1 | Construction of isochronous curves in a resistant medium |
2 | Physical dissertation on sound |
3 | On a method for algebraic reciprocal trajectories |
4 | Thoughts on a nautical problem, proposed by the illustrious Royal Academy of Sciences in Paris |
5 | Solution to the problem of reciprocal trajectories |
6 | Dissertation on a number of new types of tautochrone curves |
7 | Attempt at explanation of the phenomena of air |
8 | Solution to the problem of finding curves which is formed by an elastic strip when a force is applied to a single point |
9 | On the shortest line joining two points on a surface |
10 | A new method of reducing innumerable differential equations of the second degree to differential equations of the first degree |
11 | Solution of certain differential equations which do not admit separation of variables |
12 | On the innumerable tautochrone curves in a vacuum |
13 | Tautochrone curves in a fluid making a second resistance proportional to the square of the speed |
14 | Solution 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 |
15 | Mechanics, volume 1 |
16 | Mechanics, volume 2 |
18 | On the Indian solar year |
19 | On transcendental progressions, that is, those whose general terms cannot be given algebraically |
20 | The summation of an innumerable progression |
21 | For 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 |
25 | A general method for summing series |
26 | Observations on a theory of Fermat and others on looking at prime numbers |
28 | Example of the construction of equations |
29 | On the solution of a problem of Diophantus |
30 | Inferences on the forms of roots of equations and of their orders |
31 | Solution to differential equations of the form ax^{n} dx = dy + y^{2} dx |
32 | On the shape of the earth |
33 | An attempt at a new theory of music, exposed in all clearness, according to the most well-founded principles of harmony |
36 | Solution of problems of arithmetic of finding numbers which, when divided by given numbers, leave given remainders |
41 | On the sums of series of reciprocals |
44 | On infinite(ly many) curves of the same type, that is, a method of finding equations for infinite(ly many) curves of the same type |
45 | Addendum to the dissertation on infinite(ly many) curves of the same type |
46 | Universal methods of series |
47 | Finding the sum of any series from a given general term |
54 | A proof of certain theorems regarding prime numbers |
71 | A dissertation on continued fractions |
72 | Various observations about infinite series |
79 | A problem of geometry proposed publicly by an anonymous geometer |
81 | Thoughts on the elements of bodies |
83 | On several properties of the conic sections which intersect with an infinity of other curved lines |
90 | Analysis of the question whether the faculty of thinking can be attributed to matter or not |
91 | Physical investigations on the nature of the smallest parts of matter |
100 | On Amicable Numbers |
105 | Memoir on the Grand Equation of the Planets |
107 | Extract 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. |
115 | Method of determining the longitude of the observation site by observation of the occulations of fixed stars by the moon |
123 | Observations on continued fractions |
130 | Considerations on certain series |
134 | Theorems on divisors of numbers |
135 | Various geometric demonstrations |
141 | On the agreement of the latest eclipses of the sun and moon with my tables, to find the true times of full and new moons |
147 | On the apparent contradiction in the rule of curved lines |
148 | Proof concerning the number on points where two lines of ordinary order can intersect |
149 | Reflections on space and time |
153 | A 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 |
158 | Various analytical observations about combinations |
164 | Theorems about the divisors of numbers contained in the form paa ± qbb |
168 | On the controversy between Messrs Leibniz and Bernoulli concerning the logarithms of negative and imaginary numbers |
169 | On the cuspidal points of the second kind of Monsieur le Marquis de l'Hopital |
170 | Research on imaginary roots of equations |
171 | Research on the precession of the equinoxes and on the nutation of the earth's axis |
175 | Discovery of an extraordinary law of numbers in relation to the sum of their divisors |
177 | Discovery of a new principle in Mechanics |
180 | Notice on the subject of Research on the precession of the equinoxes |
183 | Part 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 |
184 | Part 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 |
190 | Consideration of certain series which are gifted with particular properties |
192 | Solution of a problem of geometry |
198 | On the principle of least action |
201 | Calculation of the probability in the game of Rencontre |
