Works With Completed Translations (207 as of 4 Feb 2021)

Original Titles
English Titles

1Construction of isochronous curves in a resistant medium
2Physical dissertation on sound
3On a method for algebraic reciprocal trajectories
4Thoughts on a nautical problem, proposed by the illustrious Royal Academy of Sciences in Paris
5Solution to the problem of reciprocal trajectories
6Dissertation on a number of new types of tautochrone curves
7Attempt at explanation of the phenomena of air
8Solution to the problem of finding curves which is formed by an elastic strip when a force is applied to a single point
9On the shortest line joining two points on a surface
10A new method of reducing innumerable differential equations of the second degree to differential equations of the first degree
11Solution of certain differential equations which do not admit separation of variables
12On the innumerable tautochrone curves in a vacuum
13Tautochrone curves in a fluid making a second resistance proportional to the square of the speed
14Solution to problems of astronomy: given the altitudes and time differences for three fixed stars, to find the elevation of the pole and the declination of the star
15Mechanics, volume 1
16Mechanics, volume 2
18On the Indian solar year
19On transcendental progressions, that is, those whose general terms cannot be given algebraically
20The summation of an innumerable progression
21For some given curve, it is required to find another curve joined in a certain way with that given, which is suitable for producing a tautochrone curve
23On rectifiable algebraic curves
25A general method for summing series
26Observations on a theory of Fermat and others on looking at prime numbers
28Example of the construction of equations
29On the solution of a problem of Diophantus
30Inferences on the forms of roots of equations and of their orders
31Solution to differential equations of the form axn dx = dy + y2 dx
32On the shape of the earth
33An attempt at a new theory of music, exposed in all clearness, according to the most well-founded principles of harmony
36Solution of problems of arithmetic of finding numbers which, when divided by given numbers, leave given remainders
39Solution to a problem concerning astronomy
41On the sums of series of reciprocals
42On the curve of fastest descent in whatever resistent medium
44On infinite(ly many) curves of the same type, that is, a method of finding equations for infinite(ly many) curves of the same type
45Addendum to the dissertation on infinite(ly many) curves of the same type
46Universal methods of series
47Finding the sum of any series from a given general term
54A proof of certain theorems regarding prime numbers
71A dissertation on continued fractions
72Various observations about infinite series
79A problem of geometry proposed publicly by an anonymous geometer
81Thoughts on the elements of bodies
83On several properties of the conic sections which intersect with an infinity of other curved lines
90Analysis of the question whether the faculty of thinking can be attributed to matter or not
91Physical investigations on the nature of the smallest parts of matter
100On Amicable Numbers
105Memoir on the Grand Equation of the Planets
107Extract of a letter from Mr. Leonhard Euler, Prof. Mathem. and Member of the Imperial Society at Petersburgh, to the Rev. Mr. Cha. Wetstein, Chaplain and Secretary to His Royal Highness the Prince of Wales, concerning the Discoveries of the Russians on the North-East Coast of Asia.
113Method for finding the true moments of both the new and the full moon
115Method of determining the longitude of the observation site by observation of the occulations of fixed stars by the moon
133On the surface of scalene cones and of other conic bodies
134Theorems on divisors of numbers
135Various geometric demonstrations
141On the agreement of the latest eclipses of the sun and moon with my tables, to find the true times of full and new moons
143On the friction of solid bodies
147On the apparent contradiction in the rule of curved lines
148Proof concerning the number on points where two lines of ordinary order can intersect
149Reflections on space and time
153A double demonstration of a theorem of Newton, which gives a relation between the coefficient of an algebraic equation and the sums of the powers of its roots
158Various analytical observations about combinations
164Theorems about the divisors of numbers contained in the form paa ± qbb
168On the controversy between Messrs Leibniz and Bernoulli concerning the logarithms of negative and imaginary numbers
169On the cuspidal points of the second kind of Monsieur le Marquis de l'Hopital
170Research on imaginary roots of equations
171Research on the precession of the equinoxes and on the nutation of the earth's axis
175Discovery of an extraordinary law of numbers in relation to the sum of their divisors
177Discovery of a new principle in Mechanics
180Notice on the subject of Research on the precession of the equinoxes
183Part of a Letter from Leonard Euler, Prof. Math. at Berlin, and F.R.S. To the Rev. Mr. Caspar Wetstein, Chaplain to his Royal Highness the Prince of Wales, concerning the gradual Approach of the Earth to the Sun
184Part of a Letter from Mr. Professor Euler to the Reverend Mr. Wetstein, Chaplain to his Royal Highness the Prince, concerning the Contraction of the Orbits of the Planets
190Consideration of certain series which are gifted with particular properties
192Solution of a problem of geometry
198On the principle of least action
200Essay concerning a metaphysical demonstration on the general principle of equilibrium
201Calculation of the probability in the game of Rencontre
204Extract of a Letter from Professor Euler, of Berlin, to the Rev. Mr. Caspar Wetstein, Chaplain to Her Royal Highness the Princess Dowager of Wales
210Letters relating to a Theorem of Mr. Euler, of the Royal Academy of Sciences at Berlin, and F.R.S. for correcting the Aberrations in the Object-Glasses of refracting Telescopes
212Foundations of Differential Calculus, with Applications to Finite Analysis and Series, Volume 1
214Principles of spherical trigonometry taken from the method of the maxima and minima
215Elements of spheroidal trigonometry taken from the method of the maxima and minima
226General principles concerning the motion of fluids
228On numbers which are the sum of two squares
231Proof of some of the properties of solid bodies enclosed by planes
236Explanation of certain paradoxes in integral calculus
241Proof of a theorem of Fermat that every prime number of the form 4n+1 is the sum of two squares
243Observations on the sums of divisors
244A demonstration of a theorem on the order observed in the sums of divisors
