Enestrom Numbers 001-866

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
17The Art of Reckoning
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
22On the communication of motion in collisions
23On rectifiable algebraic curves
24Solution of a remarkable case concerning tautochronism
25A general method for summing series
26Observations on a theory of Fermat and others on looking at prime numbers
27On isoperimetric problems in the widest sense
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
34Dissertation on fire
35Introduction to the Art of Reckoning, for use in the Gymnasiums of the Imperial Academy of Sciences in St. Petersburg
36Solution of problems of arithmetic of finding numbers which, when divided by given numbers, leave given remainders
37On the motion of planets and orbits
38Determination of orbits around the sun
39Solution to a problem concerning astronomy
40On the smallest oscillations of rigid and flexible bodies. A new and easy method.
41On the sums of series of reciprocals
42On the curve of fastest descent in whatever resistent medium
43On harmonic progressions
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
48Investigation of pairs of curves whose arcs that correspond to the same abscissa constitute an algebraic sum
49On the oscillations of a flexible wire weighted with arbitrarily many little weights (?)
50A method for computing the equation of a meridian
51On the construction of equations using dragged motion, and of other things pertinent to the inverse method of tangents
52Solution of a problem requiring the rectification of an ellipse
53The solution of a problem relating to the geometry of position
54A proof of certain theorems regarding prime numbers
55Universal method for summation of series, further developed
56New and easy method of finding curves enjoying a maximal or minimal property
57A physical inquiry into the cause of the ebb and flow of the sea
58Determination of the motion of a comet which can be observed in March of this year, 1742
59Theorems concerning the reduction of integral formulas to the quadrature of the circle
60On the resolution of an integral, if after integration the value for the determined variable quantity is assigned
61On sums of series of reciprocals from powers of natural numbers from another discussion, in which the sums are derived principally from another source
62On the integration of differential equations of various degrees
63Demonstration of the sum of the series 1 + 1/4 + 1/9 + 1/16
64Leonhardus Eulerus mathematicus acutissimus ad auctorem
65A method for finding curved lines enjoying properties of maximum or minimum, or solution of isoperimetric problems in the broadest accepted sense
66Theory of the motions of planets and comets
67Answers to various questions about the condition, motion, and effects of comets
68Further answers to various questions about the condition, motion, and effects of comets
69On the imparting of motion from a collision of bodies not striking each other directly
70On the construction of equations
71A dissertation on continued fractions
72Various observations about infinite series
73The solution to a geometric problem about circles shaped as moons
74On various methods for expressing the quadrature of a circle with verging numbers
75Solution of a problem proposed in the Nova Acta Eruditorum in November, 1743
76New and correct tables for computing the location of the moon
77New Principles of Gunnery
78Essay on a better construction of a capstan
79A problem of geometry proposed publicly by an anonymous geometer
80Opuscula varii argumenti
81Thoughts on the elements of bodies
82Percussion and its true measurement
83On several properties of the conic sections which intersect with an infinity of other curved lines
84Observation by Leonhard Euler on sections 83 and following of the preceding book, concerning elastic curves
85Solution to a catoptric problem proposed in this journal in September 1745 on page 523
86On the movement of bodies on movable surfaces
87Astronomical table of the sun and the moon
88A new theory of light and colors
89On the running down of the motion of the planets
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
92Defense of divine revelations against the objections of the freethinkers
93An inquiry into balances
94On the movement of a boat with oars propelled through running waters
95On differential equations which admit integration only in certain cases
96On the most profitable application of simple as well as composite machines
97On the attraction of spherico-elliptical bodies
98The proofs of some arithmetic theorems
99The solution to a certain problem proposed by the celebrated Daniel Bernoulli
100On Amicable Numbers
101Introduction to the Analysis of the Infinite, volume 1
102Introduction to the Analysis of the Infinite, volume 2
103Physical Investigations on the tail of comets, the northern lights, and the zodiacal light
104Memoir on the effect of the successive propagation of light in the appearance of the planets as well as the comets
105Memoir on the Grand Equation of the Planets
106Solution to the catoptric problem in Novis Actis Eruditorum Lipsiensibus proposed in November 1745
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.
108A dissertation on an observed tendency of magents
109Dissertation on Magnets
110Naval Science, volume 1
111Naval Science, volume 2
112Studies on the movement of celestial bodies in general
113Method for finding the true moments of both the new and the full moon
114Method of finding the true geocenter of the moon by the obsertvation of the occulation of a fixed star
115Method of determining the longitude of the observation site by observation of the occulations of fixed stars by the moon
116Memoir on the force of oars
117Reflections on the last eclipse of the sun from July 25, 1748
118On the perfection of objective lenses of telescopes
119On vibrations of excited chords
120Investigations on the question of the differences of the movement of Saturn and Jupiter
121Physical conjectures on the propogation of sound and light with other dissertations: on amicable numbers, on natural equations, and on the rectification of ellipses
122On products created from infinite factors
123Observations on continued fractions
124On the determination of the gradient of heat and cold at each point and time of a region
125Consideration of a progression suitable for finding the quadrature of a circle
126On a new type of oscillation
127An explanation of the phenomena which proceed in turn from the movement of light
128An easy method for computing the natural and artificial sines and tangents of angles
129Investigation of curves which produce evolutes similar to themselves
130Considerations on certain series
131An emmendation to astronomical tables of locating the geocenters of planets
132Method of the celebrated Leonhard Euler for determining a degree of the meridian, as well as of a parallel of the earth, based on the measurement undertaken by the celebrated de Maupertuis and his colleagues
133On the surface of scalene cones and of other conic bodies
134Theorems on divisors of numbers
135Various geometric demonstrations
136On the propagation of pulses in an elastic medium
137Examination of a design for propelling a ship by an internal principle of motion
138On the motion of the lunar nodes, and on the variation of their inclination to the ecliptic
139To what degree the motion of the earth is perturbed by the moon, more accurately investigated
140On the vibration of strings
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
142On the atmosphere of the moon as proved by the last ringed eclipse of the sun
143On the friction of solid bodies
144On the reduction of the resistance of friction
145Research into the largest and the smallest which are found in the action of forces
146Reflection on some general laws of nature which are observed in the effects of random forces
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
150Meditations on the question of determining the moment of time by observations
151A physical conjecture on the propagation of sound and light
152On amicable numbers
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
154Observations on the rectification of ellipses
155Excerpt from a letter of Herr Euler about the concept of asterisms on the celestial sphere
156Opusculorum tomus III. continens novam theoriam magnetis ab illustr. academia regia scient: Parisina praemio condecoratam a. 1744.
