Enestrom Numbers 400-499

Original Titles
English Titles

400Thoughts on the three body problem
401A new way to compare the observations of the moon with the theory
402On the movement of the apsides of the moons of Jupiter
403Herr Leonhard Euler's necessary computation for the establishment of a widows-fund
404Optics, part 3
405A 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
406Observations about the roots of equations
407An algebraic problem that is notable for some quite extraordinary relations
408On rectifiable curves on spherical surfaces
409The third chapter on the linear motion of fluids
410Natural basic principles of the study of the state of equilibrium, and the motion, of bodies that are both perfectly flexible and elastic
411On the impact of bullets exploded against a plate
412Solution to a very difficult question in the calculus of probabilities
413On the movement of ships without the force of the wind
414An investigation of the perturbations by which the motions of the planets are---on account of their action upon one another---affected
415Concerning pitching and rolling
416Reflections 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?
417Letters to a German Princess on various topics in physics and philosophy
418Theory of lunar motion
419On solids whose (entire) surface can be unfolded onto a plane
420A new and easy method for treating the calculus of variations
421Solution 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
422The solution of a certain altogether remarkable geometrical problem
423Considerations on the measurement of circles
424Section four of the motion of air in tubes
425On the perturbation of the motion of the Earth due to an action arising from Venus
426Complete theory of the construction and steering of ships
427An investigation of a certain Diophantine problem
428Observations about two biquadratics, of which the sum is able to be resolved into two other biquadratics
429On various types of integrals
430Observations on the differential equation y dy + My dx + N dx = 0
431Consideration of the differential equation (a+bx)ddz + (c+ex)(dxdz/x) + (f+gx)(zdx2/xx) = 0
432Analytical exercises
433An aside on trajectories, both orthogonal and oblique-angled
434On the collision of spinning bodies
435On the collision of hanging bodies, both oblique and spinning
436On the true tautochrone in fluids
437On the tautochrone in a thin medium, where the resistance is directly proportional to the speed
438Clarifications regarding the tautochrone
439A further inquiry into vibrating chords
440Inquiries into the Bernoulli solution, in Volume XVI of the New Commentaries, regarding the motion of strings composed of two parts of differing density
441On the vibratory motion of strings composed of an arbitrary number of parts of differing density
442On the vibratory motion of strings possessed of a density that varies arbitrarily
443On the vibratory motion of elastic laminates, where many new types of vibrations, not treated heretofore, are solved
444On the most rapid (descending) motion of weights along curves of a specified type
445Proof that every integer is the sum of four squares
446Detailed instructions to elevate any glasses to the highest level of perfection to which they are susceptible
447The summation of the progressions
sin(φλ) + sin(2φλ) + sin(3φλ) + ... + sin(nφλ);
cos(φλ) + cos(2φλ) + cos(3φλ) + ... + cos(nφλ).
448A new infinite series that expresses the perimeter of an ellipse, and which converges very rapidly
449Demonstrations about the residues resulting from the division of powers by prime numbers
450Nova ratio quantitates irrationales proxime exprimendi
451A solution of the problem of finding a triangle, in which the lines from each angle bisecting the opposite sides are rational
452The resolution of the equation Ax2 + 2Bxy + Cy2 + 2Dx + 2Ey + F = 0 by rational and integral numbers
453Eminent properties of series within which the general term is contained as x = (1/2)(a+b/√k)(p+qk)n + (1/2)(a-b/√k)(p-qk)n
454On the resolution of irrationals by continued fractions, where a certain minor new and singular type is set forth
455A determination, sought from the first principles of mechanics, of the oscillatory motion that was treated in the preceding article
456On the pressure of a weight on the plane against which it leans
457De harmoniae veris principiis per speculum musicum repraesentatis
458A new method of reducing the motions of the principal planets to astronomical tables
459A 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
460On the application of objective lenses to all types of telescopes
461Extract of a letter by Mr. Euler to Mr. Bernoulli father concerning the memoire published by them in 1771, p. 318
462On 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
463On the value of the integral formula ∫ (zλ-ω ± zλ+ω)/(1 ± z)(dz/z)(lz)μ casu quo post integrationem ponitur z = 1
464A new method of determining integral qualities
465A 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
466A singular Diophantine problem
467On 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
468On the minimal oscillations of a pendulum laden with a given weight
469On the oscillatory movement of two plates suspended from a balance
470Explicatio motus oscillatorii mirabilis in libra maiore observati
471De motu turbinatorio chordarum musicarum; ubi simul universa theoria aequilibrii quam motus corporum flexibilium simulque etiam elasticorum breviter explicatur
472Commentatio hypothetica de periculo a nimia cometae approponquatione metuendo
473Clarifications 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
474A solution of several Diophantine problems
475Analytical speculations
476Observations about a new and singular type of progression
477Meditations about a singular type of series
478General formulas for the translation of arbitrary rigid bodies
479A new method for generating the motion of a rigid body
480Regula facilis pro diiudicanda firmitate pontis aliusve corporis similis excognita firmitate moduli
481De gemina methodo tam aequilibrium quam motum corporum flexibilium determinandi et utriusque egregio consensu
482De pressione funium tensorum in corpora subiecta eorumque motu a frictione impedito. Ubi praesertim methodus traditur
483De traiectu citissimo stellae per duos circulos almucantarath datos pro qualibet elevatione poli.
484De circulo maximo fixo in coelo constituendo, ad quem orbitae planetarum et cometarum referantur.
485Answer to the question proposed by the Paris Academy for 1770
486Answer to the question proposed by the Paris Academy for 1772
487Reflections of Mr. L. Euler on new experiments in optics, communicated to the academy of sciences by Mr. Wilson
488Observations on the foregoing dissertation of Bernoulli
489On unravelling exponential formulas
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
493Vera theoria refractionis et dispersionis radiorum rationibus et experimentis confirmata
494On the figure that the wind can induce on a stagnant fluid
495Considerationes super problemate astronomico in tomo commentarior. veter. IV. pertractato.
496On the apparent figure of the ring of Saturn, according to the place of it from any perspective on earth
497On the appearance and disappearance of the rings of Saturn
498Extract of a letter from Mr. Euler to Mr. Beguelin from May 1778
499On the integration of the formula ∫ (dx lx)/√(1-xx) from x = 0 to x = 1