251On the integration of the differential equations (m dx)/√(1-x4) = (n dy)/√(1-y4)
258Principles of the motion of fluids
262Theorems about the remainders left by division by powers
275Annotations to a certain passage of Descartes for finding the quadrature of the circle
278On the motion and grinding of lenses while they are polished upon curved plates
282On the resolution of equations of any order
289Theory of the motion of solid or rigid bodies
304Considerationes de motu corporum coelestium
308Recherches sur le mouvement de rotation des corps celestes
309Solution of a curious question which does not seem to have been subjected to any analysis
310New method to eliminate the unknown quantities in equations
313On the advantage to the banker in the game of Pharaon
314Conjecture into the reasons why flat tones are generally heard in music
315Concerning the true character of modern music
327On the rectilinear motion of three bodies mutually attracted to each other
332Research concerning the flow of rivers
333Research into the curvature of surfaces
334General research on the mortality and the propagation of the human race
335Concerning annuity incomes
338On the probability of series in the Genoese lottery
341Report concerning a new method for the propagation of grain
342Foundations of Differential Calculus, with Applications to Finite Analysis and Series, Volume 2
343Letters to a German Princess on various topics in physics and philosophy
344Letters to a German Princess on various topics in physics and philosophy
352Remarks on a beautiful relation between direct as well as reciprocal power series
366Foundations of Differential Calculus, with Applications to Finite Analysis and Series, Volume 3
385Foundations of Integral Calculus, volume 3
387Complete instruction in algebra, book 1
388Complete instruction in algebra, book 2
394On the partition of numbers into a number of parts of a given type
412Solution to a very difficult question in the calculus of probabilities
417Letters to a German Princess on various topics in physics and philosophy
423Considerations on the measurement of circles
428Observations about two biquadratics, of which the sum is able to be resolved into two other biquadratics
445Proof that every integer is the sum of four squares
447The summation of the progressions
sin(φλ) + sin(2φλ) + sin(3φλ) + ... + sin(nφλ);
cos(φλ) + cos(2φλ) + cos(3φλ) + ... + cos(nφλ).
457De harmoniae veris principiis per speculum musicum repraesentatis
461Extract of a letter by Mr. Euler to Mr. Bernoulli father concerning the memoire published by them in 1771, p. 318
474A solution of several Diophantine problems
478General formulas for the translation of arbitrary rigid bodies
487Reflections of Mr. L. Euler on new experiments in optics, communicated to the academy of sciences by Mr. Wilson
490On the representation of spherical surfaces on a plane
491On the geographical projections of spherical surfaces
492On de Lisle's geographic projection and its use
494On the figure that the wind can induce on a stagnant fluid
498Extract of a letter from Mr. Euler to Mr. Beguelin from May 1778
507On the infinity of infinities of orders of the infinitely large and infinitely small
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
530Investigations on a new type of magic square
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
547Simple determination of the orbit of a comet, when it is possible to observe its transit across the ecliptic twice
564Speculations about certain outstanding properties of numbers
565On highly transcendental quantities, which may not be expressed in any way by integral formulas
579Calculations on aerostatic balloons made by the late Mr. Leonhard Euler, as they were found on his blackboard, after his death on September 7, 1783
591On the relation between three and more quantities which are to be instituted
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
600The solution of certain difficult questions in the calculus of probabilities
616On the transformation of the divergent series 1 - mx + m(m+n)x2 - m(m+n)(m+2n)x3 + etc. into a continued fraction
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
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
655General observations about series, of which the terms arising for the sines or cosines of multiplied angles come forth
661Several considerations about hypergeometric series
664Analytical exercises
675On the values of integrals where the variable term is extended x = 0 all the way to x = ∞
685An analytical exercise, where in particular a most general summation of series is given
690The expansion of the integral formula ∫ dz(3+zz)/((1+zz)*4√(1+6zz+z4)) by logarithms and circular arcs
693On the center of similarity
695A succinct integration of the most memorable integral formula ∫ dz/((3±zz)*3√(1±3zz))
698Several speculations about the area of spherical triangles
699Inquiring on whether or not the number 100009 is prime
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
709On the expansion of the power of any polynomial 1 + x + x2 + x3 + x4 + etc.
718An easy method of finding several rather large prime numbers
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
727A more accurate treatment of the problem of drawing the shortest line on a surface
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
736On the summation of series contained in the form a/1 + a2/4 + a3/9 + a4/16 + a5/25 + a6/36 + etc.
738The solution of a curious question in the scene of combinations
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
749About geometry and spheres
750A commentary on the continued fraction by which the illustrious La Grange has expressed the binomial powers
754On a problem of geometry resolved by Diophantine analysis
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
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
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
781De infinitis curvis algebraicis, quarum longitudo arcui parabolico aequatur
785Integration of a remarkable type of differential equation in analytical functions with two variables
788Letters of L. Euler and Chr. Goldbach 1729-1763
790Commentary on the use of sublime mathematics
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
807On the logarithms of negative and imaginary numbers
808An algebraic problem of finding four numbers with the sum of the three others
811The true valuation of the risk in games
812Reflections on a singular kind of lottery named the Genoese Lottery
813Analysis of a problem in the calculus of probabilities
842An Introduction to Natural Science
852Thoughts on the formation of the voice
853Meditation on experiments made recently on the firing of a cannon
855Determination of the prinicples of motion of blood through arteries