157On the extraction of roots from irrational quantities
158Various analytical observations about combinations
159On the oscillating motion of flexible bodies
160On the descent of bodies over an unevenly inclined plane
161On the movement of bodies over an uneven horizontal plane
162A method for integrating rational differential forms involving one variable
163An easier and more expedient method for integrating rational differential forms
164Theorems about the divisors of numbers contained in the form paa ± qbb
165On the motion of fluids arising from different degrees of heat
166On the reduction of curved lines to the arcs of circles
167On the solution of a most difficult problem proposed by Fermat
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
172On the parallax of the moon, with respect to its elevation and azimuth, under the hypothesis of a spherical earth
173New method of finding reciprocal algebraic trajectories
174On the motion of flexible bodies
175Discovery of an extraordinary law of numbers in relation to the sum of their divisors
176Exposé concerning the letter from Leibnitz to Koenig in the March, 1751 issue of the Acts of Leipzig on the occasion of his publication of the Principle of Least Action
177Discovery of a new principle in Mechanics
178Reflections of the different degrees of sunlight on other celestial bodies
179Research concerning the effects of a hydraulic machine proposed by M. Segner, professor at Gottingen
180Notice on the subject of Research on the precession of the equinoxes
181Research on the origin of forces
182Letter of Mr. Euler to M. Merian
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
185(Euler's preface to the work An examination of the Middle Ages, set forth according to astronomical and chronological principles, by Heinrich Wilhelm Clemm, Berlin 1752)
186Essay on the principle of least action, with an examination of the objections of M. Professor Koenig made against this principle
187Theory of the motion of the moon which exhibits all its irregularities
188Method of integrating differential equations of higher degrees, further developed
189On the determination of series, or a new method for finding the general terms of series
190Consideration of certain series which are gifted with particular properties
191On the partitions of numbers
192Solution of a problem of geometry
193On the perturbation of the movement of planets from a figure not arising from a sphere
194On machines in general
195On the tautochrone motion of pendulums
196Improvement of the magic lantern and solar microscope
197Harmony existing between the general principles of rest and movement by M. de Maupertuis
198On the principle of least action
199Examination of the dissertation of Professor Koenig inserted into the Acts of Leipzig for the month of March 1751
200Essay concerning a metaphysical experiment on the general principle of equilibrium
201Calculation of the probability in the game of Rencontre
202On the application of the hydraulic machine of Mr. Segner to all sorts of situations and its advantages over the other hydraulic machines which one typically uses
203Research on a new method to raise water proposed by M. Mour
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
205Geographic Atlas - Preface
206On the motion of water in conduits
207In depth explanation concerning different methods in which to raise water through pumps with the greatest effectiveness
208Maxims for the most advantageous arrangement of machines that raise water by use of pumps.
209Essay concerning the physical explanation of colors which are issued from extremely thin surfaces
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
211Problema, ad cuius solutionem geometrae invitantur; theorema, ad cuius demonstrationem geometrae invitantur
212Foundations of Differential Calculus, with Applications to Finite Analysis and Series, Volume 1
213Remarks on the preceeding memories of M. Bernoulli
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
216Examination of a controversy on the law of refraction of rays of different colors with respect to the different transparent media through which they pass
217Examination of the true curve that bodies which are airborne or in any other fluid
218A letter from L. Euler to E. Pontoppidan, dated 11 May 1754
219Concerning the refraction of light while passing through the atmosphere and the different degrees dependent on heat as to the elaticity of the air
220Reflections on a problem of geometry dealt with by certain geometers which nevertheless is impossible
221Research into the physics of the different refrangibilities of light rays
222A more complete theory of machines which are activated by their reaction to water
223Concerning the variation of latitude of fixed stars and the obliquity of the ecliptic
225General principles concerning the state of the equilibrium of fluids
226General principles concerning the motion of fluids
227Continuation into the research on the theory of the motion of fluids
228On numbers which are the sum of two squares
229On the construction of the best gears
230Elements of the doctrine of solids
231Proof of some of the properties of solid bodies enclosed by planes
232On the movement of celestial bodies perturbed by any number of forces
233Refined studies into the effect of windmills
234Experiments to determine the refraction of all types of transparent liquors
235On the action of saws
236Explanation of certain paradoxes in integral calculus
237Research concerning the declination of the magnetized needle
238Concerning the strength of columns
239General rules for the construction of telescopes and microscopes, using some general number of lenses.
