Enestrom Numbers 700-799

Original Titles
English Titles

700On differential equations of the second degree which admit integration
701Formae generales differentialium, quae, etsi nulla substitutione rationales reddi possunt. tamen integrationem per logarithmos et arcus circulares admittunt
702De novo genere quaestionum arithmeticarum pro quibus solvendis certa methodus adhuc desideratur
703An easy method for finding series proceeding by the multiplication of the sines and cosines of angles, of which the use in the universal theory of astronomy is very great
704Disquisitio ulterior super seriebus secundum multipla cuiusdam anguli progredientibus
705Investigatio quarundam serierum, quae ad rationem peripheriae circuli ad diametrum vero proxime definiendam maxime sunt accommodatae
706On a new type of rational and highly convergent series, by which the ratio of the periphery to the diameter is able to be expressed
707On the outstanding use of the calculation of imaginations in the calculation of an integral
708On forms of the type mxx + nyy for exploring prime numbers by idoneals of them with remarkable properties
709On the expansion of the power of any polynomial 1 + x + x2 + x3 + x4 + etc.
710Example of the transformation of singular series
711A new and easy method for expressing for all algebraic equations not only their roots but also the powers of them by constructing series
712De corporibus cylindricis incurvatis
713An investigation of a triangle in which the distances of the angles from the center of gravity of it may be expressed rationally
714Exempla quarundam memorabilium aequationum differentialium, quas adeo algebraice integrare licet, etiamsi nulla via pateat variabiles a se invicem separandi
715On various ways of examining very large numbers, for whether or not they are primes
716The resolution of the Diophantine formula ab(maa+nbb) = cd(mcc+ndd) by rational numbers
717Solution to a problem of mechanics
718An easy method of finding several rather large prime numbers
719A more general method by which all adequately large numbers may be scrutinized for whether or not they are prime
720Special observations about linear differential equations
721De integrationibus difficillimis, quarum integralia tamen aliunde exhiberi possunt
722Analytical disquisitions on the expansion of the trinomial power (1+x+xx)n
723A letter by Euler
724Research concerning some remarkable integrations in functional analysis with two variables known under the title of partial differentials
725An illustration of a paradox about the idoneal, or suitable, numbers
726A demonstration of a notable theorem of numbers a twelfth part of binomial powers
727A more accurate treatment of the problem of drawing the shortest line on a surface
728On the resolution of composite fractions into simpler ones
729Dilucidationes super Problemate geometrico de quadrisectione trianguli a Iacobo Bernoulli olum tractato
730Solutio completa problematis de quadrisectione trianguli per duas rectas inter se normales
731The solution of a memorable problem by a special artifice of calculation
732An easier solution of a Diophantine problem about triangles, in which those lines from the vertices which bisect the opposite sides may be expressed rationally
733Solutio facilis problematis, quo quaeritur sphaera, quae datas quatuor sphaeras utcunque dispositas contingat
734The integration of the differential equation dy + yydx = (A dx)/(a+2bx+cxx)2
735On an outstanding paradox, which occurs in the analysis of maximums and minimums
736On the summation of series contained in the form a/1 + a2/4 + a3/9 + a4/16 + a5/25 + a6/36 + etc.
737De transformatione functionum duas variabiles involventium dum earum loco aliae binae variabiles introducuntur
738The solution of a curious question in the scene of combinations
739An easy rule for Diophantine problems which are to be resolved quickly by integral numbers
740De lineis curvis non in eodem plano sitis, quae maximi minimive proprietate sunt praeditae
741Analysis facilis aequationem Riccatianam per fractionem continuam resolvendi
742Observations about continued fractions contained in the form S = n/(1+(n+1)/(2+(n+2)/(3+(n+3)/(4+etc.))))
