae incumbentem, mobilis. Habita frictionis ratione
570On finding longitude of a place by observing the distance between the moon and a known fixed star
571De eclipsibus solaribus in superficie terrae per proiectionem repraesentandis.
572Nova methodus integrandi formulas differentiales rationales sine subsidio quantitatum imaginariarum
573De duplici genesi tam epicycloidum quam hypocycloidum
574De curvis rectificabilibus in superficie coni recti ducendis
575De mirabilibus proprietatibus unciarum, quae in evolutione binomii ad potestatem quamcunqua evecti occurrunt
576De oscillationibus minimis funis libere suspensi
577De perturbatione motus chordarum ab earum pondere oriunda
578On the disturbance of motion concerning planets and comets
579Caculation on aerostatic balloons made by the late Mr. Euler as they were found on his blackboard, after the occurrence of his death on September 7, 1783
580Brief analytical works, volume 2
581A more complete investigation into the relationship between those quantities contained in the integral formula ∫ (\Z dz)/√(1+mzz+nz4), where Z denotes a rational function of zz.
582The fruitful development of a relation which may be established between the arcs of conic sections
583De numero memorabili in summatione progressionis harmonicae naturalis occurrente
584De insignibus proprietatibus unciarum binomii ad uncias quorumvis polynomiorum extensis
585De effectu frictionis in motu volutorio
586Considerations about a theorem of Fermat on the resolution of numbers into polygonal numbers
587An observation on several theorems of the illustrious de la Grange
588An investigation of the integral formula ∫ (xm-1 dx)/(1+xk)n in the case in which after integration it is set x = ∞
589An investigation of the value of the integral ∫ (xm-1 dx)/(1-2xkcosθ+x2k) the term to be extended from x = 0 to x = ∞
590Certain theorems in analysis, of which a demonstration is thus far desired
591On the relation between three and more quantities which are to be instituted
592On the resolution of transcendental fractions into infinitely many simple fractions
593On the transformation of series into continued fractions, where at once this not mediocre theory is enlarged
594A method for finding integral formulas, for which in certain cases a given rule holds between them, where at once a method is related for summing continued fractions
595Summatio fractionis continuae cuius indices progressionem arithmeticam constituunt dum numeratores omnes sunt unitates ubi simul resolutio aequationis Riccatianae per huiusmodi fractiones docetur
596On the sum of the series of numbers of the form 1/3 - 1/5 + 1/7 + 1/11 - 1/13 ... in which the prime numbers of the form 4n-1 have positive signs, and those of the form 4n+1 have negative signs
597A new and most easy method for summing series of reciprocals of powers
598De insigni promotione scientiae numerorum
599Solution to a question concerning the calculation of probability: How much should be paid by a couple, so that a certain sum of money can be paid to the heir after the death of the other