240Research into glasses with three lenses which represent inverted objects
241Proof of a theorem of Fermat that every prime number of the form 4n+1 is the sum of two squares
242Proof of a theorem of Fermat that every number whether whole or fraction is the sum of four or fewer squares
243Observations on the sums of divisors
244A demonstration of a theorem on the order observed in the sums of divisors
245On a method analogous to that of Diophantus in the analysis of the infinites
246A contribution to the calculations of sines
247On divergent series
248On the screw of Archimedes
249On finding the best shape for gear teeth
250A method for finding infinitely many isoperimetric curves predicated with a common property
251On the integration of the differential equations (m dx)/√(1-x4) = (n dy)/√(1-y4)
252Observations on the comparison of arcs of irrectifiable curves
253On indeterminate problems which appear to be quite determinate
254On the expression of integrals as factors
255General solution of certain Diophantine problems, which are ordinarily thought to admit only special solutions
256Example of the use of observation in pure mathematics
257On friction of rotating bodies
258Principles of the motion of fluids
259On the motion and reaction of water flowing through moving tubes
260Attempt at a theory of the friction of fluids
261Example of another new methods for comparing transcendental quantities; on the comparison of the arcs of ellipses
262Theorems about the remainders left by division by powers
263An example of a new method for the quadrature and rectification of curves and of comparing other quantities which are transcendentally related to each other
264Proof of a theorem and solution of a theorem proposed in the Acta Eruditorum of Leipzig
265On differential equations of the second degree
266A construction of objective lenses from two glasses which produces neither confusion of a spherical figure nor gives rise to the dispersion of colors
267Extract of a letter of M. Euler written to M. Duhamel, 3 February 1756
268Letter of Mr. Euler to Mr. de Lagrange
269On the integration of differential equations
270The solution of a problem about searching for three numbers, of which the sum and not only their product but the sum of their products two apiece, are square numbers
271Demonstration of a new method in the Theory of Arithmetic
272A reinforcement of some arithmetic theorems, supported by several demonstrations
273Consideration of formulas, of which the integral can be obtained by sections of arcs of cones
274Construction of the differentio-differential equation Ay du2 + (B+Cu)du dy + (D+Eu+Fuu)ddy = 0, assuming the element du to be constant
275Annotations to a certain passage of Descartes for finding the quadrature of the circle
276Clarifications into fluid resistance
277Principal theory of machines
278On the motion and grinding of lenses while they are polished upon curved plates
279On the resolution of formulas of squares of indeterminates by integral numbers
280On progressions of arcs of circles, of which the accompanying tangents proceed by a certain law
281A specimen of a singular algorithm
282On the resolution of equations of any order
283On very large prime numbers
284On the resolution of the equation dy + ayy dx = bxm dx
285Investigation of functions from a given condition of differentials
286On the vibrating motion of a flexible wire, weighted with however many small particles
287On the vibrating motion of unevenly thick strings
288Thoughts on constructing ramparts/walls
289Theory of the motion of solid or rigid bodies
290Geometria dalya ipotrevleniya v academycheskoi gymnazii [Russian]
291Research into the science of mechanical bodies
292On the movement of rotation of solid bodies around a variable axis
293General remarks on the daily motion of the planets
294Remarks by Mr. Euler on several passages which appeared in the third volume of mathematical works by Mr. d'Alembert
295On the reduction of integral formulas for the rectification of the ellipse and hyperbola
296The Elements of the Calculus of Variations
297Explanation of the analytical method in the maxima and minima
298On the notable advancement of the inverse method of tangents
299Explanation of the tautochrone in a resistant medium
300Demonstration of a Bernoullian theorem in which cycloids are ultimately produced from the evolution, continued to infinity, of any right-angled curve
301De motu corporis ad duo centra virium fixa attracti
302On the motion of vibrations in drums
303Tentamen de sono campanarum
304Considerationes de motu corporum coelestium
305On the propagartion of sound
306Supplement to the research on the propagation of sound
307Continuation into the propagation of sound
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
311Research into simple microscopes and the methods to perfect them
312Research on microscopes with three lenses and the methods by which to make them
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
316On three lens glasses which represent upright objects
317Clarifications on the movement of vibrating strings
318Research into the motion of unequally thick strings
319Research into the integration of the equation (ddz/dt2)=aa(ddz/dx2)+(b/x)(dz/dx) + (c/xx)z
320Research into a new type of construction of six lens glasses and their improvement
321Observations concerning the integrals of formulas ∫ xp-1dx(1-xn)q/n-1 setting x=1 after integration
322The use of discontinued functions in analysis
323Concerning the use of a new algorithm to solve the Pell problem
324Properties of triangles for which certain angles have a ratio between themselves
325Easy solutions to some difficult geometric problems
326Analytical observations
327On the rectilinear motion of three bodies mutually attracted to each other
328On the motion of a body attracted to two fixed centers of forces
329On the appearance of the heavens observed through transparent spherical segments
330Supplement on the shape of the teeth of wheels [gear teeth]
331On the motion of fluids arising from different degrees of heat
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
336On the motion of a rotating solid round a mobile axis
337Problem: A body is attracted by reason of the reciprocal square of the distance towards two given fixed points, find the case where the described curve by this body will be algebraic, solved by Mr. Euler
338On the probability of series in the Genoese lottery
339On the motion of a string which at the start has only been struck only in one area
340Detailed clarifications concerning the generation and propagation of sound and on the formation of echo
341Nachricht von einem neuen Mittel zur Vermehrung des Getreides
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
345On integrated equations of the type dx/√(A+Bx+Cx2+Dx3+Ex4) = dy/√(A+By+Cy2+Dy3+Ey4)
346De arcubus curvarum aeque amplis earumque comparatione
347More general development of formulas serving for the comparison of curves
348Methodus facilis motus corporum coelestium utcunque perturbatos ad rationem calculi astronomici revocandi
349Disquisition on the true law of refraction of rays of different colors
350On a new type of microscope composed of six lenses
351On a telescope made from four lenses and its perfection
352Remarks on a beautiful relation between direct as well as reciprocal power series
353Research into the confusion which exists in dioptic lenses caused by their aperture
