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400 | Thoughts on the three body problem |
| 401 | A new way to compare the observations of the moon with the theory |
| 402 | On the movement of the apsides of the moons of Jupiter |
| 403 | Herr Leonhard Euler's necessary computation for the establishment of a widows-fund |
| 404 | Optics, part 3 |
| 405 | A solution of a problem about two numbers which are searched for, of which their product, increased or decreased by their sum or difference, will be a square |
| 406 | Observations about the roots of equations |
| 407 | An algebraic problem that is notable for some quite extraordinary relations |
| 408 | On rectifiable curves on spherical surfaces |
| 409 | The third chapter on the linear motion of fluids |
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410 | Natural basic principles of the study of the state of equilibrium, and the motion, of bodies that are both perfectly flexible and elastic |
| 411 | On the impact of bullets exploded against a plate |
| 412 | Solution to a very difficult question in the calculus of probabilities |
| 413 | On the movement of ships without the force of the wind |
| 414 | An investigation of the perturbations by which the motions of the planets are---on account of their action upon one another---affected |
| 415 | Concerning pitching and rolling |
| 416 | Reflections on the question: Does the medial motion of the planets remain at constant speed, or does it, in the course of time, undergo some change? And what might be the cause of this? |
| 417 | Letters to a German Princess on various topics in physics and philosophy |
| 418 | Theory of lunar motion |
| 419 | On solids whose (entire) surface can be unfolded onto a plane |
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420 | A new and easy method for treating the calculus of variations |
| 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 |
| 422 | The solution of a certain altogether remarkable geometrical problem |
| 423 | Considerations on the measurement of circles |
| 424 | Section four of the motion of air in tubes |
| 425 | On the perturbation of the motion of the Earth due to an action arising from Venus |
| 426 | Complete theory of the construction and steering of ships |
| 427 | An investigation of a certain Diophantine problem |
| 428 | Observations about two biquadratics, of which the sum is able to be resolved into two other biquadratics |
| 429 | On various types of integrals |
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430 | Observations on the differential equation y dy + My dx + N dx = 0 |
| 431 | Consideration of the differential equation (a+bx)ddz + (c+ex)(dxdz/x) + (f+gx)(zdx2/xx) = 0 |
| 432 | Analytical exercises |
| 433 | An aside on trajectories, both orthogonal and oblique-angled |
| 434 | On the collision of spinning bodies |
| 435 | On the collision of hanging bodies, both oblique and spinning |
| 436 | On the true tautochrone in fluids |
| 437 | On the tautochrone in a thin medium, where the resistance is directly proportional to the speed |
| 438 | Clarifications regarding the tautochrone |
| 439 | A further inquiry into vibrating chords |
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440 | Inquiries into the Bernoulli solution, in Volume XVI of the New Commentaries, regarding the motion of strings composed of two parts of differing density |
| 441 | On the vibratory motion of strings composed of an arbitrary number of parts of differing density |
| 442 | On the vibratory motion of strings possessed of a density that varies arbitrarily |
| 443 | On the vibratory motion of elastic laminates, where many new types of vibrations, not treated heretofore, are solved |
| 444 | On the most rapid (descending) motion of weights along curves of a specified type |
| 445 | Proof that every integer is the sum of four squares |
| 446 | Detailed instructions to elevate any glasses to the highest level of perfection to which they are susceptible |
| 447 | The summation of the progressions
sin(φλ) + sin(2φλ) + sin(3φλ) + ... + sin(nφλ);
cos(φλ) + cos(2φλ) + cos(3φλ) + ... + cos(nφλ). |
| 448 | A new infinite series that expresses the perimeter of an ellipse, and which converges very rapidly |
| 449 | Demonstrations about the residues resulting from the division of powers by prime numbers |
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450 | Nova ratio quantitates irrationales proxime exprimendi |
| 451 | A solution of the problem of finding a triangle, in which the lines from each angle bisecting the opposite sides are rational |
