Enestrom Numbers 600-699

Original Titles
     
English Titles

600The solution of certain difficult questions in the calculus of probabilities
601De symptomatibus quatuor punctorum, in eodem plano sitorum
602Methodus facilis omnia symptomata linearum curvarum non in eodem plano sitarum investigandi
603De descensu baculi super hypomochlio cylindro fixo delabentis
604On rectilinear and oblique reciprocal trajectories
605On the remarkable properties of the elastic curves under the equation y = ∫ (xx dx)/√(1-x4)
606Speculations concerning the integral formula ∫ (xndx)/√(aa-2bx+cxx), where at once occur exceptional observations about continued fractions
607De motu globi circa axem obliquum quemcunque gyrantis et super plano horizontali incedentis
608Accuratior evolutio formularum pro filorum flexibilium aequilibrio et motu inventarum
609Considerations about rectilinear and oblique trajectories
610New demonstrations about the divisors of numbers of the form xx + nyy
611Investigatio curvarum quae similes sint suis evolutis vel primis vel secundis vel tertiis vel adeo ordinis cuiuscunque
612De motu globi heterogenei super plano horizontali, una cum dilucidationibus necessariis super motu vacillatorio
613Dilucidationes in capita postrema calculi mei differentalis de functionibus inexplicabilibus
614Commentary on tractrix curves
615De viribus centripetis, ad curvas non in eodem plano sitas describendas, requisitis
616On the transformation of the divergent series 1 - mx + m(m+n)x2 - m(m+n)(m+2n)x3 + etc. into a continued fraction
617On the summation of series, in which the signs of the terms alternate
618Consideratio motus singularis, qui in filo perfecte flexili locum habere potest
619Enodatio difficultatis super figura terrae a vi centrifuga oriunda.
620An easy method for finding the integral of the formula ∫ (dx/x)(xn+p - 2xncosζ + xn-p)/(x2n - 2xncosθ + 1) in the case in which after integration it is put from x = 1 to x = ∞
621On the greatest use of the calculus of imaginaries in analysis
622Specimen singulare analyseos infinitorum indeterminatae
623De lineis rectificabilibus in superficie sphaeroidica quacunque geometrice ducendis
624De superficie coni scaleni, ubi imprimis intentes difficultates, quae in hac investigatione occurrunt, perpenduntur
625De viribus centripetis, ad curvas non in eodem plano sitas describendas, requisitis
626On the movement of three bodies mutually attracted above a straight line
627Solutio problematis mechanici
628Clarifications on the paper by Mr. de La Grange inserted into volume 5 of the Melanges de Turin, concerning the method of taking the mean of the results of various observations
629The expansion of the integral formula ∫ dx(1/(1-x) + 1/(lx)) with the term extended from x = 0 to x = 1
630Uberior explicatio methodi singularis nuper expositae integralia alias maxime abscondita investigandi
631An easy and clear analysis for guiding those most abstruse series, by which not only the roots but even the powers of the roots of all algebraic equations are able to be expressed
632On innumerable types of most remarkable series, by which not only the roots but even too any power of the roots of all algebraic equations are able to be expressed
633De binis curvis algebraicis inveniendis, quarum arcus indefinite inter se sint aequales
634De motu oscillatorio tabulae suspensae et a vento agitatae
635Innumera theoremata circa formulas integrales, quorum demonstratio vires analyseos superare videatur
636On the multiplication of angles which are to be obtained by factors
637A new demonstration, with respect to which prevails the expansion of binomial powers by Newton even by fractional exponents
638On innumerable algebraic curves, of which the longitude is able to be measured by parabolic arcs
639On innumerable algebraic curves, of which the longitude is able to be measured by elliptical arcs
640Comparatio valorum formulae integralis ∫ (xp-1 dx)/(n√((1-xn)n-q)) a termino x = 0 usque ad x = 1 extensae
641De motu quodam maxime memorabili, satis quidem simplici, at solutu difficillimo
642On a singular rule for differentiating and integrating, which occurs in the sums of series
643A general method for investigating all the roots of an equation by approximation
644Innumerable forms of equations from all orders, of which a resolution is able to be exhibited
645On algebraic curves, of which the longitudes are expressed by the integral formula ∫ (vm-1 dv)/√(1-v2n)
646De duabus pluribusve curvis algebraicis in quibus si a terminis fixis aequales arcus abscindantur eorum amplitudines datam inter se teneant rationem
647De methodo tangentium inversa ad theoriam solidorum translata
648An easy solution of a problem, in which a circle is searched for, given three circles tangent to it
649De motu oscillatorio penduli circa axem cylindricum plano horizontali incumbentem