354Research into the methods to diminish or reduce the confusion caused by the opening of the lenses
355New method to improve the objective lenses for glasses
356Determination of the apparent field that is discovered by telescopes as well as by microscopes
357General rules for the construction of telescopes and of microscopes
358On the perfection of astronomic glasses which represent inverted objects
359The manufacture of lenses composed of two different types of glass which does not present any confusion
360The correct way to manufacture composes lenses which will reduce all confusion in the glasses
361Reflections on the ways in which to examine the refraction of glass by the way of prisms
362The necessary corrections to the theory of the magnetic declination which was proposed in Volume XIII of the Memoires
363Notebook concerning a general theory of dioptrics
364Letter written to the Royal Academy of Sciences in Berlin
365Extracts from some letters by Euler to d'Alembert
366Foundations of Differential Calculus, with Applications to Finite Analysis and Series, Volume 3
367Optics, part 1
368On a hyperbolic curve expressed by this equation y = 1*2*3*...*x
369How very large numbers are to be tested for whether they are prime or not
370A new criteria for acquiring the imaginary roots of equations
371Considerations on completing the theory of the motion of the moon and especially of its variation
372Note of certain precautions to be taken in the investigation of the inequalities by which the heavenly bodies are perturbed in their motion
373More accurate investigation of the phenomena which can be produced in the diurnal motion of the earth by celestial forces
374On the equilibrium and motion of bodies connected by flexible curves
375First section on the state of equilibrium of fluids
376Considerations on the difficulties that one encounters during the manufacture of objective lenses
377Research into reflective telescopes and their perfection
378Research on another construction of reflecting telescopes
379Concerning the confusion which exists in dioptical instruments due to the diverse refrangibility of light rays
380Concerning the new English glasses of Mr. Dolland and on the principle on which it is based
381On the advantages of telescopic glasses built with two lenses
382Remarks on the effect of friction on equilibrium
383Methods to apply for improving the degree of perfection in the manufacture of telescopic lenses
384Research on the inequalities of Jupiter and Saturn
385Foundations of Integral Calculus, volume 3
386Optics, part 2
387Complete instruction in algebra, book 1
388Complete instruction in algebra, book 2
389Research and calculations on the true elliptical orbit of the comet of the year 1769 and its periodic time
390(Considerations of orthogonal trajectories)
391On double integral formulas
392Development of a notable paradox concerning the equality of surfaces
393On the sum of series involving the Bernoulli numbers
394On the partition of numbers into a number of parts of a given type
395On finding however many mean proportionals without regard to extraction of roots
396Section two of Principles of Fluid Motion
397Exposition of methods, not only for determining the parallax of the sun from an observed transit of Venus across the sun, but also for finding longitudes of places on the earth from observations of eclipses of the sun, together with calculations and conclusions deduced therefrom
398New method to determine the perturbations during the motion of heavenly bodies caused by their mutual attraction
399Reflections on the different ways that one can describe the movement of the moon
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
487Thoughts by Mr. L. Euler concerning new experiments in optics transmitted to the Academy 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
494De figura quam ventus fluido stagnanti inducere valet
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
500On the value of the integral formula ∫ ((xa-1 dx)/lx)(1-xb)(1-xe)/(1-xn) bounded at x = 0 and extended to x = 1
501Considerations about brachistochrones
502On the effects of refraction during terrestrial observations
503De motu oscillatorio penduli cuiuscunque, dum arcus datae amplitudinis absolvit
504On the Theory of the Moon which is to be carried to a higher level of perfection
505De corporibus regularibus per doctrinam sphaericam determinatis; ubi simul nova methodus globos sive coelestes sive terrestres charta obducendi traditur
506(Elucidations about a most elegant method, which the illustrious la Grange used in the integration of the differential equation dx/√X = dy/√Y
507On the infinity of infinities of orders of the infinitely large and infinitely small
508The determination of the loads which columns are strong enough to bear
509An examination of an outstanding paradox occurring in the theory of columns
510De altitudine columnarum sub proprio pondere corruentium
511Thoughts concerning the Earth's motional inequalities caused by Venus' action, accompanied with a table of the corrections of Earth's position
512Investigatio perturbationum quae in motu terrae ab actione Veneris producunter: cum tabula perturbationum istarum
513On triangular curves
514On the measure of solid angles
515De casibus quibusdam maxime memorabilibus in analysi indeterminata, ubi imprimis insignis usus calculi angulorum in analysi Diophantea ostenditur
516De motu oscillatorio duorum corporum ex filo super trochleas traducto suspensorum
517On a certain problem in mechanics, obvious enough, but with a most difficult solution
518Solutio gemina problematis, quo motus corporis, filo alicubi alligati, super plano horizontali quaeritur
519New method to determine the motion of planets
520Essay of the theory of resistance that a prow of a ship experiences throughout its motion
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
524A universal spherical trigonometry, derived briefly and from first principles
525De motu oscillatorio mixto plurium pendulorum ex eodem corpore mobili suspensorum
526Investigatio motuum, quibus laminae et virgae elasticae contremiscunt
527A conjecture about the nature of air, by which are to be explained the phenomenon which have been observed in the atmosphere
528An annotation to the preceding dissertation
529A theory of parallaxes, accommodating the spheroid shape of the Earth
530Investigations on a new type of magic square
531Brief analytical works, volume 1
532On the remarkable properties of a series of Lambert and others
533On the oscillating motion derived from a tense hanging thread
534Elucidations about several rather difficult cases of equilibrium
535Determinatio omnium motuum, quos chorda tensa et uniformiter crassa recipere potest
536On the properties of triangles in mechanics
537On the figure of elastic curves against the objections of the illustrious d'Alembert
538Necessary cautions in the determination of the motion of planets which are to be observed
539A supplement to the calculation of integrals for the calculation of irrational formulas
540A new method for resolving all rational fractions into simpler fractions
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
544De motu libero plurium corporum filis colligatorum super plano horizontali
545De vi fluminis ad naves sursum trahendas applicanda
546De statu aequilibrii maris a viribus solis et lunae sollicitati.