204 | Extract of a Letter from Professor Euler, of Berlin, to the Rev. Mr. Caspar Wetstein, Chaplain to Her Royal Highness the Princess Dowager of Wales |
210 | Letters 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 |
212 | Foundations of Differential Calculus, with Applications to Finite Analysis and Series, Volume 1 |
214 | Principles of spherical trigonometry taken from the method of the maxima and minima |
215 | Elements of spheroidal trigonometry taken from the method of the maxima and minima |
226 | General principles concerning the motion of fluids |
228 | On numbers which are the sum of two squares |
231 | Proof of some of the properties of solid bodies enclosed by planes |
236 | Explanation of certain paradoxes in integral calculus |
241 | Proof of a theorem of Fermat that every prime number of the form 4n+1 is the sum of two squares |
243 | Observations on the sums of divisors |
244 | A demonstration of a theorem on the order observed in the sums of divisors |
247 | On divergent series |
251 | On the integration of the differential equations (m dx)/√(1-x^{4}) = (n dy)/√(1-y^{4}) |
258 | Principles of the motion of fluids |
262 | Theorems about the remainders left by division by powers |
275 | Annotations to a certain passage of Descartes for finding the quadrature of the circle |
278 | On the motion and grinding of lenses while they are polished upon curved plates |
282 | On the resolution of equations of any order |
289 | Theory of the motion of solid or rigid bodies |
304 | Considerationes de motu corporum coelestium |
308 | Recherches sur le mouvement de rotation des corps celestes |
309 | Solution of a curious question which does not seem to have been subjected to any analysis |
310 | New method to eliminate the unknown quantities in equations |
313 | On the advantage to the banker in the game of Pharaon |
314 | Conjecture into the reasons why flat tones are generally heard in music |
327 | On the rectilinear motion of three bodies mutually attracted to each other |
332 | Research concerning the flow of rivers |
333 | Research into the curvature of surfaces |
334 | General research on the mortality and the propagation of the human race |
335 | Concerning annuity incomes |
338 | On the probability of series in the Genoese lottery |
341 | Report concerning a new method for the propagation of grain |
342 | Foundations of Differential Calculus, with Applications to Finite Analysis and Series, Volume 2 |
343 | Letters to a German Princess on various topics in physics and philosophy |
344 | Letters to a German Princess on various topics in physics and philosophy |
352 | Remarks on a beautiful relation between direct as well as reciprocal power series |
366 | Foundations of Differential Calculus, with Applications to Finite Analysis and Series, Volume 3 |
385 | Foundations of Integral Calculus, volume 3 |
387 | Complete instruction in algebra, book 1 |
388 | Complete instruction in algebra, book 2 |
394 | On the partition of numbers into a number of parts of a given type |
412 | Solution to a very difficult question in the calculus of probabilities |
417 | Letters to a German Princess on various topics in physics and philosophy |
421 | Solution of a formula for the integral ∫ x^{ f-1} dx (log x)^{m/n} the integration being extended from the value x = 0 to x = 1 |
423 | Considerations on the measurement of circles |
428 | Observations about two biquadratics, of which the sum is able to be resolved into two other biquadratics |
445 | Proof that every integer is the sum of four squares |
447 | The summation of the progressions sin(φ^{λ}) + sin(2φ^{λ}) + sin(3φ^{λ}) + ... + sin(nφ^{λ}); cos(φ^{λ}) + cos(2φ^{λ}) + cos(3φ^{λ}) + ... + cos(nφ^{λ}). |
457 | De harmoniae veris principiis per speculum musicum repraesentatis |
461 | Extract of a letter by Mr. Euler to Mr. Bernoulli father concerning the memoire published by them in 1771, p. 318 |
474 | A solution of several Diophantine problems |
478 | General formulas for the translation of arbitrary rigid bodies |
490 | On the representation of spherical surfaces on a plane |
491 | On the geographical projections of spherical surfaces |
492 | On de Lisle's geographic projection and its use |
494 | On the figure that the wind can induce on a stagnant fluid |
498 | Extract of a letter from Mr. Euler to Mr. Beguelin from May 1778 |
507 | On the infinity of infinities of orders of the infinitely large and infinitely small |
521 | Analytical theories. Extracts of different letters of Mr. Euler to Mr. le Marquis de Condorcet |
522 | On the formation of continuous fractions |
523 | On three square numbers, of which the sum and the sum of products two apiece will be a square |
530 | Investigations on a new type of magic square |
541 | The expansion of the infinite product (1-x)(1-xx)(1-x^{3})(1-x^{4})(1-x^{5}) etc. into a single series |
542 | On the remarkable properties of the pentagonal numbers |
