Mémoires de l`Académie Impériale des Sciences de St. Pétersbourg

Original Titles
English Titles

613Dilucidationes in capita postrema calculi mei differentalis de functionibus inexplicabilibus
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
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