547Simple determination of the orbit of a comet, when it is possible to observe its transit across the ecliptic twice
548De variis motuum generibus, qui in satellitibus planetarum locum habere possunt.
549De motibus maxime irregularibus, qui in systemate mundano locum habere possent, una cum methodo hujusmodi motus per temporis spatium quantumvis magnum prosequendi.
550On series in which the product of two consecutive terms make a given progression
551Various methods for inquiring into the innate characters of series
552Observations about the division of squares by prime numbers
553Analytical observations
554A more exact disquisition about the residues remaining from the division of squares and of higher powers by prime numbers
555An examination of the use of interpolating methods in the doctrine of series
556On the criteria of whether equation fxx + gyy = hxx admits a resolution or not
557De quibusdam eximiis proprietatibus circa divisores potestatum occurrentibus
558Proposita quacunque protressione ab unitate incipiente, quaeritur quot eius terminos a dminimum addi oporteat, ut omnes numeri producantur
559New assistance for solving the formula axx + 1 = yy
560Miscellaneous analyses
561Various observations about angles proceeding in geometric progression
562On how sines and cosines of multiplied angles may be expressed by products
563On the smallest ellipse which is to circumsrcibe a given rectilinear parallelogram
564Speculations about certain outstanding properties of numbers
565On highly transcendental quantities, which may not be expressed in any way by integral formulas
566De inductione ad plenam certitudinem evehenda
567Dilucidationes de motu chordarum inaequaliter crassarum
568De motu penduli circa axem cylindricum, fulcro datae figurae incumbentem, mobilis. Remota frictione
569De motu penduli circa axem cylindricum, fulcro datae figurae incumbentem, mobilis. Habita frictionis ratione
570On finding longitude of a place by observing the distance between the moon and a known fixed star
571De eclipsibus solaribus in superficie terrae per proiectionem repraesentandis.
572Nova methodus integrandi formulas differentiales rationales sine subsidio quantitatum imaginariarum
573De duplici genesi tam epicycloidum quam hypocycloidum
574De curvis rectificabilibus in superficie coni recti ducendis
575De mirabilibus proprietatibus unciarum, quae in evolutione binomii ad potestatem quamcunqua evecti occurrunt
576De oscillationibus minimis funis libere suspensi
577De perturbatione motus chordarum ab earum pondere oriunda
578On the disturbance of motion concerning planets and comets
579Caculation on aerostatic balloons made by the late Mr. Euler as they were found on his blackboard, after the occurrence of his death on September 7, 1783
580Brief analytical works, volume 2
581A more complete investigation into the relationship between those quantities contained in the integral formula ∫ (\Z dz)/√(1+mzz+nz4), where Z denotes a rational function of zz.