743De serie maxime memorabili, qua potestas binomialis quaecunque exprimi potest
744On divisors of numbers of the form mxx + nyy
745On the continued fractions of Wallis
746A method for gathering the sums of infinite series by investigating differential formulas
747On remarkable series, by which the sines and cosines of multiplied angles may be expressed
748Investigatio quadrilateri, in quo singularum angulorum sinus datam inter se teneant rationem, ubi artificia prorsus singularia in Analysi Diophantea occurrunt
749About geometry and spheres
750A commentary on the continued fraction by which the illustrious La Grange has expressed the binomial powers
751Analysis facilis aequationem Riccatianam per fractionem continuam resolvendi
752De integralibus quibusdam inventu difficillimis
753Solution succincta et elegans problematis, quo quaeruntur tres numeri tales, ut tam summae quam differentiae binorum sint quadrata
754On a problem of geometry resolved by Diophantine analysis
755On cases for which the formula x4 + mxxyy + y4 can be reduced to a square
756Solution to some curious problems of mechanics
757On the problem of orthogonal trajectories, translated to surfaces
758De binis formulis speciei xx + myy et xx + nyy inter se concordibus et discordibus
759A more accurate investigation into brachistochrones
760De vera brachystochrona seu linea celerrimi descensus in medio resistente
761De brachystochrona in medio resistente, dum corpus ad centrum virium utunque attrahitur
762Unpublished letter from Euler to Lagrange
763On finding three or more numbers, the sum of which is a square, while the sum of the squares is a fourth power
764An easy resolution to a most difficult question, where this most general form vvzz(axx+byy)2 + Δxxyy(avv+bzz)2 is required to be reduced to a square
765De problemate curvarum synchronarum, eiusque imprimis inverso
766Methodus nova et generalis problema synchronarum inversum aliaque eiusdem generis resolvendi
767De curvis quarum radii osculi tenent rationem duplicatam distantiae a puncto fixo earumque mirabilibus proprietatibus
768De unciis potestatum binomii earumque interpolatione
769A solution to a problem of Fermat, on two numbers of which the sum is a square and the sum of their squares is a biquadrate, inspired by the Illustrious La Grange
770Enodatio maximi paradoxi, in problemate quodam mechanico occurentis
771Solutio trium problematum difficiliorum ad methodum tangentium inversam pertinentium
772On a notable advancement of Diophantine analysis
773A solution of a most difficult problem, in which the two forms aaxx + bbyy et aayy + bbxx must be rendered into squares
774An investigation of two numbers of the form xy(x4-y4), of which the product and the quotient will be a square
775On two numbers, of which the sum when increased or decreased by the square of one of them produces a square
776Elucidations about two sums of pairs of biquadratics, which are mutually equal
777On the resolution of the equation 0 = a + bx + cy + dxx + exy + fyy + gxxy + hyy + ixxyy by rational numbers
778A new and easy method for reducing cubic and biquadratic forms to squares
779Solutio problematis ad analysin infinitorum indeterminatorum referendi
780De infinitis curvis algebraicis, quarum longitudo indefinita arcui elliptico aequatur
781De infinitis curvis algebraicis, quarum longitudo arcui parabolico aequatur
782De binis curvis algebraicis eadem rectificatione gaudentibus
783On algebraic curves, all of whose arcs may be measured by circular arcs
784Solution to a very difficult analytical problem
785Integration of a remarkable type of differential equation in analytical functions with two variables
786The Complete works of L. Euler in French
787Solution of a problem proposed in the Leipzig Acts in 1745
788Letters of L. Euler and Chr. Goldbach 1729-1763
789A few lines from a letter of L. Euler to Albrecht von Haller, from 4 July 1744
790Commentary on the use of sublime mathematics
791Collected arithmetical commentaries
792Tractatus de numerorum doctrina capita sedecim, quae supersunt
793Thoughts concerning Diophantine analysis
794A theorem of arithmetic and its proof
795On magic squares
796Research into the problem of three square numbers such that the sum of any two less the third one provides a square number
797Further and curious research into the problem of four positive numbers and an arithmetical proportion such that the sum of any two is always a square number
798On amicable numbers
799A fragment of a commentary, the most part on finding the relation between the sides of triangles of which the area is able to be expressed rationally, and of triangles in which the lines from each angle bisecting the opposite line are rationals