650De formulis differentialibus quae per duas pluresve quantitates datas multiplicatae fiant integrabiles
651Four most noteworthy theorems on the calculation of an integral
652On the general term of hypergeometric series
653De iterata integratione formularum integralium, dum aliquis exponens pro variabili assumitur
654Methodus facilis investigandi radium osculi ex principio maximorum et minimorum petita
655General observations about series, of which the terms arising for the sines or cosines of multiplied angles come forth
656On most memorable integrations arising from the calculation of imaginaries
657A supplement to the preceding dissertation about the integration of the formula ∫ (zm-1 dz)/(1-zn) in the case where z = v(cos(φ) + √(-1) sin(φ))
658De momentis virium respectu axis cuiuscunque inveniendis; ubi plura insignia symptomata circa binas rectas, non in eodem plano sitas, explicantur
659Methodus facilis omnium virium momenta respectu axis cuiuscunque determinandi
660Foundations of Integral Calculus, Volume 4
661Several considerations about hypergeometric series
662On the true value of the integral formula ∫ dx(l(1/x))n with the term extended from x = 0 all the way to x = 1
663Plenior expositio serierum illarum memoragilium, quae ex unciis potestatum binomii formantur
664Analytical exercises
665The evolution of a problem whose analytic solution is most difficult, while the synthetic solution for it is obvious
666Problema geometricum ob singularia symptomata imprimis memorabile
667De curvis hyperbolicis quae intra suas assymtotas spatium finitum includunt
668On the integration of the formula (dx √(1+x4))/(1-x4) and of others of the same type by logarithms and circular arcs
669Memorabile genus formularum differentialium maxime irrationalium quas tamen ad rationalitatem perducere licet
670De resolutione formulae integralis ∫ (xm-1 dx)(Δ + xn)λ in seriem semper convergentem, ubi simul plura insignia artificia circa serierum summationem explicantur
671De formulis differentialibus angularibus maxime irrationalibus, quas tamen per logarithmos et arcus circulares integrare licet
672A memorable theorem about the integral formula ∫ (dφ cos(λφ))/(1+aa-2acos(φ))n+1
673A conjectural disquisition about the integral formula ∫ (dφcos(iφ))/(α+βcos(φ))n
674Demonstratio theorematis insignis per coniecturam eruti circa intagrationem formulae ∫ (dφ cos(iφ))/(1+aa-2acos(φ))n+1
675On the values of integrals where the variable term is extended x = 0 all the way to x = ∞
676Methodus succinctior comparationes quantitatum transcendentium in forma ∫ (P dz)/√(A + 2Bz + Czz + 2Dz3 + Ez4) contentarum inveniendi
677Special methods for resolving differential equations of the second degree
678A new method for investigating all cases in which the differential equation ddy(1-axx) - bx dx dy - cy dx2 = 0 is permitted to resolve
679De formulis integralibus implicatis earumque evolutione et transformatione
680De aequationibus differentialibus cuiuscunque gradus quae denuo differentiatae integrari possunt
681Specimen aequationum differentialium indefiniti gradus earumque integrationis
682On the pressure of a table weighted by a weight on a surface. From the papers of the blessed Leonhard Euler extracted by Jakob Bernoulli.
683On a singular type of Diophantine questions and a most recondite method by which they are to be resolved
684On the roots of the infinite equation 0 = 1 - (xx)/(n(n+1)) + (x4)/(n(n+1)(n+2)(n+3)) - (x6)/(n.....(n+5)) + etc.
685An analytical exercise, where in particular a most general summation of series is given
686Elucidations about the formula, in which the sines and cosines of angles are to be multiplied, where at once large difficulties are diluted
687De insignibus proprietatibus formularum integralium praeter binas variabiles etiam earum differentialia cuiuscunque ordinis involventium
688A most abstruse specimen of integral contained in the formula ∫ dx/((1+x)*4√(2xx-1))
689Integratio formulae differentialis maxime irrationalis, quam tamen per logarithmos et arcus circulares expedire licet
690The expansion of the integral formula ∫ dz(3+zz)/((1+zz)*4√(1+6zz+z4)) by logarithms and circular arcs
691Problema geometricum quo inter omnes ellipses quae per data quatuor puncta traduci possunt ea quaeritur quae habet aream minimam
692Solutio problematis maxime curiosi quo inter omnes ellipses quae circa datum triangulum circumscribi possunt ea quaeritur cuius area sit omnium minima
693On the center of similarity
694Later paper on formulas of imaginary integrals
695A succinct integration of the most memorable integral formula ∫ dz/((3±zz)*3√(1±3zz))
696On the cases in which the form x4 + kxxyy + y4 is permitted to be reduced to a square
697Investigatio superficierum quarum normales ad datum planum productae sint omnes inter se aequales
698Several speculations about the area of spherical triangles
699Inquiring on whether or not the number 100009 is prime