582The fruitful development of a relation which may be established between the arcs of conic sections
583De numero memorabili in summatione progressionis harmonicae naturalis occurrente
584De insignibus proprietatibus unciarum binomii ad uncias quorumvis polynomiorum extensis
585De effectu frictionis in motu volutorio
586Considerations about a theorem of Fermat on the resolution of numbers into polygonal numbers
587An observation on several theorems of the illustrious de la Grange
588An investigation of the integral formula ∫ (xm-1 dx)/(1+xk)n in the case in which after integration it is set x = ∞
589An investigation of the value of the integral ∫ (xm-1 dx)/(1-2xkcosθ+x2k) the term to be extended from x = 0 to x = ∞
590Certain theorems in analysis, of which a demonstration is thus far desired
591On the relation between three and more quantities which are to be instituted
592On the resolution of transcendental fractions into infinitely many simple fractions
593On the transformation of series into continued fractions, where at once this not mediocre theory is enlarged
594A method for finding integral formulas, for which in certain cases a given rule holds between them, where at once a method is related for summing continued fractions
595Summatio fractionis continuae cuius indices progressionem arithmeticam constituunt dum numeratores omnes sunt unitates ubi simul resolutio aequationis Riccatianae per huiusmodi fractiones docetur
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
597A new and most easy method for summing series of reciprocals of powers
598De insigni promotione scientiae numerorum
599Solution to a question concerning the calculation of probability: How much should be paid by a couple, so that a certain sum of money can be paid to the heir after the death of the other
600The solution of certain difficult questions in the calculus of probabilities
601De symptomatibus quatuor punctorum, in eodem plano sitorum
602Methodus facilis omnia symptomata linearum curvarum non in eodem plano sitarum investigandi
603De descensu baculi super hypomochlio cylindro fixo delabentis
604On rectilinear and oblique reciprocal trajectories
605On the remarkable properties of the elastic curves under the equation y = ∫ (xx dx)/√(1-x4)
606Speculations concerning the integral formula ∫ (xndx)/√(aa-2bx+cxx), where at once occur exceptional observations about continued fractions
607De motu globi circa axem obliquum quemcunque gyrantis et super plano horizontali incedentis
608Accuratior evolutio formularum pro filorum flexibilium aequilibrio et motu inventarum
609Considerations about rectilinear and oblique trajectories
610New demonstrations about the divisors of numbers of the form xx + nyy
611Investigatio curvarum quae similes sint suis evolutis vel primis vel secundis vel tertiis vel adeo ordinis cuiuscunque
612De motu globi heterogenei super plano horizontali, una cum dilucidationibus necessariis super motu vacillatorio
613Dilucidationes in capita postrema calculi mei differentalis de functionibus inexplicabilibus
614Commentary on tractrix curves
615De viribus centripetis, ad curvas non in eodem plano sitas describendas, requisitis
616On the transformation of the divergent series 1 - mx + m(m+n)x2 - m(m+n)(m+2n)x3 + etc. into a continued fraction
617On the summation of series, in which the signs of the terms alternate
618Consideratio motus singularis, qui in filo perfecte flexili locum habere potest
619Enodatio difficultatis super figura terrae a vi centrifuga oriunda.
620An easy method for finding the integral of the formula ∫ (dx/x)(xn+p - 2xncosζ + xn-p)/(x2n - 2xncosθ + 1) in the case in which after integration it is put from x = 1 to x = ∞
621On the greatest use of the calculus of imaginaries in analysis
622Specimen singulare analyseos infinitorum indeterminatae
623De lineis rectificabilibus in superficie sphaeroidica quacunque geometrice ducendis
624De superficie coni scaleni, ubi imprimis intentes difficultates, quae in hac investigatione occurrunt, perpenduntur
625De viribus centripetis, ad curvas non in eodem plano sitas describendas, requisitis
626On the movement of three bodies mutually attracted above a straight line
627Solutio problematis mechanici
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
629The expansion of the integral formula ∫ dx(1/(1-x) + 1/(lx)) with the term extended from x = 0 to x = 1
630Uberior explicatio methodi singularis nuper expositae integralia alias maxime abscondita investigandi
631An easy and clear analysis for guiding those most abstruse series, by which not only the roots but even the powers of the roots of all algebraic equations are able to be expressed
632On innumerable types of most remarkable series, by which not only the roots but even too any power of the roots of all algebraic equations are able to be expressed
633De binis curvis algebraicis inveniendis, quarum arcus indefinite inter se sint aequales
634De motu oscillatorio tabulae suspensae et a vento agitatae
635Innumera theoremata circa formulas integrales, quorum demonstratio vires analyseos superare videatur
636On the multiplication of angles which are to be obtained by factors
637A new demonstration, with respect to which prevails the expansion of binomial powers by Newton even by fractional exponents
638On innumerable algebraic curves, of which the longitude is able to be measured by parabolic arcs
639On innumerable algebraic curves, of which the longitude is able to be measured by elliptical arcs
640Comparatio valorum formulae integralis ∫ (xp-1 dx)/(n√((1-xn)n-q)) a termino x = 0 usque ad x = 1 extensae
641De motu quodam maxime memorabili, satis quidem simplici, at solutu difficillimo
642On a singular rule for differentiating and integrating, which occurs in the sums of series
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
645On algebraic curves, of which the longitudes are expressed by the integral formula ∫ (vm-1 dv)/√(1-v2n)
646De duabus pluribusve curvis algebraicis in quibus si a terminis fixis aequales arcus abscindantur eorum amplitudines datam inter se teneant rationem
647De methodo tangentium inversa ad theoriam solidorum translata