| 452 | The resolution of the equation Ax2 + 2Bxy + Cy2 + 2Dx + 2Ey + F = 0 by rational and integral numbers |
| 453 | Eminent properties of series within which the general term is contained as x = (1/2)(a+b/√k)(p+q√k)n + (1/2)(a-b/√k)(p-q√k)n |
| 454 | On the resolution of irrationals by continued fractions, where a certain minor new and singular type is set forth |
| 455 | A determination, sought from the first principles of mechanics, of the oscillatory motion that was treated in the preceding article |
| 456 | On the pressure of a weight on the plane against which it leans |
| 457 | De harmoniae veris principiis per speculum musicum repraesentatis |
| 458 | A new method of reducing the motions of the principal planets to astronomical tables |
| 459 | A disquisition concerning three-fold objective lens, which either create no distortion or which are capable of removing a given distortion arising from the other lens |
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460 | On the application of objective lenses to all types of telescopes |
| 461 | Extract of a letter by Mr. Euler to Mr. Bernoulli father concerning the memoire published by them in 1771, p. 318 |
| 462 | On the value of the integral formula ∫ (zm-1 ± zn-m-1)/(1 ± zn) dz in the case in which after integration it is put z = 1 |
| 463 | On the value of the integral formula ∫ (zλ-ω ± zλ+ω)/(1 ± z2λ)(dz/z)(lz)μ casu quo post integrationem ponitur z = 1 |
| 464 | A new method of determining integral qualities |
| 465 | A demonstration of a theorem of Newton on the expansion of the powers of a binomial by cases, in which the exponents are not integral numbers |
| 466 | A singular Diophantine problem |
| 467 | On the table of prime numbers continued up to one million and beyond, in which at once all the non-prime numbers are expressed by their smallest divisors |
| 468 | On the minimal oscillations of a pendulum laden with a given weight |
| 469 | On the oscillatory movement of two plates suspended from a balance |
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470 | Explicatio motus oscillatorii mirabilis in libra maiore observati |
| 471 | De motu turbinatorio chordarum musicarum; ubi simul universa theoria aequilibrii quam motus corporum flexibilium simulque etiam elasticorum breviter explicatur |
| 472 | Commentatio hypothetica de periculo a nimia cometae approponquatione metuendo |
| 473 | Clarifications on the establishing of public which are as helpful to widows as to the deceased, with a description of a new type of Tontine as favorable to the public as it is useful to the state |
| 474 | A solution of several Diophantine problems |
| 475 | Analytical speculations |
| 476 | Observations about a new and singular type of progression |
| 477 | Meditations about a singular type of series |
| 478 | General formulas for the translation of arbitrary rigid bodies |
| 479 | A new method for generating the motion of a rigid body |
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480 | Regula facilis pro diiudicanda firmitate pontis aliusve corporis similis excognita firmitate moduli |
| 481 | De gemina methodo tam aequilibrium quam motum corporum flexibilium determinandi et utriusque egregio consensu |
| 482 | De pressione funium tensorum in corpora subiecta eorumque motu a frictione impedito. Ubi praesertim methodus traditur … |
| 483 | De traiectu citissimo stellae per duos circulos almucantarath datos pro qualibet elevatione poli. |
| 484 | De circulo maximo fixo in coelo constituendo, ad quem orbitae planetarum et cometarum referantur. |
| 485 | Answer to the question proposed by the Paris Academy for 1770 |
| 486 | Answer to the question proposed by the Paris Academy for 1772 |
| 487 | Reflections of Mr. L. Euler on new experiments in optics, communicated to the academy of sciences by Mr. Wilson |
| 488 | Observations on the foregoing dissertation of Bernoulli |
| 489 | On unravelling exponential formulas |
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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 |
| 493 | Vera theoria refractionis et dispersionis radiorum rationibus et experimentis confirmata |
| 494 | On the figure that the wind can induce on a stagnant fluid |
| 495 | Considerationes super problemate astronomico in tomo commentarior. veter. IV. pertractato. |
| 496 | On the apparent figure of the ring of Saturn, according to the place of it from any perspective on earth |
| 497 | On the appearance and disappearance of the rings of Saturn |
| 498 | Extract of a letter from Mr. Euler to Mr. Beguelin from May 1778 |
| 499 | On the integration of the formula ∫ (dx lx)/√(1-xx) from x = 0 to x = 1 |