564 | Speculations about certain outstanding properties of numbers |
565 | On highly transcendental quantities, which may not be expressed in any way by integral formulas |
579 | Calculations on aerostatic balloons made by the late Mr. Leonhard Euler, as they were found on his blackboard, after his death on September 7, 1783 |
591 | On the relation between three and more quantities which are to be instituted |
596 | On 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 |
600 | The solution of certain difficult questions in the calculus of probabilities |
616 | On the transformation of the divergent series 1 - mx + m(m+n)x^{2} - m(m+n)(m+2n)x^{3} + etc. into a continued fraction |
628 | Clarifications 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 |
643 | A general method for investigating all the roots of an equation by approximation |
644 | Innumerable forms of equations from all orders, of which a resolution is able to be exhibited |
655 | General observations about series, of which the terms arising for the sines or cosines of multiplied angles come forth |
661 | Several considerations about hypergeometric series |
664 | Analytical exercises |
675 | On the values of integrals where the variable term is extended x = 0 all the way to x = ∞ |
685 | An analytical exercise, where in particular a most general summation of series is given |
690 | The expansion of the integral formula ∫ dz(3+zz)/((1+zz)*^{4}√(1+6zz+z^{4})) by logarithms and circular arcs |
693 | On the center of similarity |
695 | A succinct integration of the most memorable integral formula ∫ dz/((3±zz)*^{3}√(1±3zz)) |
698 | Several speculations about the area of spherical triangles |
699 | Inquiring on whether or not the number 100009 is prime |
706 | On a new type of rational and highly convergent series, by which the ratio of the periphery to the diameter is able to be expressed |
709 | On the expansion of the power of any polynomial 1 + x + x^{2} + x^{3} + x^{4} + etc. |
710 | Example of the transformation of singular series |
718 | An easy method of finding several rather large prime numbers |
724 | Research concerning some remarkable integrations in functional analysis with two variables known under the title of partial differentials |
725 | An illustration of a paradox about the idoneal, or suitable, numbers |
727 | A more accurate treatment of the problem of drawing the shortest line on a surface |
729 | Dilucidationes super Problemate geometrico de quadrisectione trianguli a Iacobo Bernoulli olum tractato |
730 | Solutio completa problematis de quadrisectione trianguli per duas rectas inter se normales |
731 | The solution of a memorable problem by a special artifice of calculation |
732 | An easier solution of a Diophantine problem about triangles, in which those lines from the vertices which bisect the opposite sides may be expressed rationally |
736 | On the summation of series contained in the form a/1 + a^{2}/4 + a^{3}/9 + a^{4}/16 + a^{5}/25 + a^{6}/36 + etc. |
738 | The solution of a curious question in the scene of combinations |
744 | On divisors of numbers of the form mxx + nyy |
745 | On the continued fractions of Wallis |
746 | A method for gathering the sums of infinite series by investigating differential formulas |
749 | About geometry and spheres |
750 | A commentary on the continued fraction by which the illustrious La Grange has expressed the binomial powers |
754 | On a problem of geometry resolved by Diophantine analysis |
762 | Unpublished letter from Euler to Lagrange |
763 | On finding three or more numbers, the sum of which is a square, while the sum of the squares is a fourth power |
769 | A 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 |
773 | A solution of a most difficult problem, in which the two forms aaxx + bbyy et aayy + bbxx must be rendered into squares |
775 | On two numbers, of which the sum when increased or decreased by the square of one of them produces a square |
785 | Integration of a remarkable type of differential equation in analytical functions with two variables |
788 | Letters of L. Euler and Chr. Goldbach 1729-1763 |
790 | Commentary on the use of sublime mathematics |
794 | A theorem of arithmetic and its proof |
795 | On magic squares |
796 | Research into the problem of three square numbers such that the sum of any two less the third one provides a square number |
797 | Further 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 |
807 | On the logarithms of negative and imaginary numbers |
808 | An algebraic problem of finding four numbers with the sum of the three others |
811 | The true valuation of the risk in games |
812 | Reflections on a singular kind of lottery named the Genoese Lottery |
813 | Analysis of a problem in the calculus of probabilities |
842 | An Introduction to Natural Science |
852 | Thoughts on the formation of the voice |
853 | Meditation on experiments made recently on the firing of a cannon |