648An easy solution of a problem, in which a circle is searched for, given three circles tangent to it
649De motu oscillatorio penduli circa axem cylindricum plano horizontali incumbentem
650De formulis differentialibus quae per duas pluresve quantitates datas multiplicatae fiant integrabiles
651Four most noteworthy theorems on the calculation of an integral
652On the general term of hypergeometric series
653De iterata integratione formularum integralium, dum aliquis exponens pro variabili assumitur
654Methodus facilis investigandi radium osculi ex principio maximorum et minimorum petita
655General observations about series, of which the terms arising for the sines or cosines of multiplied angles come forth
656On most memorable integrations arising from the calculation of imaginaries
657A supplement to the preceding dissertation about the integration of the formula ∫ (zm-1 dz)/(1-zn) in the case where z = v(cos(φ) + √(-1) sin(φ))
658De momentis virium respectu axis cuiuscunque inveniendis; ubi plura insignia symptomata circa binas rectas, non in eodem plano sitas, explicantur
659Methodus facilis omnium virium momenta respectu axis cuiuscunque determinandi
660Foundations of Integral Calculus, Volume 4
661Several considerations about hypergeometric series
662On the true value of the integral formula ∫ dx(l(1/x))n with the term extended from x = 0 all the way to x = 1
663Plenior expositio serierum illarum memoragilium, quae ex unciis potestatum binomii formantur
664Analytical exercises
665The evolution of a problem whose analytic solution is most difficult, while the synthetic solution for it is obvious
666Problema geometricum ob singularia symptomata imprimis memorabile
667De curvis hyperbolicis quae intra suas assymtotas spatium finitum includunt
668On the integration of the formula (dx √(1+x4))/(1-x4) and of others of the same type by logarithms and circular arcs
669Memorabile genus formularum differentialium maxime irrationalium quas tamen ad rationalitatem perducere licet
670De resolutione formulae integralis ∫ (xm-1 dx)(Δ + xn)λ in seriem semper convergentem, ubi simul plura insignia artificia circa serierum summationem explicantur
671De formulis differentialibus angularibus maxime irrationalibus, quas tamen per logarithmos et arcus circulares integrare licet
672A memorable theorem about the integral formula ∫ (dφ cos(λφ))/(1+aa-2acos(φ))n+1
673A conjectural disquisition about the integral formula ∫ (dφcos(iφ))/(α+βcos(φ))n
674Demonstratio theorematis insignis per coniecturam eruti circa intagrationem formulae ∫ (dφ cos(iφ))/(1+aa-2acos(φ))n+1
675On the values of integrals where the variable term is extended x = 0 all the way to x = ∞
676Methodus succinctior comparationes quantitatum transcendentium in forma ∫ (P dz)/√(A + 2Bz + Czz + 2Dz3 + Ez4) contentarum inveniendi
677Special methods for resolving differential equations of the second degree
678A new method for investigating all cases in which the differential equation ddy(1-axx) - bx dx dy - cy dx2 = 0 is permitted to resolve
679De formulis integralibus implicatis earumque evolutione et transformatione
680De aequationibus differentialibus cuiuscunque gradus quae denuo differentiatae integrari possunt
681Specimen aequationum differentialium indefiniti gradus earumque integrationis
682On the pressure of a table weighted by a weight on a surface. From the papers of the blessed Leonhard Euler extracted by Jakob Bernoulli.
683On a singular type of Diophantine questions and a most recondite method by which they are to be resolved
684On the roots of the infinite equation 0 = 1 - (xx)/(n(n+1)) + (x4)/(n(n+1)(n+2)(n+3)) - (x6)/(n.....(n+5)) + etc.
685An analytical exercise, where in particular a most general summation of series is given
686Elucidations about the formula, in which the sines and cosines of angles are to be multiplied, where at once large difficulties are diluted
687De insignibus proprietatibus formularum integralium praeter binas variabiles etiam earum differentialia cuiuscunque ordinis involventium
688A most abstruse specimen of integral contained in the formula ∫ dx/((1+x)*4√(2xx-1))
689Integratio formulae differentialis maxime irrationalis, quam tamen per logarithmos et arcus circulares expedire licet
690The expansion of the integral formula ∫ dz(3+zz)/((1+zz)*4√(1+6zz+z4)) by logarithms and circular arcs
691Problema geometricum quo inter omnes ellipses quae per data quatuor puncta traduci possunt ea quaeritur quae habet aream minimam
692Solutio problematis maxime curiosi quo inter omnes ellipses quae circa datum triangulum circumscribi possunt ea quaeritur cuius area sit omnium minima
693On the center of similarity
694Later paper on formulas of imaginary integrals
695A succinct integration of the most memorable integral formula ∫ dz/((3±zz)*3√(1±3zz))
696On the cases in which the form x4 + kxxyy + y4 is permitted to be reduced to a square
697Investigatio superficierum quarum normales ad datum planum productae sint omnes inter se aequales
698Several speculations about the area of spherical triangles
699Inquiring on whether or not the number 100009 is prime
700On differential equations of the second degree which admit integration
701Formae generales differentialium, quae, etsi nulla substitutione rationales reddi possunt. tamen integrationem per logarithmos et arcus circulares admittunt
702De novo genere quaestionum arithmeticarum pro quibus solvendis certa methodus adhuc desideratur
703An easy method for finding series proceeding by the multiplication of the sines and cosines of angles, of which the use in the universal theory of astronomy is very great
704Disquisitio ulterior super seriebus secundum multipla cuiusdam anguli progredientibus
705Investigatio quarundam serierum, quae ad rationem peripheriae circuli ad diametrum vero proxime definiendam maxime sunt accommodatae
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
707On the outstanding use of the calculation of imaginations in the calculation of an integral
708On forms of the type mxx + nyy for exploring prime numbers by idoneals of them with remarkable properties
709On the expansion of the power of any polynomial 1 + x + x2 + x3 + x4 + etc.
710Example of the transformation of singular series
711A new and easy method for expressing for all algebraic equations not only their roots but also the powers of them by constructing series
712De corporibus cylindricis incurvatis
713An investigation of a triangle in which the distances of the angles from the center of gravity of it may be expressed rationally
714Exempla quarundam memorabilium aequationum differentialium, quas adeo algebraice integrare licet, etiamsi nulla via pateat variabiles a se invicem separandi
715On various ways of examining very large numbers, for whether or not they are primes
716The resolution of the Diophantine formula ab(maa+nbb) = cd(mcc+ndd) by rational numbers
717Solution to a problem of mechanics
718An easy method of finding several rather large prime numbers
719A more general method by which all adequately large numbers may be scrutinized for whether or not they are prime
720Special observations about linear differential equations
721De integrationibus difficillimis, quarum integralia tamen aliunde exhiberi possunt
722Analytical disquisitions on the expansion of the trinomial power (1+x+xx)n
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
726A demonstration of a notable theorem of numbers a twelfth part of binomial powers
727A more accurate treatment of the problem of drawing the shortest line on a surface
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
762Unpublished letter from Euler to Lagrange
763De tribus pluribusve numeris inveniendis, quorum summa sit quadratum, quadratorum vero summa biquadratum
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
772De insigni promotione Analysis Diophantaeae
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
786The Complete works of L. Euler in French
787Solution of a problem proposed in the Leipzig Acts in 1745
788Letters of L. Euler and Chr. Goldbach 1729-1763
789A few lines from a letter of L. Euler to Albrecht von Haller, from 4 July 1744
790Commentary on the use of sublime mathematics
791Collected arithmetical commentaries
792Tractatus de numerorum doctrina capita sedecim, quae supersunt
793Thoughts concerning Diophantine analysis
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
798On amicable numbers
799A fragment of a commentary, the most part on finding the relation between the sides of triangles of which the area is able to be expressed rationally, and of triangles in which the lines from each angle bisecting the opposite line are rationals
800A letter from L. Euler to Christoph Jezler, dated 4 May 1765
801Three letters of Euler to Frederick the Great in 1743
802Einige Zeilen aus Briefen von L. Euler an Johannes Schorndorf vom 27 April 1743 und vom 26 Mai 1750
803Vierzehn Briefe oder Auszuge aus Briefen von L. Euler an W.J.G. Karsten 1758-1765
804Two letters of Euler to Bulffinger in 1738
805Posthumous works in mathematics and physics
806Arithmetical fragments taken from the mathematical day book
807On the logarithms of negative and imaginary numbers
808An algebraic problem of finding four numbers with the sum of the three others
809Series maxime idoneae pro circuli quadratura proxime invenienda
810Enodatio insignis cuiusdam paradoxi circa multiplicationem angulorum observati
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
814Foundations of Differential Calculus, volume 3
815Solution of problems from the theory of maxima and minima
816Thoughts on certain integral formulas for which the values can be expressed under certain circumstances by the squaring of the circle
817On curved lines, the rectification of which is measured by given quadratures
818On the comparison of irrectifiable curved arcs
819Continuation of some fragments taken from the Mathematics day book
820Six letters to Nicholas Bernoulli II of Basel, dated 1742 to 1745
821Two letters to Frederick II, King of Prussia, sent in the years 1749 and 1763
822Eighteen letters to Lagrange from 1755 to 1775
824Vera vires existimandi ratio
825De motu corporum circa punctum fixum mobilium
826On the motion of a body on a moving surface
827De motu corporum in tubo rectilineo mobili circa axem fixum, per ipsum tubum transeuntem
828Dissertation on the motion of enclosed bodies in a rigid tube mobile around a fixed axis
829De motu corporum in tubis circa punctum fixum mobilibus
830Recensio litterarum a Cl. D. Bernoullio basilea die 26. Oct. 1735 ad me datarum, una cum annotationibus meis
831De oscillationibus annulorum elasticorum
832Von der Kraft der Rammen, Pfahle einzuschlagen
833To determine the effect of a hydraulic machine invented by Mr. Segner, a Professor at Gottingen
834Astronomia mechanica adjecta Digressione de cometa A. 1757
835Solutio duorum problematum, Astronomiam mechanicam spectantium
836New astronomical tables for calculating the position of the sun
837De emendatione tabularum lunarium per observationes eclipsium lunae
838Tria capita ex opere quodam majori inedito de theoria lunae
839De atmosphaera lunae ex eclipsi colis annulari evicta
840De motu cometarum in orbitis parabolicis, solem in foco habentibus
841Research into the inequalities caused by planetary motion by random forces
842An Introduction to Natural Science
843Constructio manometri densitatem aeris quovis tempore accurate monstrantis
844General theory of dioptrics
845Seven chapters of a work on dioptrics
846Research to serve for the perfection of glasses
847De amplificatione campi apparentis in telescopiis
848Concerning the construction of microscopes
849Reflections on the determination of compass readings
850Research on the discovery of the currents of the sea
851Recensio Dissertationis de ventis
852Thoughts on the formation of the voice
853Meditation on experiments made recently on the firing of a cannon
854Several pieces about monads
855Determination of the prinicples of motion of blood through arteries
856Fragments from the mathematical day book
857Three unpublished from Euler to Johann Bernoulli I, 1729-1737
858Unpublished letters from Euler to d'Alembert
859Several lines of a letter from Euler to Johann Bernoulli I from August 27, 1737
860Fourteen letters from Euler to P. L. M. de Maupertuis, 1752-1759
861Extracts of letters from Euler to Johann Bernoulli I, 1739-1740
862Extracts of letters from Euler to Johann Bernoulli I, 1728-1729
863The correspondence between Leonhard Euler and Johann I Bernoulli, 1727-1740
864The correspondence between Leonhard Euler and Daniel Bernoulli
865Several lines of a letter from Euler to the "Royal Society" dated October 21/November 1, 1768
866Letter from Euler to J. d'Alembert from February 15, 1748